____ ____ _________ _________
/ / / / / \ / /
/ / / / / ___ / / _____/
/ / ____ / / / /__/ / / / _____
/ / / / / / / ___/ / / /_ /
/ /_/__ /_/ / / /\ \ / /___/ /
/ / / / / \ \ / /
/________/______/ /___/ \___\ \_________/
Logical Japanese Rules of Go
Germany
Spring 2002
Robert M. Pauli
(c)
all rights of the author are preserved
according to international law
last update
June 2003
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INTROOVERVIEWPOPULAR RULESPRECISE RULESCOMPENSATIONnew grade systemCYCLE REMOVALCONTROLBEFORE ENDIwamoto's refusalGo Seigen's refusalENDINGko markAFTER ENDdispute breakerJRG89 IN DEPTHCorrecting Three Points Without CapturingBESTIARYCONCLUSIONREF's
INTRO
Go is an ancient strategic board game where two players compete for
territory. This text presents new rules for it. It is not meant to
explain the game to beginners. So, in case you are one, please don't
care about the rule version you're using because it won't change the
overall characteristic of the game anyway. Take the simple ones just
below (with H=V=9), or, if you prefer to start with more commonly
used rules, read the introduction to Japanese rules provided by the
British Go Association.
In either case leave now and enjoy playing.
Why do we need a new set of rules? Well, in one way we don't.
Very simple rules can be used. Here's my guess how original go
rules could have looked like ("stone scoring", no suicide, simple
ko rule, pass as trivial ko threat, no compensation):
1. Go is played on a grid formed by H horizontal and V vertical
lines, producing H times V intersections or locations.
2. Each location of the grid is initially empty.
3. One player owns black stones. The other white ones.
4. The goal is to get more of one's stones onto the grid
than one's opponent.
5. The owner of the black stones starts, after which both
players take turns.
6. In each of one's turns one can add a new own stone to the
grid by putting it on an empty location - provided this
doesn't create a suicide or immediate ko recapture pattern.
7. After one added a stone, one has to identify all stones of
one's opponent without liberties and remove'em from the grid.
8. If the last three turns added no new stone, the game is over.
9. A suicide pattern is there if the last stone added to the
grid has no liberties, but all stones of opposite color have.
10. An immediate ko recapture pattern is there if exactly two
stones are without liberties and this just happened on the
same two locations during the last turn.
11. A stone has liberties if by starting on it and repeatedly
(including zero times) jumping to a horizontal or vertical
neighboring stone of same color one can reach a stone that
has a horizontal or vertical neighboring empty location.
These rules are "stone scoring" ones. Modifying rule 4 to include
eyes in the count leads to "area scoring" ones (which are now used
in China, Taiwan, and the USA, each with its own flavor). But since
go has spread around the western world from Japan, their "territory
scoring" rules are used widely and, unfortunately, happen to be the
most challenging (if one tries to pin them down).
Japanese-style rules can be characterized as being the ones that
stop playing soonest. This isn't merely a convention, but is part
of the rules. It leads to the question if stones are dead or not
at the end of the game and to the necessity for the rules to define
this.
In 1989 the Japanese rules were revised unanimously by the two
Japanese go associations, Nihon Ki-in and Kansai Ki-in, and a new
version of "The Japanese Rules of Go" took effect on May 15 -
"JRG89" for short. Even though this was a major improvement over
the 1949 version (which was Japan's first written one), replacing
all special rulings (precedents) by general rules, they still have
errors and are ambiguous.
First I thought of just fixing this errors and completing what
seemed to miss, but eventually I came to the conclusion that in
the 1989 effort of getting rid of all special rulings the wrong
track was chosen: sekis remain an exception and slightly too much
is ruled to be dead.
The problem is that internal ko threats have no meaning any more
for life and death because of the special pass-for-ko rule JRG89
adopts in the analysis. A ko may then only be recaptured by a
player if he passes once for this single ko. In the hypothetical
phase several kos can therefore be hot simultaneously, each waiting
for its own pass. The intention is to localize ko fights in the
analysis. Normal ko threats, including internal ones, become useless.
An example (see beast 8):
Imagine the game ending in this position. White declares the black
stones to be dead and asks if he may take'em out. Black disagrees.
You're the referee, but forgot your rule book (if you ever saw one).
Would you agree? Please think about it.
Under JRG89 White is right - under LJRG ("loja") he is NOT.
Or look at this one (beast 18):
White, muttering something about "bent four", insists that all
black stones are dead and ready for take off. Black desperately
cries for help. You rush to the scene. Could you help?
Again JRG89 supports White (at least its example does) - LJRG sees
ALL stones alive.
You may shrug: who cares? I never experienced those positions either,
but it's a matter of aesthetics to have rules that judge all cases in
a way most of us would agree - and I bet you'd find good arguments to
disagree with White in both cases if you happened to be Black.
Note that LJRG follows JRG89 again in both cases if the double ko is
"external" (separate): moonshine life as well as bent four in the
corner is dead no matter how many (external) double kos are around
(see beast 11 for the first case).
But this new rules offer more:
- Komi is decentralized and free - no Big Brother dictates his
komi (nor gets fed with individual komi preferences)
- Defects get fixed ("teire") before game end in self-interest
- Neutrals ("dame") haven't to be filled before game end
(JRG89 technically forces this to cope with sekis)
- No discussion if a game is over - there's a simple definition
- No resumption of a stopped game - there's neither a stop nor
a (ridiculous) resumption
- Internal ko threats play their role after game end (as mentioned)
- Sekis are no mysterious exception any longer - without even
having to mention them (!) they're treated perfectly
- "Cycle removal" prevents no outcome ("mushobu") and avoids hairy
and unfair super-kos - without forcing bookkeeping in advance (!)
- Evaluation of life and death is easier and more intuitive than
under JRG89 because the focus is on "control" of area, not on
life of stones
- "control" can be seen ideally as well as be played out
(see "dispute breaker")
In contrast to other rules, these rules not just describe how things
are but explain why - in the sense that an explanation is a more
elegant description. For instance, describing planet movement via
epicycles works, but only after treating the sun as the center you
end up with something worth being called an explanation.
I'd neither grant JRG89 nor any of the various (multi-phase) "play
it out" rules, emulating Japanese rules, an explaining quality:
JRG89 produces almost all effects of Japanese rules, but fails
to do this in an elegant way. Its capturable alive stones aren't
very appealing, and its treatment of sekis still is ad hoc and
invites nagging questions.
Play-it-out rules, on the other hand, are either blind about sekis
for the sake of simplicity, or they turn out to be a total mess.
In either case, playing it out inherently fails to localize kos.
Calling this new rules "Logical" Japanese Rules of Go refers to
their explaining quality - it shouldn't be misunderstood in that
other rules are not logical. See the chapter about JRG89 for my
logical interpretation of them.
In designing these rules, I couldn't resist the temptation to add
some fancy stuff you never heard of, like color choice and cycle
removal, or to kick out the fixed handicap sequence. But since all
this, as I hope, is still in line with the spirit of Japanese
rules, and in respect to Japan's contribution to go's development
and spread, I resisted to use "Territory" instead of "Japanese"
in the name. The reason for using a second qualifier at all was
to make clear that it isn't my intention to propose international
rules. Diversity shall prevail.
OVERVIEW
In the following we'll go through two simple games on unusual mini
boards (3x3 instead of the 19x19 standard) to get a quick overview
of what LJRG is about (of course not what go is about):
The first example demonstrates how live and death is defined. It
was played without komi or any other compensation (for whatever
reason):
0 0 B 0
0 0 W 0
0 0 B 0
0 0 W 0
0 0 B 0
0 0 W 0
0 0 B 1
0 0 W 2
What's that stuff under each diagram? It makes explicit all
information necessary to continue the game (beside history):
1. Number of black stones captured ("black captive count")
2. Number of white stones captured ("white captive count")
3. Color having the turn ("turn")
4. Number of trailing passes made ("pass count")
We'll call each diagram extended like this a "situation". Since
we'll also have to cope with cycles, the state of the game is
more than a situation. It must also include a list of all former
situations - its history. But since under LJRG no knowledge of the
history is needed to avoid illegal moves, let's forget the history
for the moment.
A game on a 3x3 isn't really exciting. The focus here is on how
the game ends and how the score is defined.
The last two moves (6 and 7) were passes: neither adding stones
to the board nor removing any from it. Each pass increases the
pass count by one (we'll see later what decreases it). If it
reaches two, the game is over -
P E R I O D
(screamed at the top of my voice). A resumption of the game, as
JRG89's Article 9.3 provides for, is not possible (ignoring LJRG's
variant where disputes are played out for the moment).
The only thing that follows is counting, and LJRG couldn't care less
about what method actually is applied to accomplish this. (However,
I'll recommend one below.)
So, what's the result? To understand its definition, you first
have to understand LJRG's concept of "control":
A player "controls" a location only if there's a
set of locations that can be "locked" by him and
that includes this location.
Can Black, for instance, lock the 4 locations in the lower right?
No - the proof (exemplifying the definition) is as follows:
Fill the rest of the board with "permanent" white stones, remove
captured stones (in this case none), and let White have the turn:
0 0 W 0
If Black now still can't be prevented from building 2 eyes on the
set of locations he claimed he could lock, then we'll say that
Black can "lock" this set.
You certainly agree with me that Black won't be able to do so above.
Does this now mean that Black has no territory? Not at all! There
are many other sets of locations around (512, to be exact). To cut
down their number, only those he has "bordered" are legal:
Every location in the set having a neighbor outside the
set must be of his color, and every location outside the
set having a neighbor in the set may not be of his color
If we check the set just tried, we must agree that it indeed is
bordered by Black. Is there another set around? Well, if you ever
walked beside a long wall, you might have noticed that it isn't
quite clear if one's before or behind the wall - and actually
there's no way to decide this. (Comparing the territory sizes to
both sides of the wall might be common sense, but isn't logical.)
Of course, Black could also claim to have surrounded the five
locations on the other side of the wall, that's, he could claim to
have bordered the set of all locations exclusive the lower right
corner location. But why not think big (if one can do so on a 3x3)
and claim the whole board? You don't think it's bordered? Check the
definition and you'll notice that it indeed is (trivially) bordered
by Black (and White).
So, if Black claims that he can lock the whole board, neither is
there a rest to be filled with permanent white stones, nor is there
a captured stone to be removed after this "action". Again White gets
the first turn (indicated by the "W"):
0 0 W 0
Since White neither can make any use of his first turn nor of his
later turns, he passes them all and lets Black easily build 2 eyes:
1, 3, and 5 passed
We finally reach following situation:
0 2 W 0
Black has succeeded in building 2 eyes (precise definition later)
on his claim - despite White filling the rest with his permanent
stones (none in this case) and starting.
We would now have to check if White couldn't somehow do better,
examining all other possible move sequences (with Black playing
perfectly, of course) and stopping when either 2 eyes have been
build, the pass count got 2, or a repeated situation (since proof
start, of course) had been reached - but I hope you believe me
(dispute breaking to come) that this won't change the outcome:
Black can lock this set -
he controls all 9 locations
Now we have to check if White himself controls anything. This may
not seem necessary - I'm confident that opposing controls never
will overlap - but who knows:
White could, for instance, claim the upper left corner. The test
would then start in this situation (now Black, "B", starts):
0 0 B 0
Black will capture, and White will never reach 2 eyes in his claimed
set - which was too small anyway. White's claim has been refuted.
White could theoretically also claim the whole board or the opposite
of above's claim:
0 0 B 0
0 0 B 0
But Black will refute both claims in the same way he proved his
own claim:
White controls nothing
Now that we know which locations are controlled by whom, let's
mark Black's area with B's and White's (none) with W's in the
final situation:
0 0 W 2
What remains is to count the score of each player:
1. count all locations he controls but hasn't occupied
(territory),
2. add the number of opposing stones in this set
(dead stones), and finally
3. add the number of opposing stones removed during the game
(prisoners = opposite colored captive count):
T D P
---------------
Black's score = (9 - 3) + 2 + 0 = 8 points
White's score = 0 + 0 + 0 = 0 points
--------
Black wins by 8 points
Is this really worth the effort? It is! The fine thing about not
to focus on live or death of stones, but instead to use the more
general concept of control, is
1. that sekis not even have to be mentioned (but nevertheless
are treated perfectly in line with tradition)
2. that defects (no matter how "obvious") have to be fixed during
the game even if neutrals are not filled (because one has to
anticipate the permanent stones)
3. that internal ko threats play their role after the end
(giving sensible results even in odd situations)
Believe me, this captures the essence of Japanese go rules to a
maximum!
"Control" is LJRG's heart. Everything else is secondary. We may
discuss if fixed komi should stay, if passes should not be ko
threats, or if long cycles should be treated like kos (even if
I'm not very likely to change my position) - but please don't
discuss the concept of control with me unless you believe having
detected a crack in its definition or its effects (and can come
up with a concrete example).
Here's another 3x3 game. It demonstrates how LJRG tames cycles.
Traditionally, cycles other than a ko prevent a game from ending -
giving no result ("mushobu") under Japanese-style rules. Kos are
tiny cycles one has no problem to keep in mind. Longer cycles could
in principle be handled in the same way, but are very confusing
in practice.
Since they are rare, not handling them is an option. But the
possibility that the sure winner could be stopped by a nasty
cycle is nevertheless a nuisance. Therefore LJRG includes a new
idea called "cycle removal" - to happen in the next game.
Above we saw new stuff accompanying the board. Now we'll see new
stuff on it: marks. They explicitly make clear which locations
are prohibited to change their color - either just for one turn
(temporary marks = squares) or forever (permanent marks = circles).
This game was played with compensation. One player chose the initial
situation (one temporary mark on the center and no komi in this case),
and the other chose the colors (see chapter about compensation).
Here's the game (after colors were assigned):
0 0 B -1
0 0 W 0
0 0 B 0
0 0 W 0
0 0 B 0
0 0 W 0
1 0 B -1
1 0 W 0
2 0 B -1
2 1 W -1
3 1 B -1
3 2 W -1
4 2 B -1
4 3 W -1
5 3 B -1
5 4 W -1
6 4 B -1
8 7 W 0
8 7 B 1
8 7 W 2
(Later I learned that Bill Taylor not only already had discovered
this "pinwheel ko", as he called it, but that he also already had
the idea to prohibit locations as a kind of komi [RGG090595].)
Black didn't do his best. Of course he should have passed or
extended to one of the corners with 5, but for the purpose of
demonstration he had to slip.
Marks prevent locations to change their color. During the game
only empty locations will be marked. An empty location that's
marked nevertheless serves as a liberty, thus stones contacting
one can't be caught any more if that mark is permanent. Cycle
removal will introduce permanent marks. Ko capture will introduce
temporary marks.
(If you wonder: a location is "empty" in above's sense if it's not
occupied by a black or white stone, but it still may be "occupied"
by a (physical or real) mark. To avoid confusion, precise rules
given later instead speak of locations "not colored".)
Only in deciding life and death after game end stones too will
become marked (permanently). The effect is as if (the same) two
empty virtual locations are neighboring each location occupied
by such a stone. These "permanent stones" are, as already seen,
used to build up worst-case scenarios.
When temporary marks are on the board, the pass count always is
-1, forcing 3 instead of just 2 passes iin a row to end the game.
This enables using a pass as a (trivial) ko threat!
Temporary marks don't survive a move. Their main purpose is to
model the ko rule in a transparent way. Move 6 and moves 8 to 16
all captured in a ko and left a temporary mark, preventing a
recapture in the very next move.
In the real world we could keep temporary marks in our mind, but
for the purpose of being explicit they are useful. Permanent marks,
on the other side, should be real - coins will do (in those VERY
rare events they're needed - so calm down again).
Ignoring the case in the initial situation, only a single temporary
mark is needed. Either it marks a ko, or - if it's real - it's off
the board. Instead of being idle, it could indicate the pass count:
sitting on either 0, 1, or 2.
To use a real temporary mark wouldn't be as ridiculous as it first
might seem - especially in games with plenty of time each. There
are several occasions where a professional spoiled his game because
he accidentally "immediately" recaptured a ko:
- On June 5, 1971, Ishida Yoshio (mister "precision" himself)
lost the 3rd game of the 8th Pro Best Ten Final against
Kajiwara Takeo by such a blunder [RGG220202b]
- In 1980 Cho Chikun did this in the 4th game of 1980's Meijin
(see Go World 23) [GW45a]. Fortunately for Cho, the game was
annulled ("mushobu") by referee Ishida (making it a best of 8).
Unfortunately for Cho, he had thrown away a won game. Cho and
Otake [RGG220202c] both "enjoyed" byoyomi, which was managed
by one scorekeeper. Cho asked him if he could take the ko and
was told yes - which happened to be false. In was decided that
in the future neither a single person will have to manage two
players in byoyomi nor that an illegal move can be excused by
a false answer - it loses nevertheless. [RGG110997][RGG120997]
- 1997 Kudo Norio recaptured a ko too soon with move 202 in game
3 of the 23th Tengen against Ryu Shikun and lost [DGZ0198a].
The purpose of being that explicit isn't to prevent such a mistake
- even if this is a very good side effecct - but rather to arrive to
an absolutely clear understanding of repeated situations:
One situation "repeats" (or is "similar" to) another only
if both are the same while ignoring their captive counts
So, not only the configuration on the board (positional super-ko)
or additional the turn ("situational" super-ko) are relevant, but
also how many passes would be needed to end the game as well as
what locations are prohibited and for how long.
Therefore 15 does NOT repeat the situation after 7 under LJRG:
1 0 W 0
5 4 W -1
The idea behind this is that every move sequence (without cycle
removals) possible in one of the two repeated situations should
also be possible in the other - with the same color starting.
White could have captured 7, but not 15. Since the ko rule isn't
generalized by LJRG, the next layer of cycle treatment, cycle
removal, has to take its effects into account.
While 15 does not repeat a situation, 16 does - the one after 8:
2 0 B -1
6 4 B -1
It's Black's turn and he decides to "remove the cycle". All
locations that changed their color since 8 are cleared and
permanently marked. (Of course, Black must posses a game record
starting at least from 8 to do this.) All stones removed are
treated as if captured:
8 7 B -1 (situation in progress!)
To treat removed stones as captured not only fits with what we
normally do with stones removed from the board, but additionally
punishes you if you instead continue the cycle: your opponent may
remove the cycle before he answers your move, being one prisoner
better off. After removing a cycle the turn isn't over and a stone
may still be played!
In our case, Black can't find any legal location for a stone and
omits it (I'm intentionally not saying "he passes"):
8 7 W 0
The pass count is set to 0 if the move neither is a ko capture nor
a pass, which was the case. (It's only a pass if no stones enter or
leave the board.) A ko capture would have set the pass count to -1,
and a pass would have increased the pass count by 1.
Since all locations are now either occupied or prohibited, White
has nothing left but to pass - increasing the pass count by 1.
Black passes too for the same reason, and the pass count reaches
2 - the game ends (final diagram spared).
Even if it may look so, White can't claim any control. His only
bordered set is the whole board, but in this case the permanent
marks (which stay on the board) prevent him from building a "2-eye
formation" (to use LJRG's technical term). The same holds for Black.
Therefore only the captive counts score:
T D P
---------
Black's score = 0 + 0 + 7 = 7 points
White's score = 0 + 0 + 8 = 8 points
--------
White wins by 1 point
Now you know almost all about LJRG. Just two rules concerning cycle
removal added lately are missing:
- no cycle removal allowed if pass count is 1 (pass instead),
and
- stones with permanent liberties may not fill their last
non-permanent liberty (no "pseudo suicide").
How about trying to apply what you've learned so far by judging the
introducing examples again?
What follows are precise definitions and lots of examples - plus a
critical look at JRG89.
POPULAR RULES
For those that hate the idea of shuffling around marks or those
not able or willing (including me for most of the time) to enter
my "torture chamber" below and digest precise rules - here are
equivalent "unofficial" rules in a more popular form:
Logical Japanese Rules of Go
(popular version)
1. "Go" is played by two players with black and white lens-shaped
stones on a finite set of locations (for instance, the 361
intersections created when 19 parallel lines cross a second
set of 19 parallel lines - to take the standard).
Additionally, it must somehow be defined if any two (different)
locations are neighbors or not (for instance, when both share
the same line without a third location between - to again take
the standard). All locations start empty.
2. To start, one of the players, randomly chosen, has to decide
which locations are initially prohibited (possibly none) and
how much points (a non-negative integer) the player getting
second turn is ahead ("komi"). The other player then has to
decide whom to give first and whom second turn. The player
that got first turn is called "Black" and uses black stones.
The other player is called "White" and uses white stones.
3. The players take turns. The player having the turn has up to
two actions at his disposal:
- he can remove a disturbing cycle, and
- he can play a stone (the normal action).
Each action may (occasionally must) be omitted, but if both
are performed, this must happen in the given order.
4. If a player neither adds nor removes stones in his turn, this
is called a "pass". If a player passes in a situation in which
no location is temporarily prohibited and his opponent then
passes too, the game is over and scores are compared.
5. A player scores one point
- for each location he controls that is not
occupied by one of his stones ("territory"),
- for each opposing stone that sits on a
location controlled by him ("dead stones"), and
- for each opposing stone that was removed (no
matter by whom) during the game ("prisoners").
White's score additionally benefits from komi. The player
with the higher score wins - otherwise it's a tie ("jigo").
6. "Playing" a stone means
- to put a new stone on an unprohibited empty location,
- to identify all opposing stones thereafter being without
liberties, and, in case some are around,
- to remove them from their locations.
7. To "remove a cycle" means to remove all stones sitting on
locations "used" by the cycle - which are those locations to
which stones were added or from which stones were removed
while the game went from the cycle's start to the cycle's end.
8. A "cycle" exists if a former situation (its "start") is
similar to the current situation (its "end").
Two situations are "similar" if in both
- the same player just has got the turn,
- the same number of passes are needed to reach game end,
- the same locations are occupied by black stones,
- the same locations are occupied by white stones,
- the same locations are temporarily prohibited, and
- the same locations are permanently prohibited.
A cycle only is "disturbing" if a pass in the current situation
wouldn't end the game.
9. An empty location is "prohibited" if
- putting a stone on it makes suicide or pseudo suicide,
- it is initially prohibited and no turn yet was made,
- it was cleared by a ko capture in the preceding turn, or
- it was once used by a removed cycle.
Locations prohibited because a removed cycle once used them are
called "permanently" prohibited. Those prohibited initially or
after a ko capture are called "temporarily" prohibited.
10. Putting a stone on an empty location makes "suicide" if after
placement all stones of opposite color still have liberties,
but this stone has none.
11. Putting a stone on an empty location makes "pseudo suicide"
if after placement this stone and all stones of opposite
color still have liberties, but this stone only has
permanently prohibited ones.
12. Putting a stone on an empty location is a "ko capture" if
after placement exactly two stones have no liberties and
their colors don't match.
13. A stone "has liberties" if by starting from its location and
repeatedly (including zero times) jumping to a neighboring
location that is occupied by a stone of the same color one can
reach a location that has an empty neighbor. Each such empty
location is called a "liberty" of the original stone.
14. A player "controls" a location if it is member of a set of
locations he has bordered and he can't be prevented from
building a 2-eye formation on this set even if
- all locations outside this set are cleared and each
becomes occupied with a new stone of his opponent,
- two new empty locations are created and each becomes
a new neighbor of each location outside this set,
- all stones thereafter being without liberties are
identified and then removed,
- all former situations are forgotten,
- all permanent prohibitions stay in effect, and
- his opponent is allowed to start.
15. A player has "bordered" a set of locations if
- each location inside this set that has a neighbor
outside this set is occupied by one of his stones, but
- each location outside this set that has a neighbor
inside this set is not occupied by one of his stones.
16. A player has build a "2-eye formation" on a set of locations if
- this set is not empty,
- no stone of his opponent sits on a location in this set,
- he has bordered this set,
- each location in this set has at least one neighbor (possibly
outside this set),
- no empty location in this set ("eye") has an empty neighbor,
and
- each stone sitting on a location in this set has at least two
liberties inside this set.
PRECISE RULES
Here are precise rules, but be warned - it's in a h e a v i l y
mathematical style (no time, no space, no change). Maybe you should
skip it first (grin).
Who's familiar with Prolog will recognize similarities, but it's
no pure Prolog: this avoids to clutter up things with even more
details (implementing sets as lists, for instance) and helps to
be widely understood (if I'm not too optimistic about that one).
This doesn't mean that it's nonconstructive in the sense that an
answer is certain if only someone knew how to find it. This is
trivially true because each answer is always searched in a finite
domain, but I hope it's also practically constructive in the sense
that one could develop a computer program that gives answers in
an acceptable time - at least for "regularly" sized territories.
However, that a 19x19 board with 72 black stones filling the first
line and an empty "outback" is lockable by Black will probably never
be proven, even if it seems to be in practice [RGG300196].
This mathematical form is admittedly somewhat awkward, but that's
the price to pay for referential transparency: names never change
their meaning or value. For instance, in formal mathematics you
don't speak of changing the board by putting a stone on an empty
location. Instead you talk of one board B1 related to a second
board B2 in such a way, that all locations on B1 are in the same
state as on B2 - except for one, which is empty on B1 and colored
on B2 (and B1 and B2 floating in the Platonic world of ideas).
The only mathematical objects - not to mention integers, of course -
you need to be familiar with are (finite) lists and sets. So let me
risk some words on them:
Lists are ... well, you know what lists are, don't you? So let me
just make clear what it means that "L2 is L1 with X appended to
it": this means that L2's value is similar to that of L1, except
that it has the further member X at its END.
And what's a set? You can think of a set as a list that "hates"
repetition and order: it deletes duplicates as soon as they enter
and does not order its members in any way. Therefore it makes no
sense to speak of a set's first or last member, to ask how often
something is in a set - either it is or it is not - or if it
compared to another set has something appended to it - it's added
to it. Therefore two sets are the same only if each member of one
of them also is member of the other.
Sets as "defined" above would produce the well known antinomies,
for instance, try to figure out if Russell's set of all sets that
aren't member of themselves is member of itself. But since the sets
we deal with here are not of this pathological type - they're finite
and finitely nested - this won't bother us.
The following rules are meant to be precise and complete. They
therefore are designed not to depend on any commentary. I hope
this excuses their degree of detail and hyper-fussy style.
The rules are ordered top-down (B and C being parallel). If you
rather prefer reading a definition before its first use, please
start at the end and work your way up (advised).
Logical Japanese Rules of Go
(precise version)
A. Game
A1. "Two players play an even game of go on some board according to
Logical Japanese Rules of Go "
by doing - essentially - the following in the given order:
1. Randomly decide which player chooses first and which last.
2. The player choosing first must choose an initial state whose
board is the one in use. This state is called "current state".
3. The player choosing last must choose which player is called
"Black". The other is called "White".
4. While the current state is not final, the player having the
turn in it must replace it with one of its successors.
5. When the current state is final, the player with the higher
score in it wins. If both are equal, it's a "jigo" (tie).
A2. "A state is initial" only if all this holds:
1. Its set of black locations is empty.
2. Its set of white locations is empty.
3. Its set of temporarily marked locations is a subset of its
set of locations. (Includes the case that both are the same.)
4. Its set of permanently marked locations is empty.
5. Its black captive count is a non-negative integer not
greater than the number of members of its set of locations.
6. Its white captive count is 0.
7. Its turn is "black".
8. Its pass count is 0 if its set of temporarily marked
locations is empty, otherwise its pass count is -1.
9. Its history is empty.
(A state's "komi" is its first situation's black captive count
minus its first situation's white captive count, and
a state's "first situation" is the first member of the list
formed by appending its situation to its history.)
A3. "Black has the turn in a state"
only if this state's turn is "black".
A4. "White has the turn in a state"
only if this state's turn is "white".
B. Successor
B1. "State S4 is a successor of state S1"
only if some state S2 and S3 fulfill all this:
1. S1 is not final.
2. a) S1's turn is "black", and
S4 is a white successor of S1; or
b) S1's turn is "white",
S2 is colored reverse to S1,
S3 is a white successor of S2, and
S4 is colored reverse to S3.
B2. "State S4 is a white successor of state S1"
only if some state S2 and S3, text T1 and T2,
integer set K, and integer P fulfill all this:
1. S1's turn is "black".
2. a) S2 is S1, and T1 is "no cycle removed"; or
b) S2 is reachable by removing a cycle in S1,
and T1 is "cycle removed".
3. a) S3 is S2, K is empty, and T2 is "no stone played"; or
b) S3 is reachable by playing a black stone in S2 that
clears set K by ko, and T2 is "stone played".
4. a) T1 is "no cycle removed", T2 is "no stone played",
and P is S1's pass count plus 1; or
b) K is not empty, and P is -1; or
c) K is empty, T1 is "cycle removed" or T2 is "stone played",
and P is 0.
5. S4's history is S1's history with S1's situation appended to it,
S4's set of temporarily marked locations is K,
S4's pass count is P,
S4's turn is "white",
and everything else in S4 is as in S3.
B3. "State S2 is reachable by removing a cycle in state S1"
only if some list of situations H, list of integer sets L,
integer set B and C and D, and integer NB and NW fulfill
all this:
1. S1's pass count isn't 1.
2. H is a trailing sub-list (a suffix) of S1's history,
and H's first member is similar to S1's situation.
(This includes the case that H is S1's history.)
3. L is the list that would result if every member of H
would be replaced by the union of its set of black
locations with its set of white locations.
4. B is the union of all members of L.
5. C is the intersection of all members of L.
6. D is the set of those members of B not member of C.
7. NB is the number of members of the intersection of D
with S1's set of black locations.
8. NW is the number of members of the intersection of D
with S1's set of white locations.
9. S2's black captive count is S1's black captive count plus NB,
S2's white captive count is S1's white captive count plus NW,
S2's set of black locations is the set of those members
of S1's set of black locations not member of D,
S2's set of white locations is the set of those members
of S1's set of white locations not member of D,
S2's set of permanently marked locations is the union
of S1's set of permanently marked locations with D,
and everything else in S2 is as in S1.
B4. "State S3 is reachable by playing a black stone in state S1
that clears integer set K by ko" only if some integer X and
Y and N, state S2, and integer set W fulfill all this:
1. S1's turn is "black".
2. X is member of S1's set of locations, but neither colored
nor marked in S1.
3. S2's set of black locations is S1's set of black locations
extended by X, and everything else in S2 is as in S1.
4. W is the set of all members of S2's set of white locations
that have no liberties in S2.
5. If W is empty, then X has contact to Y in S2 and either
Y is not colored and not permanently marked in S2
or Y is black and permanently marked in S2.
6. N is the number of members of W.
7. S3's set of white locations is the set of those members
of S2's set of white locations not member of W,
S3's white captive count is S2's white captive count plus N,
and everything else in S3 is as in S2.
8. K is W if N is 1 and each neighbor of X in S2 is white in
S2, otherwise K is empty.
C. Score
C1. "Integer N is Black's score in state S1"
only if some integer set L and integer N1 and N2 and N3
fulfill all this:
1. L is the set of those members of S1's set of locations
that Black controls in S1.
2. N1 is the number of members of L that aren't black in S1.
3. N2 is the number of members of L that are white in S1.
4. N3 is S1's white captive count.
5. N is the sum of N1, N2, and N3.
C2. "Integer N is White's score in state S1"
only if some state S2 fulfills all this:
1. S2 is colored reverse to S1.
2. N is Black's score in S2.
C3. "Black controls integer X in state S1"
only if some integer set L fulfills all this:
1. X is member of L.
2. Black can lock L in S1.
C4. "Black can lock integer set L in state S1"
only if some state S2 fulfills all this:
1. L is bordered by Black in S1.
2. S2 is Black's worst case for L in S1.
3. White can't prevent a black 2-eye formation on L in S2.
C5. "Integer set L is bordered by Black in state S1"
only if all this holds:
1. L is a subset of S1's set of locations (this includes the
case that both are the same), and
2. for every member X of L that is neighbor of a Y not member
of L all this holds:
1. X is black in S1, and
2. Y is not black in S1
C6. "State S3 is Black's worst case for integer set L1 in state S1"
only if some integer set L2 and state S2 fulfill all this:
1. S1's set of locations is the union of L1 with L2.
2. S2's history is empty,
S2's set of temporarily marked locations is empty,
S2's black captive count is 0,
S2's white captive count is 0,
S2's pass count is 0,
S2's turn is "white,
S2's set of black locations is the intersection
of S1's set of black locations with L1,
S2's set of white locations is the union
of S1's set of white locations with L2,
S2's set of permanently marked locations is the union
of S1's set of permanently marked locations with L2,
and everything else in S2 is as in S1.
3. S3's set of black locations is the set of those members
of S2's set of black locations that have liberties in S2,
and everything else in S3 is as in S2.
C7. "White can't prevent a black 2-eye formation on integer set L
in state S1" only if at least one holds:
1. Black has build a 2-eye formation on L in S1; or
2. S1's turn is "black",
S1's situation is not final,
S1's situation is not similar to a member of S1's history,
and at least one successor S2 of S1 has the property that
White can't prevent a black 2-eye formation on L in S2; or
3. S1's turn is "white",
S1's situation is not final,
S1's situation is not similar to a member of S1's history,
and each successor S2 of S1 has the property that
White can't prevent a black 2-eye formation on L in S2.
C8. "Black has build a 2-eye formation on integer set L in state S1"
only if all this holds:
1. L is not empty.
2. L shares no member with S1's set of white locations.
3. L is bordered by Black in S1.
4. Every member of L is member of at least one member of
S1's neighbor relation.
5. Every member of S1's neighbor relation that's subset of L
shares at least one member with S1's set of black locations.
6. Every member of L that is colored in S1 has contact to
at least two (different) members of L in S1 which both
are not colored in S1.
D. Contact
D1. "Integer X has liberties in state S1"
only if at least one holds:
1. X is colored and permanently marked in S1. Or
2. X has contact to some Y in S1; and either
a) Y is not colored in S1, or
b) Y has the same color as X in S1 and
Y is permanently marked in S1.
D2. "Integer X has contact to integer Y in state S1"
only if X has contact to Y in state S1 avoiding V,
and V is the set whose only member is X.
("contact" neither is symmetric, reflexive, nor transitive.)
D3. "Integer X has contact to integer Y in state S1 avoiding
integer set V1" only if some integer Z and integer set V2
fulfill at least one:
1. X is neighbor of Y in S1; or
2. Z is neighbor of X in S1,
Z has the same color as X in S1,
Z is not member of V1,
V2 is V1 extended by Z, and
Z has contact to Y in S1 avoiding V2.
D4. "Integer X is neighbor of integer Y in state S1"
only if the set whose only members are X and Y is member
of S1's neighbor relation.
("neighbor" is symmetric, but neither reflexive nor transitive.)
D5. "Integer X is black in state S1"
only if X is member of S1's set of black locations.
D6. "Integer X is white in state S1"
only if X is member of S1's set of white locations.
D7. "Integer X is marked temporarily in state S1"
only if X is member of S1's set of temporarily marked locations.
D8. "Integer X is marked permanently in state S1"
only if X is member of S1's set of permanently marked locations.
D9. "Integer X is colored in state S1" only if at least one holds:
1. X is black in S1, or
2. X is white in S1.
D10."Integer X is marked in state S1" only if at least one holds:
1. X is marked temporarily in S1, or
2. X is marked permanently in S1.
D11."Integer X has the same color as integer Y in state S1"
only if all this holds:
1. X is black in S1 only if Y is black in S1, and
2. X is white in S1 only if Y is white in S1.
E. State
E1. "A state is final" only if its situation is final.
E2. "A situation is final" only if its pass count is 2.
E3. "Two situations are similar" only if either
1. they are the same, or
2. they are not the same, but only differ in their
captive counts.
E4. "State S2 is colored reverse to state S1"
only if some text T fulfills all this:
1. a) T is "black" and S1's turn is "white", or
b) T is "white" and S1's turn is "black".
2. S2's set of black locations is S1's set of white locations,
S2's set of white locations is S1's set of black locations,
S2's black captive count is S1's white captive count,
S2's white captive count is S1's black captive count,
S2's turn is T,
and everything else in S2 is as in S1.
E5. A "state" consists of exactly 3 parts of the given
names and sorts:
1. its "board" - a board
2. its "situation" - a situation
3. its "history" - a list of situations
The first two parts again consist of named parts - subparts of
the state. Since all these subparts have unique names, it's save
to omit the part name when referring to a state's subpart.
(For example, "the state's set of black locations" is short
for "the state's situation's set of black locations".)
E6. A "board" consists of exactly 2 parts of the given
names and sorts:
1. its "set of locations" - a finite integer set
2. its "neighbor relation" - a set of unordered pairs,
where each such pair is a set containing exactly two
(different) members of the board's set of locations
E7. A "situation" consists of exactly 8 parts of the given
names and sorts:
1. its "set of black locations" - an integer set
2. its "set of white locations" - an integer set
3. its "set of temporarily marked locations" - an integer set
4. its "set of permanently marked locations" - an integer set
5. its "black captive count" - a non-negative integer
6. its "white captive count" - a non-negative integer
7. its "turn" - either the text "black" or "white"
8. its "pass count" - either the integer -1, 0, 1, or 2
COMPENSATION
In this chapter I'll try to motivate LJRG's style of compensation
and also talk about handicap and grades.
Compensation is a means to give both players equal opportunities.
It depends on the board in use (a 19x19 grid being the standard)
and on the players' strengths. If strengths differ, one can make up
for it by allowing some stones in advance on the board ("handicap
stones"), some points in advance ("handicap points" or "komi"), or
a combination of both.
If strengths match ("even" games), one either has to play a series
of games and alternate who starts in each or one has to compensate
the one not starting.
The usual compensation for White not having the first turn is to
give him a lead of points, called "komi" (short for "komi-dashi").
The first komi game was played 1852 [RGG090299]. Honinbo Shuwa
gave 5 points to a team led by Yasui Sanchi at a promotion party
for Hattori Hajime (and no idea if "jigo" was White's win or not).
Japan mostly used komis of 4.5 (or as they said: 4 with White
winning "jigo") as well as 5.5. Prior to 1976 both were in use
(depending on the title), from 1976 on only 5.5 [RGG090299].
The first title to increase from 4.5 to 5.5 was Oza in 1955. Meijin
was last - 1975, after a sponsor switch from Yomiuri to Asahi.
Recently, September 2002, komi was scheduled to increase to 6.5.
Two months later it first appeared in the Women's Honinbo, and just
a day later in the Gosei. All other Japanese tournaments will catch
up as soon as each's new term starts. [W-NK0902] ([DGZ0502c])
So, what's my reason to abandon this tradition?
The first reason is to make the rules independent from a special
board. They would either have to prescribe a komi for each board
possible or make an exception for a bunch of selected boards -
the former is impossible and the latter is odd. On the other hand,
a fair start should be part of core rules, not tournament rules.
The second reason is the main one: nobody certainly knows what
komi is fair - knows the "perfect" komi (for the standard board).
Therefore nobody is in the position to dictate "his" komi to all
of us. Since this includes myself, I'll not do it either.
For instance, compensation for the Milton Keynes go board (simply
those town's street map [W-MK]) is defined by following formula:
handicap = 1 + (X DIV 6) [free placement]
komi = 6 - ((X MOD 6) * 2) [possibly negative]
with X being the (positive) strength difference (e.g., a 10-kyu
facing a 1-dan places 2 stones and GETS 2 prisoners). But I wonder
how they concluded that 6 (for X=0) is the perfect komi for this
board, and I wonder how they found out that strength differences
defined via the standard (!) board translate exactly this way ??
The first time new komi of 6.5 points actually affected the outcome
of a game (according to www.go4go.net) was in the quarter final of
the 16th Fujitsu Cup on 07.06.2003: Takao Shinji (B) lost by half a
point against Song Taekon (who additionally was the youngest player
ever to enter Fujitsu's semi-final - he's 16). Honda Kunihiso (9d),
who experienced the change from 4.5 to 5.5 in the late 50s and 60s
as well as that from 5.5 to 6.5 now, neither thought about komi nor
changed his way of play in either case [W-NK0902]. It's not unlikely
that Takao and Song neither would, producing the very same game even
under old komi. Now, isn't it a nuisance for Takao to imagine that
he'd have won in this case? Under compensation a la LJRG this can't
happen. Either you yourself proposed the komi, or you had the chance
to refuse it (by choosing black). In either case it makes no sense
to complain about it afterwards - you only can regret your decision.
And what's the reason for ruling out fractional komis?
The answer again is quite simple: they're unfair. Why? Because the
perfect komi, which certainly exists, must tie all games between
two perfect players, and since the difference of their scores
certainly is an integer, the equalizing komi has to be one too.
(Couldn't it vary? No, because perfect players always wring out
the maximum of points possible.)
The idea behind fractional komi is to force a winner, but this is
as silly as its origin (if the story in [GW50c] is true):
Around 1935, drawn games had to be replayed in knockout tournaments.
Two pros took advantage of this and faked two jigos in a row to earn
some additional game fees. The sponsoring Nichinichi Newspaper felt
fooled and protested to the Nihon Ki-in. After the two culprits
"begged for forgiveness on bended knees and promised to play the
next game seriously", the furiously fought third game turned out to
be - you guessed it - a jigo. To calm the heat the Nihon Ki-in took
up an idea of Murashima Yoshinori, 5-dan then, and declared to play
all future newspaper knockouts with a half-point komi extension.
The sponsor wants the crowd, and the crowd wants a hero or winner,
but to force one by half points is as unreasonable as tossing a coin.
There's nothing wrong with a jigo. It's a perfect game. It's very
satisfying. In case you've already assimilated the "there must be a
winner" idea and consequently are striving to become the best, you
should reconsider your attitude. Why? Because if everybody else had
the same goal and reached it - nobody would have reached it. Until
then everybody will realize what he should instead strive for:
perfection - which naturally leads to jigo.
Since perfection never will be reached in practice - at least
not on a 19x19 board - these thoughts admittedly are somewhat
philosophical, but nevertheless convince me (as well as I'm
convinced that zero neither is a positive nor a negative number).
Certainly I don't know if statistics along with human efforts to
improve play will approximate perfect komi in the end, but I
neither can imagine that we're far off.
But how do we then decide what komi to use?
A fair way to divide a cake between two persons is to let one
person split it into two pieces and then to let the other person
choose whichever piece seems bigger. The same idea can be applied
to fix the komi. One player chooses a komi, and the other chooses
which player has to take it. Since traditionally Black starts,
always White takes the komi (in even games). Therefore we could
also say that the second step chooses the color.
This would be totally fair. In case the existing perfect komi was
chosen, don't care about your color. But if not, you can refuse
one that's too small by choosing to be Black, or you can accept
one that's too big by choosing to be White. Of course, since nobody
knows the perfect komi, you have to guess - to refuse or accept as
well as how much to offer. Statistics are welcome to guide us, but
they shouldn't rule us.
Exactly this was practiced in a match between Imamura Fumiaki and
Hirata Hironori in May 1994 for the title of the strongest Japanese
amateur [DGZ0794a]. In the first game, Imamura chose 6.5 and Hirata
black. In the second game, Hirata chose 7.5 and Imamura white.
(Imamura won both games (with white) and the title.)
With this scheme nobody can take an edge by choosing a fractional
komi, so why not allow it again? In practice we could, but I hate
both the idea that the player choosing first could rule out jigo at
his will as well as the idea to rule out jigo completely by always
having to choose a fractional komi. (The latter wouldn't fit the
needs of perfect players, and why should we exclude them?)
And why those additional temporary marks?
Take a 3x3 board as example. Its perfect komi is 8. The proof is
simple. After Black takes the center, he controls the whole board.
But since controlled locations colored by the controller aren't
counted, Black's score isn't 9 but 8. White's is 0. He therefore
needs a komi of 8 to level up. Since Black certainly can't do
better, 8 is the perfect komi for a 3x3 board.
Now suppose for the moment that we would have no komi. To be fair
we could adopt following alternative scheme: Black plays the first
stone as usual, but White is allowed to switch colors instead of
playing his first stone if he feels Black's start was too good.
This idea is from hex.
(In hex two players each try to connect their two edges. Since the
game is played by putting black and white stones on the hexagonal
cells of a honeycomb, only one side will succeed. Actually hex lets
White exchange Black's first stone with a white one [SW0902]. This
would be equally fair for go - of course, without capturing the
initial black stone - but in hex the edge colors would have to be
switched too. Instead, the replacing white stone is "swapped into
White's coordinates" [W-PS].)
Is this scheme fair on the 3x3 board? Yes, it is. Black won't start
with the center any more because White would switch colors and win
by 8. But if Black starts on one of the center's neighbors, a jigo
by seki will result (and therefore Black fears no color switch).
The advantage of this scheme over komi on the 3x3 board is that
jigo is made on the board and not by adjustment afterwards.
I'd have kicked out komi completely for this scheme if there
weren't one problem: since nobody knows if there's a jigo start on
every board, this might be as unfair as fractional komis (which, of
course, is only slightly unfair, but I'm striving for perfection).
So if a board has no jigo start, then we would additionally need
some komi to adjust for a perfect compensation. This komi will
certainly be less than that without color switching, going in the
right direction, but will only be zero if that jigo start exists.
(By the way, is d4 a jigo start on 5x5 under LJRG?)
If we now translate this scheme back into the choosing scheme, we
get: the player choosing first chooses a komi and Black's start, and
the player choosing second chooses the color. But choosing Black's
start is the same as to prohibit all but one location for Black's
start, which is almost the same as to prohibit some (or all) for
Black's start - and to prohibit locations for exactly one turn is,
guess what, nothing else than to mark them with temporary marks.
It would, of course, be very painful to put coins or whatever on
hundreds of locations on a 19x19. A way out would, for instance, be
that everybody prepares some cards with his believed fair initial
states. If he happens to choose first, he simply "plays" one of them.
Or - if we don't want to risk go to fall between board and card
games - we could exploit symmetry and restrict us to one sector of
the board (a triangle area bounded by a center diagonal, the center
horizontal or vertical, and one edge - like c3,d3,d4,e3,e4,e5 on the
5x5) and either mark the allowed starts with black or the prohibited
starts with white stones - whatever takes less. Needless to say that
these stones go back to their source uncaught after serving their
purpose.
Please note that if the game starts with at least one temporary
mark on the board, the pass count has to start with -1, not 0.
This admitedly only serves aesthetics: after two passes Black
could make use of the by now unmarked locations, so the rules
shouldn't prevent him from doing so by declaring the game ended.
But analyzing the case that both players initially pass (B1, W2)
and Black then continues (B3) reveals that it wouldn't happen in
the perfect world:
If Black would gain X points by continuing with B3, White should
have continued himself with W2 to gain X points in the same manner,
and if Black would gain nothing or would even lose points by
continuing with B3, Black should, of course, have passed with B3
to either end sooner or lose by less.
(
komi result advice reason new result
-------------------------------------------------------------
0 W wins B3 pass better jigo
0 jigo B3 pass shorter jigo
0 B wins by X W2 stone better W wins by X
N+1 W wins by N+1+X B3 pass better W wins by N+1
N+1 W wins by N+1 B3 pass shorter W wins by N+1
N+1 W wins by N+1-X W2 stone better W wins by N+1+X
N+1 jigo W2 stone better W wins by 2(N+1)
N+1 B wins by X W2 stone better W wins by 2(N+1)+X
)
But nevertheless it pleases me more to always (and only) have
a pass count of -1 if there are some temporary marks around.
Since practical matters are excluded from these rules, I'll have
to mention it here:
Choosing the initial state and the color is part of the game and
can take its time, especially the latter. Therefore both choices
should be done while the clock is running (if one is used).
Some words on how to decide whom to give the first choice:
The traditional Japanese way to toss the dice is that one player
takes a handful of stones and the other guesses if it's an odd or
even number by putting one or two stones on the board ("nigiri").
But deciding who has to (or may?) guess by checking who's younger,
weaker, less honorable, or whatever is just ridiculous. I would
therefore advice to replace it by "symmetric nigiri":
EACH player takes a handful of stones. If their sum is
odd, the player using black stones has won, otherwise
the one using white stones did (odd for black and even
for white for the obvious reason - an even game's record).
The rest of this chapter covers board, handicap, and grades.
Since it's a side-issue and not very LJRG-specific, you might
want to skip it.
Go can be played on all kinds of boards (or topologies), not only
on the standard 19x19 grid.
The simplest variation, of course, is to shrink the board's size.
Many modern books introduce the game via 9x9 or even 5x5 boards.
This should also become practice in face-to-face introduction.
I really wonder how I survived dragging through my first games
on a 19x19.
Increasing the board size, on the other hand, seems to be less
common: In the year 1915, for instance, a no-komi game between two
Japanese pros took place on a 21x21 "monster" board - on the second
day and 335 moves later, Black had won by (just) 2 points [GW60].
Need something a bit more freaky? Here you are:
- the void board:
to start with the simplest, having not one location
- those boards composed of triangles insstead of squares:
never worry about a cut - there's none
- cylinders (pipe surfaces):
glue two opposite edges without a twist together
(the letters below only connect - they're no locations)
- tori (plural of "torus" - ring surfacees):
glue all opposite edges without a twist together
- Moebius strips:
glue two opposite edges with a twist together
- Klein bottles:
glue all opposite edges together - one pair without and the
other with a twist
- projective planes (ball surfaces identtifying diametric points):
glue all opposite edges with a twist together
- round boards ("diagonal" cylinders):
take a diagonal strip, glue two opposite edges together,
and seam the other two
then - to please the eyes, justify the name, but add confusion -
arrange the two seams (beyond D) as concentric circles [DGZ0796]
- map boards:
play on your home town's street map - each street intersection
and each end of a dead end being one location [W-MK]
- 3-D boards:
plenty of liberties - but pretty involved
- etc... an endless list - and absolutelly irrelevant to rules
Ok - back to our standard board (and sorry in advance for defining
something that's obvious - fading jerks of my "be formal" trip):
S1. "The standard board" is the normal rectangle board with
19 columns and 19 rows.
S2. "A board is the normal rectangular board with C columns and
R rows (both non-negative integers )" only if all this holds:
1. its set of locations is the set of all non-negative
integers smaller than C times R, and
2. its neighbor relation is the set of all those subsets of
its set of locations that have exactly two members and
whose non-negative difference of their members is either
1 or R.
S3. "A board is a rectangular board with C columns and R rows"
only if it is essentially, besides location naming, the same
as the normal rectangular board with C columns and R rows.
Note that we can't speak of "the" rectangular board of most
extensions because it's arbitrary how the integers are assigned
to the locations. That's the reason for picking one and calling
it "normal".
For instance, board ( {0,1,2}, {{0,1},{1,2}} ) is essentially the
same as board ( {0,1,2}, {{0,1},{0,2}} ).
Each is a rectangular board with 3 columns and 1 row (or the other
way round - CxR = RxC if C or/and R = 1). The first board calls its
center "1", the second "0". Equalizing renamings of the second are
either {0=>1, 1=>0, 2=>2} or {0=>1, 1=>2, 2=>0}. The first board is
the "normal" rectangular board with 3 columns and 1 row (as well as
that with 1 column and 3 rows).
The correspondence between a normal rectangular board and its usual
visual presentation is quite simple:
Take a grid formed by C columns and R rows, having C x R locations.
Start at the lower left corner and give it number 0. Number all
locations above it with increasing numbers from bottom to top. After
each column continue at the bottom of the next column to the right.
(One can do it this way or that way, but:
To start at the lower left corner fits best to mathematics, to start
with 0 leads to the nice property that the coordinates of location N
are X = N DIV R and Y = N MOD R, and going along the columns fits to
the sequence of X-Y's after a lexical sort.)
Now notice that the location directly above of some location L has
L's number plus 1, and that the one directly to the right has L's
number plus R. Since two locations only are neighbors on the visual
board if they share the same row or column without any location
between them, one of them has to be directly above or to the right
of the other. So the visual representation and the abstract one are
essentially the same.
An alternative naming for each locations of the standard board is
the algebraic one. The columns are named a,b,c,...,r,s,t (omitting
either i or j to avoid confusion) from left to right, and the rows
are named 1,2,3,...,17,18,19 from bottom to top. Each combination
then denotes one location: a1, for instance, denotes the lower left
corner. This certainly serves the purpose better than numbers, but
only works for rectangular boards. The location (or integer) on a
normal rectangular board that corresponds to such an algebraic
combination X Y is
((#X - 1) * R) + (Y - 1)
provided #X is the ordinal of X in the column letter sequence.
For instance (on a 19x19):
lower left hoshi = d4 = (( 4 - 1) * 19) + ( 4 - 1) = 60
tengen = k10 = ((10 - 1) * 19) + (10 - 1) = 180
lower right hoshi = q4 = ((16 - 1) * 19) + ( 4 - 1) = 288
Everything said so far was meant for two player of equal strength.
This is defined to be the case if both win on the same rate in a
(long enough) color-alternating series of no-komi games.
Such a series can be expressed relative to one player as
0 1 0 1 0 1 ...
Each number corresponds to one game of the series and represents
the handicap that player takes. In other words, the number of his
stones already around when yielding the turn to his opponent.
Thus, 0 means that he has white, 1 that he has black (without komi,
of course), 2 that he takes 2 stones handicap (and has black because
traditionally Black places the first stone - handicap or not), and
-1 that he gives 2 stones handicap (as iif his own first played stone
vanishes in a matter-antimatter reaction with his negative handicap
stone - puff).
Since infinite series aren't very handy, let's only consider
periodical ones with a period of, say, 6 games. Further, because
we're not concerned with the mixture here, let's sort the numbers
in a period. Above then becomes
0 0 0 1 1 1 (even)
Player B will use this series when strengths match, but if player
A is stronger than player B, A will win a higher percentage of the
games in the long run. To adjust for this, B adds 1's to the period
till the winning rates match again (traditionally he takes one stone
more every time he's 4 games down). The next series to try is
0 0 1 1 1 1 (Japanese 1-pro-dan gap = BWB)
(0 0 0 1 1 2 is no series because the numbers in a period shouldn't
differ by more than one.) This will continue with trying
0 1 1 1 1 1
1 1 1 1 1 1 (handicap 1)
1 1 1 1 1 2
1 1 1 1 2 2
1 1 1 2 2 2 (handicap 1.5)
1 1 2 2 2 2
...
till the match is found. If it were the last row above, this would
mean that, facing A, B takes 2 stones handicap in 4 games out of 6
and only enjoys black in the remaining two games.
Another way to express this is simply to say that B takes a handicap
of (1+1+2+2+2+2) / 6 = 10/6 =
1 + 2/3 stones
against A. This number can be converted back to a unique period for
any given length (but only certain ones will yield integers). If A
were the (busy) reference player everyone compares to, each player
could use his personal handicap against A to denote his strength.
Now let's come to the tricky part. Imagine two players being G
stones apart in strength. What handicap would you advice? Did you
suggest G stones? WRONG - a common error. The correct handicap is
half a stone bigger. Here's why:
Suppose the stronger player is A himself, our reference player. His
strength is not zero, as one might expect, but 1/2 - this is because
A plays an even series against himself (0 0 0 1 1 1 = 3/6 = 1/2).
Since his opponent B takes SB stones from A when B's strength is SB
simply by definition, the handicap H (= SB) is 1/2 bigger than the
strength gap G (= SB - 1/2):
_______________________
/ H ______________\
/ / G \
+---------+------ ... ------+
0 1/2 SB
If this is correct when comparing to A, it must also be correct
when comparing to someone else - just shift all strengths till the
stronger player ends up with 1/2, and then pretend him to be the
reference player: Half a stone has to be added to the strength gap
(measured in stone units) to reach the correct handicap!
Maybe an analogy helps. If a plane, starting in A, takes two hours
to reach B, and the next two hours to reach C, B isn't necessarily
midway between A and C. If planes usually had to taxi for, say, half
an hour before takeoff, the net time between A and B is just one
hour and a half. Since comparing two flights starting from the same
origin only yields a net time, a flight from B to C will not take
two hours, but two hours AND a half (now taxiing on B's ground).
So, if you take one stone from Guru and Dummy takes two, rejoice:
you're no half-dummy - you're twice as near to Guru than to Dummy.
Let's call this the "handicap paradox".
The traditional Japanese strength names or grades (in other fields
as well) in decreasing order are
9-dan
8-dan
7-dan
6-dan
5-dan
4-dan
3-dan
2-dan
1-dan (shodan)
1-kyu
2-kyu
3-kyu
:
Note that there's nothing higher than 9-dan. Note further that among
dans higher numbers are the stronger ones, whereas among kyus lower
numbers are. If you silently try to fix by adding a minus sign to
the kyu numbers, you notice another defect: zero is missing.
At least one would expect dans to be the masters and kyus to be the
advanced players and beginners, but on top of this mess there's
another distinction - that between professional dan and amateur dan.
Reminds me to tell you that amateur dans actually only get as high
as 6-dan (with "of course" some 7-dan exceptions), which might fit
to the saying that an amateur 6-dan is about a pro 1-dan [P-WD].
After all - "great", isn't it?
Are at least the strength gaps sound? I'm afraid no. Amateurs grades
are 1 stone apart. Sounds good, but taking black in all games - the
natural step - is taking half a stone more than compared to an even
series: the 1/2-stone gap is the canonical choice!
What about the (Japanese) pros? Of course, you guessed it - they
take their own gap. Everybody will tell you that it's a 1/3-stone
gap, but look at this [GW50b]:
pro-dan gap series
0 0 1 0 0 0 1 1 1 (even)
1 0 1 1 0 0 1 1 1 1 +1 (BWB)
2 1 1 1 1 1 1 1 +2
3 1 1 2 1 1 1 1 2 2 +2
4 1 2 2 = 1 1 2 2 2 2 +2
5 2 2 2 2 2 2 2 +2
6 2 2 3 2 2 2 2 3 3 +2
7 2 3 3 2 2 3 3 3 3 +2
8 3 3 3 3 3 3 3 3 3 +2
(Mixture dropped, e.g. 0 1 1 instead of 1 0 1. Last 5 rows added.)
This is the system of series said to be used in the "Oteai", Nihon
Ki-in's rating tournament. I added the last 5 rows (4 - 8) only to
complete the picture. They're not necessary because the maximal
pairing gap in the Oteai is kept to 2 dans, which only occasionally
could become 3 dans due to a meanwhile promotion.
Notice that all steps add 2/6 = 1/3 stone - except the first one
from even to BWB: it adds 1/6 stone. Nevertheless, since the
majority of games played in the Oteai are 0- and 1-gap games (an
unhealthy inbreeding in my opinion, by the way), the BWB series
dominates in defining the Japanese pro-dan gap: it's 1/6 stone.
A Korean pro 7-dan pointed to this irregularity in Baduk-1189 and
suggested a system were all steps are the same, 1/4 stone [DGZ0490]:
pro-dan gap series
0 0 0 1 1
1 0 1 1 1
2 1 1 1 1 (handicap 1)
3 1 1 1 2
4 1 1 2 2
5 1 2 2 2
6 2 2 2 2 (handicap 2)
7 2 2 2 3
8 2 2 3 3 (handicap 2.5)
(Mixture dropped. Last 2 rows added. VVGV's G read as W.)
The period is a bit longer than before, 4 games instead of 3, but
Kang Chol-Min's system is indeed logical and its handicap of 2.5
stones between pro shodan and pro 9-dan seems to be more reasonable
than former's 3 stones because "the margin between a top [pro] 9-dan
and an average [pro] 1-dan seems more like two stones" [GW50b].
If this quote really means 2 stones and not 2.5, steps of 1/6 would
be even more reasonable. A pro shodan playing a pro 9-dan would then
only take (9 - 1)/6 + 1/2 = 11/6 = 1 + 5/6 stones - almost two.
The 1/6-gapped system looks like this:
pro-dan gap series
0 0 0 0 1 1 1 0 1
1 0 0 1 1 1 1 0 1 1 (BWB)
2 0 1 1 1 1 1 0 1 1 1 1 1
3 1 1 1 1 1 1 1
4 1 1 1 1 1 2 = 1 1 1 1 1 2
5 1 1 1 1 2 2 1 1 2
6 1 1 1 2 2 2 1 2
7 1 1 2 2 2 2 1 2 2
8 1 2 2 2 2 2 1 2 2 2 2 2
The advantage of the 1/6 system over the 1/4 system is that it
preserves the traditional Japanese BWB series played for a pro 1-dan
gap and that it fits well to a komi of 6 points. The drawback is its
lengthy 6-game period for a pro 2-dan gap. Since gaps above 3 don't
occur in the Oteai, the other two 6-gamers don't really bother.
But are the original series actually used in the Oteai anyway? What
puzzles me is the color distribution in [GW50b]'s example of how
Michael Redmond earned his (pro) 3-dan:
opp gap Oteai games he got expected
str series played black by series
------------------------------------------
1-d -1 WBW 7 0 2 1/3
2-d 0 BW 4 3 2
3-d +1 BWB 6 6 4
4-d +2 B 7 7 7
Take the first row. Mike, 2-dan at the time, played 7 games against
shodans without ever getting black? But the series for a pro-dan gap
of -1 is WBW, giving him a 1/3 chance. Then consider the third row.
He played 6 games against 3-dans without ever having to take white?
But the series for a pro-dan gap of +1 is BWB, giving him only a 2/3
chance to avoid white.
Are Oteai series played between individuals? This hardly would make
any sense: in the 24 games played (from Nov. 25, 1981, to Sept. 21,
1983) Mike faced not one of his opponents for a second time - let
alone for a considerable number of games to create a fair series.
On the other side, there must be some series - otherwise Oteai's
points-per-game system (distributing 120 points between both players
per game) wouldn't have to cover cases where the weaker player takes
white. Either I don't understand it, or it fits into the whole mess.
By the way, recently the Nihon Ki-in replaced Oteai by promotions
due to performance in regular tournaments. The reason seems to be
- guess what - money. No public attentioon, no sponsors - no money.
Ryu Shikun, for instance, didn't attend the Oteai for years. So,
despite being in the top ten, he still was a "7-dan". [DGZ0103a]
Let's leave Japan's jungle again and step out into the clearing.
The Oteai might or might not have used series, but they aren't in
use anywhere else. Why then mention them? Because they serve well
in explaining the handicap paradox and, to come now, the relation
between partial handicap stones and komi.
A handicap of, say, 1.5 can be translated to a series with a 2-game
period: 1.5 = 3/2 = 1 1 + 0 1 = 1 2, giving the weaker player black
in one game and 2 stones in the other. But what if only a single
game is to be played? The idea is to convert 1.5 to an integer via
komi. But how much komi would Black have to pay to buy half a stone
and increase 1.5 to 2? Or should he rather sell half a stone and
decrease 1.5 to 1?
If you play someone of your own strength, you take a "handicap" of
1/2. This either means a "0 1" series or a single fair game. The
latter is either you taking black and paying some komi or you taking
white and receiving some komi. One can also put it this way:
Before you yield turn, you place your handicap onto the board - in
this case it's half a stone. But since you can't play with chopped
stones, you either have to buy a second half or have to sell the
first one. After this transaction, either one black stone is around
and you paid komi, or no stone is around and you got komi. The first
case matches an even game with you being Black, the second an even
game with you being White - therefore the komi to be used must be
that used in an even game:
The price for half a handicap stone is the perfect komi
Don't confuse this with buying sente. In this case you have no stone
on the board and would have to buy two half-stones - costing TWICE
the perfect komi.
If the "handicap" is 1/2, there's a symmetry between buying and
selling. For all other handicaps this is not the case. Since komi
should be kept as small as possible (primary criterion), fractional
parts greater 1/2 should be completed by buying their complement
(to one), and parts below 1/2 should be sold. Fractions of exactly
1/2 should also be sold to favor a lesser number of handicap stones
(secondary criterion).
For instance, assuming a perfect komi of, say, 5 points:
gap H N K
----------------------------------------
-1.6 -1.1 -1 1 (= giving 2.1)
-1.2 -0.7 -1 -3 (= giving 1.7)
-1 -0.5 0 5 (= giving 1.5)
-0.5 0 0 0 (= giving 1 )
0 0.5 0 -5 (or 1 5 )
0.5 1 1 0
1 1.5 1 -5 (not 2 5)
1.2 1.7 2 3 (not 1 -7)
1.6 2.1 2 -1 (not 3 9)
2 2.5 2 -5 (not 3 5)
2.5 3 3 0
3 3.5 3 -5 (not 4 5)
3.5 4 4 0
4 4.5 4 -5 (not 5 5)
...
with
gap = your strength minus his strength
H = gap plus 1/2 = handicap you take
N = number of stones you place before you yield turn
K = number of points you pay before you yield turn
(|K| <= perfect komi)
It would be more logical to swap the sign of the komi K since more
handicap stones are "positive" for Black and putting them into the
lid as komi is "negative" for Black. But since everybody is used to
speak of positive komi in the normal case of an even game, I left
it to avoid confusion. (To make up some "logic": both handicap
components count stones of the same color if their signs match. ;-)
The "negative" rows may be a bit confusing. What's a handicap of
-1.1? It's 1 - (-1.1) = 1 + 1.1 = 2.1 seeen from the other side. To
convert a handicap to your opponent's view, take its complement to
1 or, for a pair, its complement to (1,0). This is academic. It's
clearer to stick to N > 0. This is Black's point of view since
always Black puts down the first stone - handicap or not. (This
wasn't always so, but nowadays it is.)
By now you should be convinced that a, say, 1-kyu has to give a
3-kyu not 2 stones, but 2.5 stones, that's, 2 stones plus komi
paid by White (negative komi). In fact, if strengths are 1 stone
apart, there are no games without komi! Either it's an even game
and Black pays komi, or it's a handicap game and White pays komi
- besides giving handicap stones accordiing to the strength gap.
If you don't agree - just relax, you're in "good" company: even the
German Go Federation (DGoB) ignores this fact. Recently it invited
clubs to take part in the German Club Championship - played with
"full" handicap. This was defined as the stronger player taking
white and giving N handicap stones to a N grades weaker opponent
[DGZ0103b]. "Great". As just explained, negative komi is missing.
But can't we just define it this way? No, we can't! It would not be
consistent. The step from even game to black is half a stone, but
that from black to handicap 2 is 1 stone. It makes no sense to vary
the step. If grades are 1 stone apart, and if perfect komi were 5
points, you "take" 1 stone and pay 5 points in an even game. If you
are 1 grade weaker, you take 1 stone more, but since fewer handicap
stones should be preferred, use 10 points more instead, that's, you
still take 1 stone, but now receive 5 points instead to pay them.
Each further step adds 1 handicap stone - and leaves komi negative.
(Not to minimize the number of handicap stones wouldn't avoid komi.
It just became positive instead, in trade for 1 handicap stone more.)
But the German Go Federation should know better. Its former grade
system, still around when I started in about 1975 and at least in
use until 1993 in the Netherlands [RGG011093], called its grades
"classes". The gap between two neighboring classes wasn't 1 stone,
but 1/2 stone. This, as already mentioned, is the canonical choice.
It recommends itself because the step from even to black is half a
stone. Handicap was then defined as follows [P-WD] [RGG011093]:
H = (gap + 1) / 2
N = (gap + 1 + E) / 2
K = E * 5
E = 0 for odd gaps
E = 1 for even gaps
For even (class) gaps that's:
gap H N K
-------------------------
0/2 0.5 1 5
2/2 1.5 2 5
4/2 2.5 3 5
6/2 3.5 4 5
8/2 4.5 5 5
:
This was based on the assumption of 5 points being the perfect
komi and no synergic effects among the handicap stones. Notice
that always Black paid komi. Just trade 1 handicap stone for a
komi-sign reversal to get to the negative-komi system I favor:
gap H N K
-------------------------
0 0.5 0 -5
1 1.5 1 -5
2 2.5 2 -5
3 3.5 3 -5
4 4.5 4 -5
:
Since the dan/kyu system has full-stone gaps, but the class system
has half-stone gaps, one dan/kyu grade matched two classes:
dan/kyu class
strong 7-dan 6
weak 7-dan 7
strong 6-dan 8
weak 6-dan 9
strong 5-dan 10
weak 5-dan 11
strong 4-dan 12
weak 4-dan 13
strong 3-dan 14
weak 3-dan 15
strong 2-dan 16
weak 2-dan 17
strong 1-dan 18
weak 1-dan 19
strong 1-kyu 20
weak 1-kyu 21
strong 2-kyu 22
weak 2-kyu 23
:
The German class system was a very good grade system: no artificial
distinction between dan and kyu grades, canonical strength gaps of
half a stone, and sound handicaps. I don't quite understand why it
was dropped nor why the former president of the DGoB (1966-1981) and
EGF (1967-1969), Karl-Ernst Paech, takes pride in having initiated
its removal [DGZ0602c]. Sometimes it's better to stick to your own
tradition.
Let's design a new (international?) grade system. First, there
should only be a single measurement unit - of course a full stone.
Then, each grade or strength should (at least try to) tell what
handicap the perfect player would give its owner. This forces us
to assign the perfect player the strength 1/2. Then, we would have
to guess where to put the best pros. How about strength 2 (perfect
player gives pro 9-dan 2 stones and no komi). If pros are 1/4 stone
apart (handier than 1/6), pro shodan is of strength 4. If this
equals an amateur 7-dan (instead of 6-dan for this nice 9p=9d join),
amateur 6-dan is of strength 5. All in all that's
strength name
----------------------
0.5 perfect (= pro 15-dan)
2 pro 9-dan (= ama 9-dan :-)
2.25 pro 8-dan
2.5 pro 7-dan
2.75 pro 6-dan
3 pro 5-dan (= ama 8-dan)
3.25 pro 4-dan
3.5 pro 3-dan
3.75 pro 2-dan
4 pro 1-dan (= ama 7-dan)
5 ama 6-dan
6 ama 5-dan
7 ama 4-dan
8 ama 3-dan
9 ama 2-dan
10 ama 1-dan
11 1-kyu
12 2-kyu
13 3-kyu
:
This system actually has no fixed strength gap, since any weird
strength is possible. But if used as a grade system, on which
handicaps are based, at most missing multiples of 1/2 should be
added. This brings down the gap between neighboring amateurs
strengths to the canonical gap of 1/2 stone - and is precise
enough.
If you don't agree to the right side, just take it as defining
"nicer" names for the left one. If you think that all multiples
of 1/2 deserve a name too, how about using "strong 2-dan" for 8.5,
"strong 1-kyu" for 10.5, etc. (avoiding "weak" ;-). But it might be
even better to forget all these names again. What's wrong with "My
handicap is 8.5" ? Totally plain. ("Once in a while I play with
Him, taking 8 stones and komi." ;-)
The handicap taken by the weaker player already was defined above:
Add 1/2 to the non-negative strength gap and either sell the
fraction or buy its complement - whatever brings komi nearer to
zero and leads to fewer handicap stones, favoring the former.
There's another way to put it. One can use a price system (or
function) P. P(N) is defined as
the number of points a perfect payer
playing another perfect player gains
in the result when he uses N handicap
stones instead of none
P(1) then has to be twice the perfect komi PK because taking 1
handicap stone (that's, taking black) wins by PK, but taking 0
(that's, taking white) loses by PK:
P(1) = 2 * PK
Now we know P(1). What about the rest? If one assumes P to be
linear, that's having the property P(A+B) = P(A) + P(B), the
rest follows easily:
P(1) = P(0.5) + P(0.5)
P(1.5) = P(0.5) + P(1)
P(2) = P(1) + P(1)
P(2.5) = P(1.5) + P(1)
P(3) = P(2) + P(1)
:
P(X) = 2 * PK * X
and of course P(0.5) = PK.
We could now guess some PK, for instance 5, produce a price table
based on it, and calculate the handicap pairs (N,K) by going the
opposite direction - from P(gap+0.5) to best fitting P(N), and
adjusting the rest in K. This wins nothing - but wait.
This price system is linear. 2 stones cost twice as much as 1, etc.
But this was just an assumption. Nobody knows if this is the case,
but it's very likely that it is not and that a couple of handicap
stones create synergy. A table could cope with these irregularities.
In the time of the German class system, a rating system called
"Karlsruher Methode" (KM) was around that used such a price table.
It was based on a perfect komi of 5 and took synergy into account
by increasing the price of each handicap stone, starting with the
third. For instance, 6 handicap stones wouldn't be worth 60 points
but 10 + 10 + 11 + 12 + 13 + 14 = 70 points (actually all prices
were 5 points less to spare increasing the class gap by one before
it was multiplied with 5). In other words, a strength gap of 6.5
would only yield a handicap of 6 stones because 6 stones' synergy
adds up to a virtual 7th one in KM's believe. [P-BZHZ]
KM's price table thus looked like this:
N P(N)
------------
1 10
2 20
3 31
4 43
5 56
6 70
7 85
8 101
9 118
10 136
11 155
12 175
13 196
14 218
15 241
16 265
17 290
:
(Or as formula: P(N) = (N * (N + 17) / 2) + 1, but P(0.5) = 5)
To find (N,K) for a gap G, one has to search for the first P(N)
with a difference D = P(N) - (P(1) * (G+0.5)) nearest to zero
and set K = D.
The Karlsruher Methode would therefore advice following handicap
pairs (actually its gaps were measured in classes, its K sign was
reversed, and handicap fraction elimination could go in either
direction):
or
gap N K N K
-----------------------------------
0.5 1 0
1.0 1 -5 2 5
1.5 2 0
2.0 2 -5 3 6
2.5 3 1
3.0 3 -4 4 8
3.5 4 3 3 -9
4.0 4 -2
4.5 5 6 4 -7
5.0 5 1
5.5 5 -4 6 10
6.0 6 5 5 -9
6.5 6 0
7.0 6 -5 7 10
7.5 7 5 6 -10
8.0 7 0
8.5 7 -5 8 11
9.0 8 6 7 -10
9.5 8 1
10.0 8 -4 9 13
10.5 9 8 8 -9
11.0 9 3
11.5 9 -2
12.0 9 -7
12.5 10 6 9 -12
13.0 10 1 9 17
13.5 10 -4 9 22
14.0 10 -9 9 27
14.5 11 5 9 32
15.0 11 0 9 37
15.5 11 -5 9 42
16.0 11 -10 9 47 [KM used (12,10) for (11,-10)]
16.5 12 5 9 52
17.0 12 0 9 57
17.5 12 -5 9 62
18.0 12 -10 9 67
18.5 13 6 9 72
19.0 13 1 9 77
19.5 13 -4 9 82
20.0 13 -9 9 87
20.5 14 8 9 92
21.0 14 3 9 97
Let's now put the pieces together and codify handicap games:
If two players' strengths are equal or if handicap is ruled out,
it's an even game and the rules stay unchanged. Otherwise it's a
handicap game and the rules are extended by the rules about boards
mentioned above and changed by replacing A1 and A2 as follows:
A1. "Two players play a handicap game of go on the standard board
according to
Logical Japanese Rules of Go "
by doing - essentially - the following in the given order:
(This requires (1) that a strength, given by a rational number,
is assigned to each player and (2) that a price function P is
defined that maps each non-negative integer N to a non-negative
integer P(N).)
1. They call the weaker player "Black" and the stronger
player "White".
2. They determine the "strength gap" G = |S1 - S2| (with |X|
being -X for X<0, and X otherwise) using their strengths
S1 and S2 (two rationals). A handicap game requires G > 0.
3. They determine the "handicap" H = G + 1/2.
4. They determine H's "handicap pair" (N,K) by finding integer
N and rational K' that satisfy P(N) = (P(1) * H) + K',
favoring smaller |K'| over smaller N ("best table fit").
If K' >= 0, K = round(K'); otherwise K = -round(-K')
(with round(X) being the integer nearest to X + 1/2 if X
is no integer, and X otherwise).
For linear P (P(A+B) = P(A) + P(B)) this is the same as
a) to split H into integer I and rational Q that satisfy
0 <= I, 0 <= Q < 1, and I + Q = H; and
b) to determine N and K depending on Q:
if Q <= 1/2 ("sell"): N = I, K = -round(P(1) * Q)
if Q > 1/2 ("buy" ): N = I+1, K = round(P(1) * (1 - Q))
5. Black must choose a state that's initial for N and K on the
standard board. This state is called "current state".
6. While the current state is not final, the player having the
turn in it must replace it with one of its successors.
7. When the current state is final, the player with the higher
score in it wins. If both are equal, it's a "jigo" (tie).
A2. "A state S1 is initial for N (handicap stones) and (a komi of)
K (points) on the standard board" only if all this holds:
1. N is a non-negative integer.
2. K is a (possibly negative) integer.
3. S1's board is the standard board.
4. S1's set of black locations is a subset of S1's set of
locations having no more than N members (possibly less).
5. S1's set of white locations is empty.
6. S1's set of temporarily marked locations is empty.
7. S1's set of permanently marked locations is empty.
8. S1's black captive count is K for K > 0, and otherwise 0.
9. S1's white captive count is -K for K < 0, and otherwise 0.
10. S1's turn is "white".
11. S1's pass count is 0.
12. S1's history is empty.
Both, the strength system and the price system, are purposely left
open. The only implied requirement for the strength system is that
a gap of 1/2 in it would mean that the weaker player takes black
and no komi from the stronger player, because otherwise it wouldn't
fit to whatever price system is defined. The price system, on the
other hand, is totally free - at first sight. But its purpose, of
course, is to bring Black's and White's winning chances as close as
possible together.
The most prominent price system candidate is the plain linear
P(N) = N * 2 * EK
with EK being the (rounded down) komi that seems to be fair for even
games. This ignores synergy created by handicap stones. But since
synergy is hard to figure out anyway (KM obviously just made a wild
guess) and only seems to exist for gaps above two, this is no big
problem: up- and down-grading should depend on results made against
grades in the neighborhood - not on teaching games (starting with
more than, say, three handicap stones).
That the perfect komi might differ from EK is neither a problem.
It's better to match the winning chances in the real, unperfect
world than to have unmanageable high komis. In the same sense I
dropped the requirement that P(1) had to be even, as it certainly
is in the perfect world. That the komi is an integer was kept to
allow jigo. I love jigo as well as seki.
The only problem with a grade system based on handicap is that
official handicap games have to be played. Otherwise the system
could lose touch and float, letting gaps globally or locally
either shrink or grow. Japan is going exactly in this direction by
abolishing Oteai (if they not already were on this track by neither
using series nor handicap stones in it). Needless to say that a
further necessity for keeping up a sound grade system is to permit
down-grading or demotion (which the Oteai also failed to do).
Since games played in one's home club are done with full handicap,
they could (and should) go into the grading process. But solely to
depend on them would be like inbreeding. Tournament games too have
to be considered, even if played without handicap.
If the strength gap doesn't go beyond one, every even game can in
retrospective be interpreted as a handicap game simply by adjusting
it with the proper komi before the grading process takes it into
account. So, for instance, if 1-kyu wins with white by 4 points
against 2-kyu in an even game, this would be an adjusted loss by 8
points under a komi of 6 (White returns 6 points and gives further
6). (By the way, the stronger grade should always take white, even
if no handicap is used.) In this case each player can choose to
look at it positively: 1-kyu made a point in the tournament, and
2-kyu improved his winning percentage in the grading process.
Each even game with a larger gap could also retrospectively be
adjusted, treating each missing handicap stone to be worth P(1)
points for the side that lacks it (ignoring synergy again). But
since the character of those games compared to a handicap game
has changed, those games should be of lesser weight than the
former ones.
I'll leave the details of the grading system open. A simple scheme,
for example, would be to grade up after 4 wins in a row and to grade
down after the same number of losses in a row (adjusted and weighed
games, of course). The step for increasing or decreasing strengths
would be 1/2 among amateurs and 1/4 among pros.
The traditional locations for Black to place the handicap stones
on the standard board are (in this order)
bottom being Black's side
On a (real) standard board all nine locations used above are
emphasized to support orientation. Each is called "hoshi".
Black shows awareness if he "colors" them in the traditional
order. However, there are two exceptions:
1. If the last handicap stone is to be placed and it's also the
first, every location may be used (but see polite start).
2. If the last handicap stone is to be placed and its ordinal
is odd and greater three, the center hoshi ("tengen") is
to be used.
Note that no stone lands on tengen if not last - in contrast to
some sources that suggest to always occupy tengen with the fifth
stone - and that the third stone avoids tengen even if last.
There's no tradition for the case where the number of handicap
stones exceeds nine. Let's make up one just for fun. Watch this
progression (ONLY hoshis are shown):
1 - 4
5 - 8
9 - 24
25 - 52
53 - 80
Not that anyone cares, but in case you plan to play on a 31x31 and
to get up to 81 stones handicap, you now know exactly where and in
which (darn) order you have to place them. The first 25 hoshis fit
on the standard board (9 traditionally emphasized ones plus 16 in
between) and are more likely to be useful.
My set of generating rules, as you might have discovered, is
G1. Start with 2 horizontal and 2 vertical lines. Their
intersections create the first 4 uncolored hoshis.
G2. As long as there are uncolored hoshis besides tengen
(center), color that one that fits best to following
preferences, considering lower preferences only to
break a tie:
P1. Prefer a greater distance to tengen.
P2. Prefer more symmetry.
P3. Prefer the right side.
P4. Prefer the upper side.
G3. If all hoshis besides tengen have been colored, insert
new lines halfway between all older lines. Each new
intersection is a new, uncolored hoshi. Continue with G2.
This generalizes the traditional handicap position and order.
Notice the funny coincidence in above's procedure that tengen isn't
yet created when the third stone is to be placed, "explaining" why
it doesn't go to tengen.
But the first exception, free placement in case of a handicap of
exactly one, still is a miracle - isn't it? Wouldn't it be logical
also to place the first stone of a one-stone handicap game on the
upper right hoshi - only allowing its free placement if Black pays
komi?
The reason for this inconsistency seems to be that free placement
was invented before komi. In ancient times the game started with
a fixed pattern of four stones - each player occupied the hoshi in
his upper right and lower left corner with a stone. Japan abolished
this "zuozi" practice in the 14th or 15th century [P-MK]. From then
on they started the game with an empty board. Since there was no
komi, all games were in fact one-stone handicap games - with free
placement of the first stone.
Wouldn't it only be consistent to also "free" the rest of the
handicap stones? Even if this spoils my generalization efforts
above - yes, it is. That's why LJRG prescribes no fixed pattern.
By the way, the play-off between amateur and professional Honinbo,
sponsored by the Mainichi Shinbun for now 40 years, uses free placed
handicap since 1995. On November 4, 2002, amateur Honinbo Samejima
Ichiro made his first appearance and boldly placed his two handicap
stones on two diagonal 5-5's. After 282 moves heavy fighting and
several large ko fights, Honinbo Kato Masao (returning after 23
years, by the way) had to resign. [SL1] [DGZ0602a]
Also interesting is that this event's handicap varies depending on
last year's outcome. If Black loses, komi decreases by 2.5 points.
If he wins, komi increases by the same amount. Half of the games
thus enable jigo. A komi of -7.5 is converted to 5.0, while adding
one handicap stone. Similarly, a komi of 7.5 is converted to -5.0,
while taking away one handicap stone. One handicap stone's price
is thus 12.5 points. Since the 2002 event saw a handicap of 2 stones
and -5.0 points and was won by Black, 2003 will see a handicap of
2 stones and -2.5 points (as 2001 did). Had Kato won, the amateur
would have gone down to 3 stones and 5.0 points.
In the diagram above, I labeled the handicap stones with 1 to 9.
This was only to show their order of placement. Usually handicap
stones are not labeled. But silly me likes to
- know in which order the handicap was placed
- always have odd numbers for black and even for white stones
(except in variation diagrams, of course)
- be prepared for the handicap liberation
Therefore I strongly recommend to label handicap stones with 1a,
1b, 1c, etc. Of course, in case of just one the label is 1.
(A one-stone handicap game being the same as a no-komi game.)
The placement of stones is free, but not all locations are polite.
A remaining chance for Black to show awareness is to keep his first
stone, handicap game or not, in the half-past-one-till-three-o'clock
sector of the board (triangle k10-t10-t19 on the standard board).
[DGZ0994] motivates this with anticipation of where White would like
to answer (Black's upper left corner), but I rather think it stems
from old Japanese (and, of course, older Chinese) writing direction,
which starts in the upper right corner and fills one column after
the other from right to left.
This preference of right side over left side and - in this order -
upper side over lower side naturally selects this sector (and also
influenced the handicap sequence, as we saw). Each location on
the left side of the board has at least one symmetric partner on
the right side (that with the complementary first coordinate - e.g.
b3 = 2,3 <=> 18,3 = s3), and likewise each location on the lower
side of the board has at least one symmetric partner on the upper
side (that with the complementary second coordinate - e.g. b3 = 2,3
<=> 2,17 = b17).
According to our preference of right and upper side, no location on
the left or lower side of the board will ever be chosen because
there always is a "better" partner. Similarly, each location above
the diagonal from the lower left to the upper right corner has at
least one symmetric partner below this diagonal (that with swapped
coordinates - e.g. b3 = 2,3 <=> 3,2 = c2), and, since this partner
always is more to the right, we can as well forget all locations
above this diagonal:
What remains is the sector in question.
(Could it be reduced further? No.)
One would believe that at least Japanese pros stick to form without
any rule, but that's not the case. In 1999's Meijin final between
Cho Chikun and Yoda Norimoto, Yoda, after having boldly announced
his victory and losing the first two games, placed the first stone
of game three in his upper left corner - above the hoshi [DGZ1099].
Hopefully this sets no bad example, even if it incidentally led to
Yoda's only win over Cho in this best-of-seven match.
Yoda may argue that the sector rule isn't followed strictly, for
instance: Kitani Minoru at least once started a game in his lower
right corner (1941 in a game against his former teacher Kubomatsu
Katsukiyo), and left-handed Osawa Ginjiro (1844-1906) even made
it his habit as Black to start in his upper left corner [GMR0469].
But the overwhelming majority of games indeed start in the "right"
sector (selected by historic incident, of course). Restricting the
first stone to one sector avoids confronting White with unusual and
irrelevant symmetric variations without costing Black anything. It's
a matter of courtesy (but I wouldn't even bother if some rule would
take care).
Today, with computers, is takes nothing more than to press a button
to mirrow the game record so that its first stone sits in the right
sector. Please don't do it. Please tell the truth! Keep it to
rotations, and if Black doesn't end up at the bottom, please mention
his side.
CYCLE REMOVAL
First some points about detecting a cycle.
Imagine some game. The game starts in some initial situation (or
state). Both players take turn to manipulate the situation. Only
the situation itself and the rules of this game constrain how this
can be done - nothing else.
Now imagine that one of them comes to you, shows you the situation
he is confronted with, and claims that this could go on forever.
You have absolutely no knowledge about the game that goes beyond
the information given above. What to do?
Your only chance to decide on this issue is to ask them to show you
all former situations. Then you search for one that is IDENTICAL to
the one in question. If you find none, you stay undecided. But if
you do, it's obvious that the claim was correct: this could go on
forever.
Now imagine that it's not you who has to decide, but LJRG. And
further imagine that LJRG has some special goodies for anybody
that suffers from a cycle, but that it wants to make sure that
he or she deserves it. Well, then LJRG has to apply the same
test as you did - and that's (almost) exactly what it does.
In LJRG's case the game to decide on already includes a treatment
of short cycles (ko and double pass) - therefore the treatment
of long cycles is the next layer of cycle treatment. This may
seem complicated, but enables LJRG to treat long cycles in a
different way than short ones.
I'm telling you all this to let you understand why LJRG doesn't
just compare the stone configurations or additionally the turns
of two situations to decide if cycle removal is legal. Even if
it's true that a running cycle will necessarily repeat those
aspects, this doesn't has to be the only cause. LJRG tries to
stay on the save side.
So, why are the captive counts totally ignored when testing for
similarity? First, because they don't influence what can be done
in a go situation in any way. Second, because this allows the
removal of unbalanced cycles like the one possible below (no dead
bent four - see beast 31):
0 1 W 0
To avoid losing, White could try to repeatedly sacrifice two stones
and capture one. This "cycle" can't really hurt Black. He patiently
answers till he has piled up enough white prisoners. Then he sticks
to passing. This eventually forces White to pass too, since there's
no suicide, which ends the game.
But why not give Black the means to stop it earlier?
Actually it's redundant to keep two captive counts because what
matters is only their difference, but since I decided to even ignore
that for the reason just given, I kept it more in sync with reality.
Second, to avoid a bunch of diagrams cycles notoriously produce,
some abbreviations to shrink each situation to one line:
. empty location
# empty, but temporarily prohibited
* empty, but permanently prohibited
x black stone
o white stone
B Black's turn
W White's turn
0 pass count is 0 (implies no #)
1 pass count is 1 (implies no #)
pass count is -1 (implies one #)
For instance
0 0 B 0
with following 7 locations of interest
0 0 B 0
gets squeezed to
________ neutral is empty
/ ________ black stone in left ko
/ / _______ white stone in lower right ko
/ / / ______ black stone in upper ko
/ / / / ______ Black's turn
/ / / / /_______ pass count is 0
/ / / / //
. x. o. .x B0
If the cycle only runs on kos, as above, each ko is squeezed
further to a single letter:
. x o x B0
The letter is capitalized if its stone is neighboring
a temporary mark:
. #o o. .x B
. O o x B
Let's now see what the effect of allowing cycle removal is.
What if two double-ko sekis are around and the game is still
in progress?
1 0 B 0
with following 8 locations of interest
Black is behind. What if he tries to reach no outcome
by producing a cycle? It could continue like this:
S1 xoxo B0 (1 0)
S2 xXxo W (1 1)
S3 Oxxo B (2 1)
S4 oxxX W (2 2)
S5 oxOx B (3 2)
S6 Xxox W (3 3)
S7 xOox B (4 3)
S8 xoXx W (4 4)
S9 xoxO B (5 4) not similar to S1 (temporary mark!)
S10 xXxo W (5 5) similar to S2 (ignoring prisoners)
In S10
5 5 W -1
White is allowed to remove the cycle:
8 6 B 0
Notice how the stones in the cycle were treated as if captured,
increasing the black captive count by 3 and the white one by 1.
What did Black "accomplish"? He lost a stone and he lost sente.
Losing a stone is only the case when the number of black and white
stones in the set of locations used by the cycle match, but if not,
like in a triple ko (beast 8), the disturber "only" loses sente.
Losing sente, on the other hand, is for sure if one side "disturbes"
by staying in the cycle. His opponent will eventually remove it and
nevertheless be allowed to play his stone subsequently.
We conclude that Black can't gain anything in playing this cycle:
that's exactly what LJRG intends.
You may think the story is over now and everything worked out just
fine, but there is still a nuisance left.
Black may leave the cycle uncompleted and play 9 elsewhere (if the
board were bigger). Since after 8 both captured 4 stones, it's as
if the whole sequence never happened. Though Black can't stop the
game's progress, he can slow it down drastically - disturbing.
It would be nice if White could now himself chase Black through the
cycle and eventually remove it, but this costs a stone and sente as
we've seen. So, this will only work if White can afford it.
Even though I'm not totally satisfied, in the long run cycle removal
prevents no outcome.
What if no kos are involved like in a "round-robin ko"?
In this case the starting situation will be repeated - not the one
following it, as above - and Black will have the chance to remove
the cycle himself:
1 0 B 0
The first flip
produces
3 2 B 0
The next flip
results in
5 4 B 0
Black could now remove the cycle since this situation is similar
to the first - but he aims for no outcome and continues to
5 4 W 0
Since this repeats the second situation, now White can remove the
cycle: Black loses his recent stone and sente. Black would have
been better off removing the cycle himself. So again, Black can't
disturb forever.
End of the story? I cheated a bit. Sly Black could play 9 here:
5 4 W 0
This situation didn't happen yet. So, another flip will
be played, repeating the situation after the first flip:
7 6 B 0
Now finally the same arguments as above apply, convincing Black
to remove the cycle in his own interest.
Believe me: I hate bookkeeping of situations to detect cycles as
much as I guess you do. But cycles only happen rarely, and if, I
see no way to cope with them without some sort of bookkeeping.
In practice we certainly won't draw down situations - please don't
get me wrong.
Everything till now comprises the first design of cycle removal.
But then I discovered that there are cases where both players try
to avoid to pass ("pass fight"), which is silly. The solution was
to add a further condition:
Cycle removal only is allowed
if the pass count is not 1
This makes sense by itself because cycle removal should help the
disturbed player, but certainly nobody can claim being disturbed
when he could end the game at the same time - which is exactly the
case when the pass count is 1.
Here's an example for both avoiding to pass first without this
rule:
0 0 B 0
If the game ended as above, Black would win by 1 point: he controls
12 locations at the left side, giving him 3 points, White controls
11 locations nearby, giving him 2 points, and nobody controls the
rest (see beast 8 for a discussion why) - including that neutral at
the left that will be important (but shouldn't).
If White removed a cycle from the three kos in a situation similar
to above's, he would make jigo by removing 2 black stones compared
to only 1 white stone. Therefore White will try to create a cycle.
Here's one possible sequence of situations:
S1 . xox B0 (the situation above)
S2 . xox W1
S3 . Oox B *
S4 . oXx W
S5 . oxO B
S6 . Xxo W
S7 . xOo B
S8 . xoX W
S9 . Oox B * (is similar to S3)
White keeps on forcing after Black's initial pass, but Black gets
the first chance to remove the cycle in S9. He does and wins: one
black stone more was removed by capture, but therefore one white
stone more was removed by cycle removal (as a short cut, pretend
that Black already removed the cycle in S3 - this works if passes
in the cycle are balanced).
First it would seem that cycle removal succeeded in convincing
White to abstain from "disturbing" - but look at this sequence:
S1 . xox B0 *
S2 . xox W1 **
S3 . Oox B
S4 . oXx W
S5 . oxO B
S6 . Xxo W
S7 . xxo B0
S8 . xxo W1
S9 . Oxo B
S10 . oxX W
S11 . oOx B
S12 . Xox W
S13 . xox B0 *
S14 . xox W1 **
This time White passes in S6. If Black again (as in S1) refuses
to fill the "useless" neutral and passes instead, White forces a
similar sequence leading to S13.
S13 is similar to S1. Black can remove the cycle, but since an
equal number of black and white stones was captured and there
happen to be more black than white stones in the cycle's arena,
this is of no use for Black - but passing is neither because White
would remove the cycle (S14 is similar to S2) and enjoy jigo again.
Considering all this, Black will fill the neutral (and win):
S1 . xox B0
S2 x xox W0
S3 x Oox B *
S4 x oXx W
S5 x oxO B
S6 x Xxo W
S7 x xxo B0
S8 x xxo W1
S9 x Oxo B
S10 x oxX W
S11 x oOx B
S12 x Xox W
S13 x xox B0
S14 x xox W1
S15 x Oox B *
White applies the same strategy as above, but now S15 is the first
chance to remove the cycle and this favors Black again: one black
stone more was removed by capture, but therefore one white stone
more was removed by cycle removal. Black keeps his 1-point winning
margin - regardless if White passes or continues in S14.
Now what if it were not one, but two neutrals? If Black takes one,
White takes the other and reaches jigo via the 2nd sequence (that
was played as if there were no neutrals). Should Black pass instead,
White again plays the 2nd sequence to reach S13, in which Black
only can choose between cycle removal, passing, or taking the first
neutral - each leading to jigo.
It seems that Black will only win if the number of neutrals is odd.
Anyway, since the number of neutrals should NEVER change the outcome
of a game played under Japanese-style rules, above's condition was
added to stop this fuss:
White is now barred from removing the cycle in S14.
Here's the cause of the next fix of cycle removal:
After game end this is a big (dynamic) seki: nobody controls
anything. But before game end Black could disturb the ends
(continually atari all white groups except that in the center),
force White to remove the cycle (suppose White is ahead), and
then - backed up by the permanently marked liberties that come
with cycle removal - capture White's center group.
But this is a dynamic seki and it should stay one. The problem seems
to be the exploitation of the permanently marked liberties. To grant
stones neighboring a removed cycle immunity shouldn't enable them to
become aggressive. Therefore:
You may not play a stone if after you'd
placed it on the board all stones of your
opponent still enjoy liberties but this
stone either has none (suicide) or only
permanently marked ones (pseudo suicide).
This rule prohibits stones neighboring a removed cycle to fill up
their last non-permanent liberty. In the example above Black is
prohibited to fill either ko in the center after cycle removal.
Here's a historic "cycle" [DGZ1093].
At the end of the initial game of 1993's Honinbo league between
Komatsu Hideki (White) and Rin Kaiho (or Lin Hai Feng, born on
6.5.1942 in Shanghai, China), this was the situation (watch the
lower left corner):
[0 2] W 0
(There are 143 black and 140 white stones on the board and it's
White's turn, so I guess Black captured 2 stones more than White.)
Rin is leading by 8 points (before komi), but now got shocked by
White's attempt to revive the stones in the lower left corner:
1 3 W -1 (4 recaptured at A)
Even after Rin played his absolute ko threat at 2 and recaptured,
Komatsu continued to "disturb":
2 5 B -1
4 6 W -1
Of course, it would have made no sense for White to capture the
next-step ko with 9 because Black would have captured the corner
stone and next, since White is without any ko threat, the 3 white
pivotal stones.
The situation after 10 repeats the one after 4. After some further
tries both players agreed to an eternal life: jigo in the league.
Under LJRG Komatsu could have removed the cycle after 10 and,
still having the turn, would play the last point, after which
both would pass:
5 7 B 2 (12 and 13 passed)
White would win by 43 - 7 + 5.5 - 31 + 5 = 15.5 points.
Rin should have connected the ko earlier under whatever rule
set - provided it leads to a cycle.
Note that the 2 black positions enclosing the permanently marked
locations don't control anything because each can't build 2 eyes
on its own, and joining them via the corner wouldn't work either
because the permanently marked locations would prevent the 2-eye
formation. Therefore the 5 locations enclosed by them don't count.
But the cycle is an illusion, as Werner Fabry discovered [DGZ1293].
Rin could have connected the next-step ko with 8 instead of playing
his ko threat. White, lacking any ko threats, would then have to
approach from the outside, after which Black could have recaptured
again with 10:
2 6 W -1
Since White has no ko threats, he only can take the last point.
Black will fill or capture, and White will rub his eyes and realize
that he just has fed Black with two additional prisoners (the stone
Black added to his corner must be added by him anyway - see below).
The ko threats on the lower edge have the disadvantage that by
using them one produces the next ko threat for one's opponent.
Black's 8 above avoided this, but was only possible because of
the outside liberty at 9.
Rin's agreement to eternal life was an error. Repeatedly he missed
the chance to do as explained and win.
The best thing for Komatsu would have been to ignore the lower
left corner and to take the last point immediately. If both then
passed, we'd have this:
0 2 B 2 (2 and 3 passed)
Under JRG89 (details below) the game isn't over yet - it only has
stopped. Besides filling neutrals, Black would now have to connect
the ko (or capture) because his stones around the lower left corner
would otherwise be "dead in no territory" after game end (kind of
seki). This is because White could capture using the pass-for-ko
rule without enabling a new uncapturable white stone. Black would
win by 51 - 43 - 5.5 = 2.5 points.
Under LJRG there's no (silly) stop - there's just an end. All
dependencies with the context have to be detected and removed by
ONESELF and BEFORE the end. If Black passes too early, as above,
he'll be punished hard and lose:
He couldn't claim to be able to lock the lower left corner because
in this proof he would neither enjoy his outer liberty nor the
absolute ko threat any more - both being buried under permanent
white stones.
Notice that there never will be a situation under LJRG where
both players keep on playing a cycle because it's always better
to remove a cycle instead of continuing it:
If you continue, you give your opponent the chance to remove it,
but then he has sente and you lost a stone compared to having
removed the cycle yourself.
But (unfortunately) this doesn't mean it's never wise to start a
cycle! In the example below Black shouldn't pass.
0 0 B 0
White would pass too, the game would end, and Black would have
lost by 10 points - White controls both corners at the bottom.
Instead, Black should force White into a cycle by alternately
giving atari in the left and the right lower corner. Even if
White has the first chance to remove the cycle, costing Black
a stone and sente, White controls nothing after cycle removal
and Black wins by 7 points.
Under "New Ko Rules" (below) Black wouldn't be allowed to atari
a second time in each corner. New Ko Rules establish a kind of
local view before the end. This fits well with how things would
be ruled after the end, but one can question why other positions
aren't then viewed locally too:
0 0 B 0
The lower left corner would be controlled by White after game end.
White wouldn't have to capture the single black stone (see beast
10). But the game hasn't ended yet, and if Black fills the neutral
White should hurry to capture that single black stone to avoid ko:
Black would win it thanks to his (external) ko threat on the right
side.
If we connect things far away, why should we make an exception if
cycles are involved? So, LJRG allows as much as possible during the
game. If cycles happen, they are treated as a kind of dynamic seki.
The local view only applies AFTER the game end.
At last let me say something about super-ko and the kind.
A ko is a cycle with a length of 2: after 2 moves the situation
repeats - ignoring ko rule or temporary marks for the moment.
Then someone had the idea to prohibit this repetition, producing
this fascinating tactical event of a ko fight. So, why not
generalize this prohibition and convert all cycles into ko fights?
Wouldn't that make things even more interesting?
I don't think so because for me it seems unfair. Imagine again the
double-ko example. Black is behind and one part of the board looks
like this:
0 0 B 0
Why should we disturb harmony and let Black invest his
ko threats into killing one of the white groups above?
I can't see the point.
Now to be fair, Robert Jasiek defined "New Ko Rules" [W-RJ1],
trying to nail down Ing's 1991 ko rules. Their idea is to separate
the case where one or both players disturb(s) (for instance, in a
double-ko seki) from the case where both may fight (for instance,
in a triple ko). In the first case, restarting the cycle is
prohibited. In the second case, completing it is. I've not yet made
up my mind if this definition is clear or complete, but be sure -
it's very complicated (Fred Hansen's proposal, risking to go his
own way, seems simpler [W-FH2]).
In the case above both Black and White would certainly be called
"disturber" by "New Ko Rules" if they cycled in it and would be
prohibited to do so (if I got it), but in, for instance, a triple
ko both would have to treat it as a (super) ko and fight it out.
Don't expect me to go into details - I just want to say this:
The step from no outcome to fight for life and death in, for
example, the triple-ko case is in my opinion a too big one.
Let's illustrate this by an example ([P-IK] - this type of triple
ko also occurred in a "rating tournament in 1971 between Cho Chikun,
then 3-dan, on black and Fukui Masaki, then 5-dan" [GW50a]):
0 3 B 0
If Black connects the upper ko, White will capture the 4 stones in
the lower right corner. Meanwhile Black will take one ko and connect
it. White will connect the last ko and both will pass, giving:
4 4 B 2
White has won by 2 points.
So Black wouldn't want to connect with his first move. He'll start
cycling in those kos. Is he disturbing? White certainly has the
feeling because it's obvious that Black can't capture him (at least
as long nobody has ever heard about super-ko or "New Ko" rules).
Black, on the other side, will agree to that, but claim that the
purpose of his tactics is not to capture the white stones but to
dynamically defend his own stones from being captured.
If "New Ko Rules" classify this as disturbing (life) just because
there seem to be stable states - those with only one black stone
in all kos - then why is White allowed to "disturb" such a stable
state by approaching the 4 black stones in the corner? Don't they
also somehow belong to the local situation?
Under super-ko, Black would get a chance to capture White because
both would alternately need to make (super) ko threats. Is this
any fairer? Cycle removal instead tries to leave dynamic sekis
what the are: dynamic sekis.
Imagine this triple ko fight to go on forever. It's getting faster
and faster. The stones that come and go can't be seen any more.
The rest of the board is clearly visible, but in the part of the
board the cycle runs, you only see a flickering. It looks as if
gray stones are sitting there.
If we now treat those gray stones as permanent liberties and
somehow decide who gets the first turn on the rest of the board
- the game could continue, leaving the ccycle as a kind of seki.
That's exactly what cycle removal is about.
Another point in favor for cycle removal is that you don't have
to record past situations to avoid making illegal modifications
(moves). The only risk you take is to stick to a game forever -
but certainly it's never to late to start bookkeeping. Therefore
cycle removal will gently prevent you from being forced into an
endless cycle by your opponent without committing you to perform
bookkeeping in advance:
If you start bookkeeping "too late", you only lose the chance of
getting out of the cycle with sente, but since your opponent has
started it, this shouldn't be a problem.
I don't want to give the impression that I'm satisfied with cycle
removal nor that it's perfect. For instance, Black will lose his 4
stones in the example above also under improved cycle removal, but
he won't if you let the white stone at the right edge neighboring
the black corner jump into the 2-point eye. Is that logical? It's
nothing but a good try. I don't think that I'll ever change the
definition of control, but it's hard to resist fiddling around with
cycle treatment.
CONTROL
First a technical note. The predicate "control" applies to ONE
location. The predicate "lock" applies to a set of them. Of course
we can say that "player P controls location L1 and L2", but this
doesn't necessarily mean that P can lock them both together!
It could be that one of P's lockable sets includes both locations,
but it could as well be that not one does. The only thing for sure
is that L1 as well as L2 can be found in one of P's lockable sets.
If I hadn't made this distinction, had overloaded "control", the
statement above would be ambiguous.
What's a "2-eye formation"?
I expect you to know inside out what it means to have two eyes,
but let's repeat LJRG's formal definition:
A player has made a 2-eye formation on a set of locations if
(take your breath) beside the technical properties that
- the set isn't empty,
- contains no "lonely" (i.e. neighborless) locations (since LJRG
doesn't exclude 1x1 (sub)boards),
- and is bordered by him (to prevent chains to be torn apart and,
together with the other properties, to make sure that at least
one of his stones is in the set),
- all stones in it are of his color,
- each contacts at least two empty locations (eyes) in it,
- and no empty location is neighbored by another (minimal eyes).
So, roughly spoken and compared to the normal sense of having two
eyes, you additionally have to shrink all eyes to their minimal size
(of one location) to fulfill the definition. Why? The idea is to
throw out all opposing stones as well as to hinder any new ones to
enter again - even for the shortest time. To "lock" some locations
in this way is part of the process to prove being in control of
one of them.
In case disputes are broken by a referee, this idea serves him to
decide who controls what - nobody will actually need to build a
2-eye formation. But in case disputes are played out and your
opponent disagrees to your claim, you really have to build one.
Note that it isn't necessary to end with exactly two eyes - a
2-eye formation can have more than two eyes. The name refers to
the fact that each stone in the formation contacts at least two
eyes. Of course, every 2-eye formation can be converted to one
with exactly two eyes, but restricting the definition in this
way wouldn't make it a bit simpler and would lengthen proofs.
To shorten proofs further, couldn't we at least use D.B. Benson's
definition [P-DB]? It allows for larger eyes. Roughly spoken and
not using original terms, a stone completely contacts an eye (an
area bordered by the stone's color) if it contacts all liberties
in that eye, and a stone is statically safe if there are some eyes
and this stone as well as every other stone of same color that
contacts any of them at least contacts two of them completely.
Benson proves that statically save stones can't be captured, even
if the defender keeps passing, and that stones of the second sort
are of the first. The proof depends on ruling out suicide.
Not only that eyes don't have to be minimal with this definition,
this even allows opposing stones sitting in them. For instance:
Each black stone in the left-side diagram completely contacts both
eyes. Since all black stones contacting these eyes do so, all are
statically save. Black could keep passing without having to fear
that his stones could be captured. After removing the white stone
this isn't the case any more. The single black stone now fails to
contact the cleared location. If Black kept passing, White could
capture all black stones - despite them being alive in the normal
sense (dynamically safe, if you like).
But Benson's definition is of no use for LJRG because of its focus
on stone safety instead of on area control. Take this (6x1) example:
The black stone is statically safe (under no-suicide), but neither
color controls anything. If Black claims to control the whole board,
for instance, White waits till he captures and plays in the center
of the cleared area: seki (again).
At last let me make some simple proofs about 2-eye formations:
1. Every eye in a 2-eye formation has an occupied neighbor in it:
It at least has one neighboring location since it may not be lonely.
If this neighbor were empty and in the set, the eye wouldn't be
minimal. If this neighbor were empty and not in the set, the set
wouldn't be bordered. Therefore this neighbor is occupied. If it
weren't in the set, the set again wouldn't be bordered. Therefore
it must be in the set. Finished.
2. Every 2-eye formation includes at least one stone:
Since the set isn't empty, there's at least one location in it.
If it's occupied, we're finished. If not, it's an eye, which has
on occupied neighbor in the set (1). Finished.
3. Every 2-eye formation at least includes three locations:
The stone in it (2) has to contact at least two empty locations
in it. Finished.
4. The smallest 2-eye formation consists of three locations:
There is one (3x1, center filled), but none smaller (3). Finished.
5. It's impossible to add an opposing stone to a 2-eye formation:
No eye in it has an empty neighbor. So filling the eye has to
capture the neighboring stone in it (1). But that stone contacts
at least another eye. Finished.
6. The union of two 2-eye formations is also one.
How about proving this one by yourself?
Who controls what in this situation?
1 0 B 2
You think Black controls the right side and White the left? Well,
that's certainly true in the common sense, but not in the precise
sense control was defined by LJRG.
For example, if Black claims he could lock the right side including
the bordering black stones, White would simply refute this claim by
setting up the worst case for Black:
0 0 W 0
and proceed as follows:
After 3 it's impossible for Black to build a 2-eye formation that
covers EVERY location in the set he claimed because 1 and 3 are now
connected to a permanent stone of their color and thus will never
fail to have liberties.
Therefore we'll shortcut the proof at this point. Strictly followed
it would continue by taking all possible move sequences into account
that don't go beyond a final or repeated situation.
Black can't reduce his claim because the only other sets bordered
by him are
- the whole board
- the complement of the set just tried above
extended by the same bordering black stones
In both cases White will easily build a 2-eye formation himself
inside Black's claimed set and refute those claims too.
A similar argument will refute every claim White could make.
It's hopeless for White to claim the whole board, and following
tries aren't better:
0 0 B 0
Not much to be said about this one.
Now the same as above, but swapping inside with outside,
that's, the whole board except one location:
0 0 B 0
Besides that White won't be able to hinder Black from building
a 2-eye formation at the right side inside his claim, Black can
simply capture the 3 white stones and extend his permanent stone
into White's claim.
It's boring to go through all of White's possible claims. All will
fail. At least I'll show you how to find them systematically.
First remove all black stones:
Then identify all separate empty areas. In this case we find three.
Let the groups of stones bordering each also belong to each. For
instance, the set B would be
Now every union of some of these sets in the original situation
that
- neither is empty
- nor falls apart
- nor contains permanent marks
- nor contains bordering stones without an inner liberty
is a claim that makes (some) sense.
The empty claim won't lead to points, and the ones having borders
without an inner liberty will fail trivially because setting up the
permanent stones will already capture those border parts, allowing
the refuting player to extend one of his permanent stones into the
now cleared area immediately.
Most claims with bordering stones having only a single inner liberty
will also fail, but of course you know the exception: snapback.
But don't the claims that fall apart make sense? No, because if you
can prove them, you certainly can prove their parts separately. But
if you can't prove them (due to ko threats), it's still possible
that proving their parts separately will work.
And what about the claims that include permanent marks? Permanent
marks during the game only come when cycles go. Every permanent mark
always has at least a second as a neighbor because of the nature of
cycles. Since both permanently marked locations are empty, either
bordering fails or a 2-eye formation is impossible.
I'm sure you know exactly what you think you can claim at the
end of your games. Only computer programs will have to go through
above's trouble, so let's forget about the rest and just take a
look at White's natural claim:
0 0 B 0
The defect in White's border now lets Black refute White's claim
easily: Black captures 2 stones and extends his permanent stones
into White's claim.
What did we learn? That control has to be independent from the
outer context and the turn. Even in the toughest circumstances the
claiming player has to be able to fill up his claim with a 2-eye
formation. Neither Black nor White were able to do so above because
their borders each had a (trivial) defect.
Suppose Black had fixed his defect before game end:
1 0 W 2
Now Black could claim to be able to lock the right side without
fearing a refutation because his worst case would now be
0 0 W 0
and you certainly agree with me that White can't prevent Black
from building a 2-eye formation on Black's claimed set this time.
(White can fix his defect equally simple, of course: just has to
capture the single black stone before end.)
Let's look at another example:
0 0 B 2
Black now claims that his stones on the left side are not dead
because he could atari 2 white stones as a ko threat. How about
that?
Indeed, this possibility refutes Whites claim of being able to
lock the whole board exclusive the upper right corner. After we
fill up the rest with permanent black stones to serve the rules,
Black - having the first turn - will proceed as follows:
4 recaptured
5 threatens the 2 white stones and thereby White's whole claim,
but if White answers it, Black will win the ko and live in the
corner - refuting White's claim again.
Does this mean that those black stones are not dead? No. Sly White
can prove his control step by step. In the first step he excludes
the 2 white stones and their liberties from his claim to get rid of
the ko threat. Notice that this claim is still bordered by White and
that Black can't win the ko any more:
After 3, White recaptures in the ko and Black finds no ko threat.
Does this mean that White can't count the 2 empty locations at the
right? Again no. Sly White delivers his second punch and claims to
be able to lock the "diagonal":
0 0 B 0
It's obvious that White will complete his 2-eye formation here,
even taking second turn.
So we find that each labeled locations below
is in a set White can lock - the B's even in two. Therefore White
controls each of these locations, and the black stones sitting in
the A area are dead.
White has shown by his 2-step proof that the ko threat and the ko
are independent from each other, that they don't belong to the same
local fight. (Ever searched for a definition? Now you've got one.)
Just to serve perfection, Black could have lost by 1 point less
if he had started the ko before letting the game end:
2 1 W 1 (4 recaptured at A, 5 passed)
Now the ko has become direct, without Black having invested more
stones than White. Since Black's pass with 5 is a (trivial) ko
threat and White has no reasonable ko threats, White must give
up 1 point by connecting the ko. (Even if passes didn't serve as
trivial ko threats, that's, if the second pass in succession
always ended the game, White would have to connect since direct
kos spoil control.)
This example showed that two lockable sets of the same player can
indeed overlap. But I'm confident that this never will happen if
they belong to opposite players. I don't have a proof, but consider
this:
If a location is controlled by both players, both at least have
one lockable set that includes it. The first player can lock his
set even under the worst circumstances: its outside filled with
permanent opposing stones and him taking second turn. If now the
second player makes his lock, the first player's set's outside as
well as itself partially stays unchanged and partially becomes
filled with his own permanent stones. On top of that, the first
player gets the turn. Everything just turned in his favor. Why
shouldn't he be able to lock his set again, including the location
in question and spoiling the lock of the second player? Because
of symmetry, the second player can spoil the first player's lock
likewise: contradiction. (Again: this is NOT a proof!)
But please note that LJRG doesn't depend in any way on the property
that a single location at most can be controlled by one player (or
that a stone can't both be alive and dead at the same time). If it
happened it wouldn't prevent us from scoring since LJRG scores
without removing dead stones! Either such a pathological location
is empty and both players earn one point, or it's occupied and one
player earns two points and the other just one. As simple as that.
What if we shift the white stone from A to B?
0 0 B 2
Things would change dramatically. With the same argument as above,
White can't lock the whole board exclusive the upper right corner.
But worse, now White neither could shake off the ko threat. If he
reduces his claim by excluding B and all white and empty locations
contacting it
0 0 B 0
White would have lost too many liberties to win the ko and prove
his claim. Since White can't separate the ko from the threat with
the divide-and-conquer strategy as above, they are not independent
from each other.
The only thing White can claim to be able to lock is the diagonal:
0 0 B 0
But this is a cold comfort for White because now he would have
lost by 1 point.
So in the shifted-stone case White should have connected the ko.
(Eliminating the ko threat or capturing the black stone in the
upper left corner would work as well.) Note that there's no need
at all for Black to continue the ko in this case. He rather should
leave White the chance to fail.
If White can't claim the left side now, does this mean that Black
can claim something there? No, Black still can't claim more than
the upper right corner - try it out yourself. The whole left side
(we labeled with A, to be precise) would be controlled by nobody,
would be sort of seki.
BEFORE END
LJRG's definition of control has some consequences on what to do
before the game ends because there's neither a discussion if the
game should be continued nor a chance that it will:
The result of the game is fixed
in the very moment the game ends!
(At least if LJRG's ideal form is used, that's, diputes aren't
played out - but even then the consequences remain the same.)
Any following method to count the game is only a method and is not
part of the rules. We won't care how the game actually is counted
at all. We'll be satisfied to know that its result is precisely
defined - even in unlikely situations too complicated for humans.
Let's follow an example game [P-JDRB]:
resulting after move 17 in the already known situation
1 0 W 0
Even though the authors now tell you that only neutral points
remain to be taken - this is a bit misleading. Location A may be
neutral technically, but it matters who plays it. Not being able
to surround something doesn't mean one can't manage to make points:
Black can destroy a point by playing at A, White can save one.
They then let the game continue beyond A, treating neutral fill
up and defect elimination (connecting both hanes) as part of the
game. But Japanese style of ending is that White would play 18 at
A, and then both players would agree that the game has ended
because nobody can gain anything more:
1 0 B 0
This would be the last diagram in the newspaper. What remains is
counting.
But if both players had passed in the situation above, according
to LJRG nobody would control any location on the board because any
set of locations a player claims he can lock must be independent
from its outer context. We've gone through this in detail in the
last chapter.
So, the conclusion is that under LJRG self-interest will lead both
players to continue with
giving
2 0 B 0
and NOW both players may pass without being punished by LJRG:
Black can lock the right side including the black stones, White
can lock the left side including the white stones, and nobody
controls the lower left corner location. (Proofs left to you.)
Everybody gets what we expect him to get:
B = 11 + 0 + 0 = 11
W = 6 + 0 + 2 = 8
----
Black wins by 3 points
Isn't that great? Both have to fix their defects BEFORE the game
ends. Their opponent is relieved from having to force them to do
so by filling up neutrals at the outside.
This isn't a big deal when considering the number of stones you
have to handle because with the common counting method neutral
locations are filled anyway.
But in official games filling up before the game ends is a nuisance
because those stones would belong to the official game record. LJRG
induces exactly the right number of moves to be done and recorded -
(extra) trailing moves explicitly proving awareness of defects.
Detecting defects may be trivial in most cases and one assumes the
opponent knowing about them - but you never can be sure. So, if no
punishment existed, it would end up in filling all neutrals, no
matter what, just not to give one's opponent a clue in those rare
cases he might not be aware of his defect.
Shifting defect elimination into the game is "only" a side effect.
The real purpose of defining control as LJRG does is to be sensible
about internal ko threats without giving up localization and to
fairly deal with situations like "one slips" (beast 4), where one
player can't be prevented from capturing either of two groups, but
isn't able to capture both.
Following, two famous teire incidents:
Iwamoto's refusal
At the end of the first game of a 10-game match between Go Seigen
(born in China as Wu Ch'ing-Yuan) and Iwamoto Kaoru in June 1948,
Iwamoto (Black) refused to eliminate the ko by capturing at A (or
filling above 1), arguing that he leads in ko threats.
last two moves shown
A Nihon Ki-in bylaw from Shusai's time was dug out and Iwamoto
got his way. White still won by 1 point - but pros were alarmed.
This triggered the first rules written down by the Nihon Ki-in
and published on October 2, 1949. It required all direct kos to
be eliminated before the end - contrary to above's decision.
So far Ing Chang-Ki's story in [GW72]. You get the impression that
Go Seigen wanted to convert his 1-point win into a 2-point win by
having Iwamoto add a stone. But according to [GW45a], Go Seigen
actually agreed with Iwamoto and argued that "White cannot possible
win this ko and has nowhere left to play".
Note that Black has two ko threats in the lower left corner and one
ko threat on the right side (connecting his two single stones), but
White only has one ko threat on the upper side.
According to [GW45a] the "game was declared a 1- or 2-point White
win". Well, that certainly should trigger some work on the rules.
Go's "nowhere left to play" is interesting. It seems to reveal
Go Seigen's view that for him only neutrals can serve as last
resort for (trivial) ko threats - that for him a pass play never
makes up a (trivial) ko threat because the opponent may pass too,
ending the game.
With their 1949 rules the Nihon Ki-in didn't follow him in this.
But instead of allowing passes as (trivial) ko threats, which would
naturally lead to the solution, they added their direct-ko-removal
obligation.
Let's now see how JRG89 or LJRG would handle the case.
Under JRG89 Black would eliminate the ko before the game ends
(possibly AFTER two successive passes) because otherwise the single
black stone at 1 would be called dead. This would make the location
above 1 a dame and infect all of Black's stones and "territory" on
the right and upper side with seki.
Under LJRG Black would also add a stone before end (and BEFORE the
ending passes), but his punishment if not wouldn't be that big -
he would lose control of only four locations: A, 1, the one between
them, and the one above 1.
This would cost Black three points compared with capturing at A
(the one above 1 no more counting one point, and the one to his
left no more counting two points). The reason for losing control is
that Black can't use his stone at 1 as a border of a lockable set -
White would capture it and couldn't be prevented from extending his
permanent stones into Black's claim.
Go Seigen's refusal
This example is from [GW72] and [GW45a]. According to [GW45a] you
find the game's record in Go World 41. It's also in [GMR1069].
At the end of the second game in a 3-game match between Go Seigen
and Takagawa Shukaku in 1959, Takagawa insisted that Go Seigen
(White) must connect at A to eliminate the possibility of a ko.
Go Seigen refused. The dispute was undecided for some MONTHS.
Finally Go Seigen - lacking support - connected and lost by half
a point.
19[+4.5] 12 (244 moves)
First a detail. [GMR1069] wrote "Komi: None", but this can't be
true. I counted the game and came to 123 (=9+65+37+12) points for
Black and 119 (=32+47+21+19) points for White. I double checked it
with area-style counting: 181 for Black, 177 for White, 3 neutrals.
This fits to the figures above (244 moves or 122 stones each, 16
dead black, and 17 dead white stones):
Neutral 3 = 3
Black (122 - 19 - 16) + (123 - 12 - 17) = 181
White (122 - 12 - 17) + (119 - 19 - 16) = 177
------
361
Black leads by 4 points on the board. If Black won by 0.5 points
after White added a stone, the komi must have been 4.5 points.
Now to the ko. The aji in the center is as follows:
If Black could win this ko, he would capture White's center group.
White holds back the A-for-B exchange as a ko threat.
Go Seigen's reading, Takagawa agreed to, was as follows:
9, 12, 15, and 18 took the ko - 14 passed
8 is better than passing because it removes a "threat". Remember
that, as explained in Iwamoto's refusal, for Go Seigen two passes
in a row end the game. Therefore neutrals are valuable ko "threats".
White started the ko and continued it as long as he found internal
ko threats (10 and 16), but after 19 he had none and had to remove
the ko with 20. This reduced his territory by 1 point, but Go Seigen
argued that he would get 19 as compensation because he wouldn't need
to connect this second ko:
24 recaptured ko
After 24 Black has no ko threat - not even of the smallest kind:
neutrals. Therefore Black would pass, letting White pass too and
end the game without connecting the second ko.
Go Seigen [GW45a]:
I think it best not to create intricate provisions to the game
of go. If all the liberties of a group are filled the group is
taken off the board, a ko may not be retaken until a move is
first played elsewhere, the side with the most territory wins;
fundamental principles such as these are sufficient regulation.
One desires simplicity in the rules. This will also aid in
increasing the go population. Intricate rules are only
manifestations of elaborate technique.
The Chinese rules play everything out to its conclusion; there
is no perception of irrationality. The Japanese rules produce
situations such as a seki on the same board as a 'bent four in
the corner' ... or the provision that White must add a stone to
his center area in [the current game]. These problems do not
stand to reason.
If a one-move ko is thought to demand a preventative move,
then the shape must be incomplete [in the sense that the game
has not yet ended]. Completing the shape, in case of a yose ko
also, is the necessity here. Stones are alive not only because
the can not be captured ... I hope that irrationality in the
rules is corrected as soon as possible.
This sounds well, but is a bit cloudy. I'm curious how Go Seigen
would argue that his stone to the right of 19 is alive. If, for
instance, he would define stones that can't be captured if they
possessed the first turn to be alive, then 19 would be alive too,
spoiling his territory.
But maybe he would argue that the history still is alive and that
trailing passes are to be ignored in the post-end analysis, which
would prohibit capturing 24 immediately and give 19 no chance to
avoid capture. Another advantage of such a view would be that a
single double-ko seki couldn't be used to cycle. The drawback, of
course, is that the outcome of a game, even under Japanese-style
rules, could depend on the number of neutrals - something LJRG
manages to avoid.
Under either JRG89 or LJRG White can avoid the connection at A,
because if Black starts above's sequence after the end, White
captures in the ko first and will win it.
Under JRG89 this is because Black would have to pass for that ko.
Under LJRG because Black doesn't find enough internal ko threats
in White's claim:
9 and 12 took the ko, 14 connected it
Does this now mean that under JRG89 or LJRG White omits the stone
at A and wins? Only if Black lets the game end too early. But if
he continues (Go Seigen's sequence) to a certain point - under
JRG89 till 6, under LJRG till 12 - White will again have to add a
stone and lose by half a point.
In both cases Black managed to force White to take the ko before end,
allowing Black to take the ko back after the end. Under JRG89 Black
doesn't has to fear internal ko threats because only a pass can open
the ko again. Under LJRG Black has to take care that White used up
all his internal ko threats before the end - that's why it takes a
bit longer.
White's threat with 16 is no internal ko threat under LJRG because
it will be covered under the permanent stones. So if White switches
the order of his threats and plays 16 before 10, Black has to
continue until White finally has used up 10.
So if the game proceeds until this certain point and White lets
the game end without connecting the ko, White will lose by much
more than half a point. Under JRG89 White's stone that took the
ko would be dead and the empty location above it would be dame,
infecting White's whole claim shown above with seki. Under LJRG
the argument isn't that weird. White simply won't be able to lock
above's claim because Black will refute it: Black, playing first
in the proof, takes the ko and, since White finds no internal
threat, gives atari and captures.
What do you think about Black playing at A?
0 0 B 0
(It threatens to throw-in at C and to capture four stones,
of course.)
According to Iwamoto Kaoru [GR-Sp74], Black's A lacks "kihin",
which "means etiquette shown in a good game fought by the rules
of knighthood". "In days gone by [...], if a player lacked this
quality of 'kihin', he would never have been allowed the degree
of shodan." (I suppose "kihin" to be the same as "ki-in" and
"kiin".) Likewise, White starting with B lacks kihin.
There's no doubt of missing kihin if A is accompanied by a
statement like "there seems to be no other place for a move".
But why is A by itself nasty?
Well, having the turn has no meaning at this point, and present
custom would indeed be to leave it as it is, but under LJRG Black
at A incidentally still belongs to the game because it secures
control, as does B. So under LJRG, Black's A as well as White's B
have good reasons beyond tactical tricks - neither is nasty. Maybe
one could call answering A with C nasty: to keep sente is pointless
in this situation and, under LJRG, White still needs to reinforce
at B.
To catch the spirit, let's transform Iwamoto's example (I shrunk,
by the way) to fit LJRG:
0 0 B 0
A move at A still threatens the same, but now it's not even under
LJRG necessary any more. If you can expect your opponent to answer
correctly, then to play it only prolongs the game and is pointless.
We shouldn't condemn Black if he dares to play A, especially among
double-digit kyus, but among, say, amateur dans I would agree that
Black lacks kihin if he can't resist A. On the other side, we as
well as the referee must accept if Black ignores kihin and
nevertheless plays A - he's perfectly obeying the rules.
Rules are one thing, social conduct is a different. Referees have
to judge rule obedience, not social behavior (provided it violates
no rules). So, if Black plays A, he may do so, but he shouldn't be
surprised to end up in the (social) pillory afterwards.
Likewise we must accept if our opponent starts filling neutrals
before the end. Viewed strictly, unfortunately, he can even give
a sound reason to stick to this practice:
He keeps the option to exploit defects BEFORE game end, capturing
an entire group instead to just let its "territory" be spoiled.
Does this now mean that we end up filling neutrals, contrary to
what LJRG was praised for? Well, since in most cases the capture
will only be partial, spoiled territory will be the better option.
Therefore, whoever refrains from neutral fill-up on principle will
only pay a tiny price for keeping his membership in the "I'm so
clever to recognize the end" club.
The focus here was on not to drag on a game when there is not even
a technical reason to do so. If we wanted to force this by rules,
we would have to refer to perfect play. In fact, LJRG already does
refer to perfect play in its definition of control. But to now also
define to stop as soon as possible would go a bit too far in my eyes.
I'm satisfied that LJRG excludes any technical reason to fill dame.
Let social pressure take care of the rest, but don't let it get too
strong: If everything would be forced by rules (of whatever nature),
it would become impossible to demonstrated kihin - you only can show
kihin VOLUNTARILY. For instance, when your opponent captures a ko
immediately, it would show kihin to let him redo his move - but of
course he has no right to expect you to do so.
Here's an example of a professional missing his chance to show
kihin (compiled from [DGZ0102] and [RGG220202a]):
The 5th game of the 26th Kisei, played on February 20 and 21,
2002, between O Rissei [9d, born in Taiwan as Wang Licheng], and
Ryu Shikun (7d, Black) was almost finished. Doing move 293, Ryu
asked, "It's over, isn't it?", but got no reply from O. They
continued filling neutrals.
As O filled a neutral with 298, 6 stones of Ryu went into atari.
Only after Ryu filled an unrelated neutral, he noticed this and
tried to redo his move, but O declared, "I didn't say anything",
meaning that he had not yet agreed that the game was over. Ryu
didn't understand. O repeated his statement and asked the game
recorder to confirm, but the recorder wasn't able to.
O called the referee, Ishida Yoshio, and explained the situation.
Either before or after Ishida's arrival, O complained that Ryu
already had redone a move ("matta" - 285 according to Michael
Redmond) without a protest by him, but that he wouldn't permit
this for a second time.
Ishida Yoshio and representatives of the Nihon Ki-in and the
sponsoring newsletter Yomiuri Shinbun discussed the issue and
looked at the video tape for about an hour. Since there was no
evidence on the tape of both players agreeing to an end [a stop,
technically] - in fact, not even one of Ryu offering end - O was
allowed to continue.
O clearly felt bad about the situation, not just Ryu, and there
should be sympathy for O - said Richard Hunter. After O asked
Ishida, reassuring that it was his turn, he captured the stones.
Ishida didn't refer to the alleged matta when he resumed the game.
After O's capture Ryu drew some deep breaths and stopped the game
for the second time by asking Ishida about it. Ishida admitted
that Ryu's move in question (285) was close to matta, but finally
concluded that no matta had occurred - said Hisashi Fukui.
The camera angle didn't reveal if Ryu released 285 twice or not.
O insisted that, nevertheless, 299 had been released (on the wrong
spot). So finally Ryu gave up.
Two weeks later O Rissei also won the 6th game and the 26th Kisei
[DGZ0202a]. Sorry, Richard, if I hesitate to congratulate.
Let's take a closer look at the situation after 283:
13 21 W 0 (1-3 = 281-283)
The only things left are the 2 kos (at both sides beneath center).
Since it's White's turn and he can capture in both, White will win
one for sure - and that he can't win both should be understood.
The normal sequence would therefore be that White takes one, Black
connects the other, White connects the first, and both then agree
to game end (capturing 283 and fellow is useless since White had
to invest 2 stones), giving Black a win by 9 - 5.5 = 3.5 points
and a 3-2 lead in this best-of-7 match.
But White's 284 filled the false eye beneath center instead:
20 24 B 0 (4-20 = 284-300)
(According to Richard Hunter, 297 and 299 were played in reverse
order - playing the more "important" dame first.)
285 is the alleged matta. Strange - was this Ryu's second thought?
Why not answer 284 at 286? 285 lets White gain a point in sente with
286 and, after coming back with 288, still having the chance to win
the remaining ko - even if this now depends on ko threats.
But anyway, White didn't try to win this ko. Strange again - what
then was his purpose to continue?
If 285 really was matta, a redone move, then Ryu already must have
believed that the game was over after 283 (or 281). How can this be?
Did Ryu already offer end before 293? Or was he using the silent
gentleman agreement that a game is over when having the turn got
meaningless? If White had more ko threats, the game would indeed
be over in this sense after 283 (or 281) because White wins one ko
no matter who starts - but it seems to me that Black leads in ko
threats. Black may not care if he wins by 4.5 or 3.5, but in above's
sense the game wouldn't yet be over.
Anyway, after Black connected the second ko with 293, it's
kyu-obvious that turn possession became meaningless. O Rissei may
have troubles with his ears (since 1998 they say), but he isn't
blind. One therefore can understand that Ryu, after expressing the
obvious (again?), on which O didn't oppose (to put it in Ryu's
favor), was convinced that (sloppy) preparations for counting were
on their way. Isn't this the beauty of omission, Japan is so proud
of?
I would be very curious if O always fills dame before he agrees
to stop, or if he only did so in this game. In the latter case
I'm afraid that O, being aware of Ryu's false belief since 285,
exploited the situation - sorry to say.
Another thing that annoys me is that O was tolerant as long it
didn't matter - provided talking during the game or undoing moves
doesn't lose - but went strict as soon it did matter.
Rules shouldn't depend on kihin, but if it's custom to ignore their
technical details - in this case not to express one's opinion that
the game is over by PASSING, as JRG89's Article 9 calls for - then
nobody should suddenly insist on technical details either.
That Ryu asked about the end instead to pass indicates that this is
common (bad) practice among pros. Why else would Ryu have done so
in an important title match? Further questions: Is it also common
practice to say nothing if you disagree? Did Ishida consider local
custom in his decision?
Don't get me wrong - I prefer a more formal conduct during "game".
Generally it should be possible to play the game without having to
utter a single word. You may not like pushing marks around, fine -
even though nothing could be more transparent for spectators - but
actions should be formalized in some way or the other.
If players operate the clock themselves, switching it without
playing a stone would be a clear way to pass. But since pros in
Japan don't operate the clock themselves, how about letting them
grab a stone even in case they're about to pass, aim at the recorder,
time keeper, referee, or whatever official is hanging around and
seems to be a good target - and "deliver" him the stone (and maybe
kensho).
Ok, let's get serious again. The problem that caused this
embarrassing incident isn't one of when or when not to fill dame.
I would neither want rules that prohibit me to fill them nor rules
that force me. The problem to solve is how to clearly end the game
and, additionally, how to make this state of the game transparent.
Maybe this example would fit better into the chapter about ending.
The "ko mark" introduced there (no joke at all), combining the
temporary mark with the pass count, would solve these problems
instantly. On the other hand, the topic we're talking about is
exactly what O had the chance to demonstrate, but missed: kihin.
Japanese style is to pass as soon as it becomes meaningless who
possesses the turn. This sometimes even leads to incomplete
borders:
0 0 W 1
Black just has passed because he can't reduce White's territory
any more. Japanese style would now be for White to pass too since
he neither can increase his territory. You don't believe it? See
the 4th game of 1973's Honinbo (final) for this example [GR-Au73]
(I made up the seki at the left just to shrink it). Under LJRG
White needs to play A to count 6 points.
More (shrunken) examples:
Inspired by the 5th game of 1975's Meijin [GR-Wi75]:
0 0 W 0
White would pass under Japanese style because Black can't make any
use of sente. But under LJRG, White would have to add 2 stones at
A before game end. The first stone will close White's border. The
second will make his claim independent from the context.
The 7th game of 1975's Honinbo [GR-Au75] molded this one:
0 0 B 0
Black would pass under Japanese style. Under LJRG he should connect
at A to close his border and gain control before game end. (White
will play B, of course.) Playing above A wouldn't establish control.
This type happened in the 7th game of 1975's Meijin [GR-Sp76]:
0 0 W 1
Under LJRG White should continue at A instead to pass (because
he has to imagine permanent black stones crowding the outside).
Game four of 1987's Meijin ended with this sort of gap in the
center [DGZ0687b]:
0 0 B 0
Under LJRG Black should play A instead of omitting it. (He
gains nothing by playing to the right of A, of course, because
of the double-atari threat that pops up when dame is filled.)
This kind of gap was left in the second game of the first
Bohae-Cup ("World Women's Go Championship") [DGZ0395]:
0 0 B 0
Under LJRG Black has to capture the two white stones before
the end if he wants to count anything - not matter if White
approaches or not.
The first game of the 50th Honinbo featured this one [DGZ0595]:
0 0 B 0
The only move missing is A. Black is justified and urged by LJRG
to play it before game end. (Playing left of A, of course, gains
nothing because of the seki threat produced by dame fill-up.)
So, since LJRG provides no "confirmation" phase in which missing
stones could be added, the habit of uncomplete borders would have
to be dropped (and no one should miss them anyway):
If you want to count points after game
end, close your border BEFORE game end!
We've seen that you'd better eliminate defects before game end
if those defects spoil your control, for instance,
0 0 W 1
White shouldn't pass here. He wouldn't be able to claim any control.
He should connect at A instead to anticipate the worst case: the
rest filled with permanent black stones.
But, as it turns out, not all "defects" affect your countable
control. In all of the following situations Black could indeed
pass without loosing any point:
0 0 B 0
White controls the 10 locations on the upper side. Nobody
controls the rest - even if Black connected the bamboo.
0 0 B 0
Black may leave his single stone unconnected. He controls the 9
locations in the lower left corner. The location occupied by the
the single black stone and its 2 liberties are controlled by
nobody. The rest is controlled by White.
0 0 B 0
White shouldn't pass because he controls nothing in the strict
sense. He has to capture at least one black stone to gain control
(of what should be obvious. Black will then, of course, save the
other).
Black may leave it miai ("one way or the other"). He already
controls the 4 center locations, the 2 locations below them,
and the 4 locations in the lower left corner.
0 0 B 0
Black may omit to fill his false eye. Black controls the 4 empty
locations he has surrounded plus the locations of his surrounding
group. White controls nothing in the strict sense because no matter
how small he makes his claim always a white border stone is ataried,
enabling Black the refutation. White should fill his false eye at A.
Viewed superficially this last example may seem illogical: one
side has to connect its false eye - the other not. The difference,
of course, is that White's territory isn't yet independent from
what's going on beyond its fence - Black's is.
Eliminating Black's harmless defects in any of the above cases
wouldn't increase Black's countable control nor would it reduce
White's. Not claiming something or - to be precise - not being
able to lock something doesn't mean that your opponent can lock
it. And even if - he may not be able to turn it into points.
Players will only care to eliminate defects that harm their
territory, which is always the case if that territory depends
on outside liberties.
Test yourself. Expect LJRG in effect in all examples.
Black just has passed. You're White. What would you do
in the following - not totally symmetric! - situation:
0 0 W 1
You connected on san-san (3-3) in the upper right corner? Right -
after 2 passes the result is a jigo. You passed? I'm sorry having
confused you - you lost by 2 points. You should have connected as
mentioned because otherwise White doesn't control anything on the
diagonal. No matter how small you make your claim there, always
one of your border stones will be ataried by the permanent black
stones crowding the rest of the board.
You think neither does Black control anything on the diagonal?
Wrong. Black's 6 stones including their 2 eyes in the lower left
corner are independent from the context. Therefore Black controls
them. Only the rest of the diagonal isn't controlled by Black. He
could, of course, extend his control by filling some false eyes,
but this wouldn't entitle him to count more points.
After this made-up example a realistic one [RGG190202].
Black just has played 1. Figure out where both sides should add
further stones before they pass:
[8 0] W 0
(I assume that White was leading with 8 prisoners because there are
145 white but only 138 black stones on the board. I don't know what
komi was used. Let's pretend that it was a no-komi game.)
Only another four stones are needed to complete the game under LJRG:
[8 5] W 2 (6 and 7 passed)
That's it: 2 and 3 each reinforce a border, 4 may look silly but
is technically necessary because it makes the 9-point eye as well
as the 2-point eye independent from the context, and 5 prevents seki
if White enters here after dame are filled. Each side counts 41
points: jigo. Needless to say that neither Black's false eye on the
lower edge nor on the upper right edge is controlled or counted.
But actually the (IGS) game dragged on much longer. After 1 White
noticed that Black had to reinforce at 5 to prevent seki. Not to
hint Black (otherwise he could have played 5 himself to make it
obvious), White played neutrals here and there. As soon as he could
afford it, Black kept on passing. Eventually Black asked White very
polite to (quote) "please pass as it is game over". White answered,
"I think you need to play one more move", and continued. Only after
the last dame was played, Black made the necessary defensive move,
leaving White with the impression that Black hadn't noticed his
problem till the discussion about the end had alerted him.
Under LJRG White would simply pass when Black passes with 5. If
Black then claims anything in his upper right group, White could
disagree and the dispute would either be decided by a referee or
played out (see chapter "After End" below). In either case, and
in a perfect world, it would be White who wins.
Here's another test (not easy). You're Black.
Would a pass lead to your 1-point win?
2 0 B 0
No. You should add a stone inside your territory and be satisfied
with jigo. If you pass instead, White will pass too, the game will
end, and White will refute your claim:
(2 at 8 won't do better because of again 3, and
2 at 5 will also fail: 3, right of 6, 8, 7, 4.)
This actually is a slightly adjusted tsume-go problem from
[DGZ0198b]. Under JRG89 Black risks nothing by passing. He waits
if White sees the aji (weakness) and only adds a stone in that
case. Under LJRG he could try the same, but risks losing the game.
Some people think that area scoring relieves Black from deciding
if aji exists or not. Black could simply add a stone without
losing a point, they argue. But this is only true if nothing else
but an even number of neutrals remain - not the typical case. If
not, White will at least get the last neutral.
You're certainly suspicious by now. You're Black. Would you pass?
0 0 B 0
Well, since you need the outside liberty to live unconditionally
you shouldn't pass under LJRG. Black hasn't yet secured his control.
Kudo Norio [GW45b]:
By the Japanese custom the game has already ended before the
liberty [...] is filled. [...] If the shape [above] appeared,
the stronger player would instruct his opponent to add a move,
in the spirit of counselling a family member. But it would be
funny for this kind of advice to be given among professionals.
Well, for me this kind of advice is funny in ALL cases, and under
LJRG you'll never need to give it. Instead, Black won't be able to
count 8 points if he omits to add a stone BEFORE the end. His lock
will be refuted either by seki or ko:
The sequence at the right is tricky (at least for me). If White
goes astray by capturing 2 with 3 or 5, Black would play 2-2 and
succeed in building 2 eyes.
Here's another slightly adjusted tsume-go problem [DGZ0202b].
Will Black win by 1 point if he passes, or should he rather
invest another stone and be satisfied with jigo?
0 0 B 0
If Black lets the game end as is, White could point to this
sequence:
and tell Black that it was a good try to win, but since he actually
controls nothing he has thrown away jigo and has lost.
Note that White hadn't to hint Black by filling the neutrals nor
did he felt any need to convince Black to add a stone.
How should Black continue here? (13 points each, 3 neutrals.)
0 0 B 0
Of course, Black has to connect his two stones in the center in
either direction before game end to make his border independent
from the outside, but what about the ko?
If Black removes it, he certainly will lose by one point, so this
is out of question. Nothing else left to do, Black connects to the
upper side. Do you agree? Decide now.
If you play under stone scoring, it's always a good idea to connect
groups - if they need it or not. But under LJRG this can be a big
mistake. Why? The situation above is an (constructed) example. If
Black makes one big group, White takes the opportunity and fills
the "neutral" below. Now Black is lost. He forgot that proofs of
control can't rest upon (non-trivial) ko threats - only refutations
can (but only on internal ones).
The effect of White's last stone was that all claims of Black that
include the ko in the lower left corner now also have to include at
least one of the 2-point eyes on the upper side (else border stones
will be in atari when the proof starts - not very promising). This
creates two internal ko threats for White - enough for him to win
the indirect ko.
(Note that White can't be satisfied by Black making one group. If
White also lets Black connect to the lower side, the ko threats
wouldn't be internal to the ko any more because Black could omit
both eyes on the upper side in his claims covering the ko - it not
only depends on being in one group or not!)
Black could now connect below his two center stones to get rid of
the internal ko threats, but would lose by this point. So, he risks
nothing by trying to omit this stone - a rare example of riskless
avoidance of defect elimination under LJRG.
But after game end White can refute Black's (pretended) belief in
controlling the corner and jigo easily, for instance:
4 recaptured
Considering all this the solution for Black is to connect his two
stones in the center to the LOWER side. Now a claim starting with
his territory in the lower left corner only has to be extended as
far as to his territory on the lower side (including the borders,
of course). This time White will find no threat after Black's
recapture, giving Black five points in the lower left corner plus
four on the lower side. A second proof yields four points on the
upper side: jigo. (Black's stones in the center take part in both
proofs - another example of overlapping lockable sets.)
Please check for yourself that White can't win by starting the ko
during the game (Black has two ko threats on the right side).
So, with LJRG we get the almost ultimate solution:
1. Defects affecting countable control will be fixed during game
2. There is no need to fill up neutrals before the game ends
This is fully in the spirit of Japanese-style rules.
ENDING
Why on earth don't we simply end when two passes in a row occurred?
Well, look at following situation:
0 0 B 0
If Black connects, White will do so too and nobody has won:
nothing can be claimed on the board and nothing has been captured.
Now, what if Black captures instead? White can't recapture due
to the ko rule, and filling one of his two liberties would atari
himself - so he must pass. Black would now love to pass too and
end the game:
0 1 W x
This would be a win for Black if x is 2: nothing can be claimed on
the board, but now Black leads in the captive count: not very fair.
That's the reason for having this seemingly odd pass count of -1
after a ko capture. The effect is that 3 passes in a row are needed
after a ko capture instead of just 2 - leaving the chance for ko
recapture.
Under LJRG the game would continue after Black's pass: White would
recapture, Black would be forced to connect his stones, and White
would also connect (since giving atari would lead to disaster).
Then both would pass and the game would end in jigo:
1 1 B 2
Another example:
0 0 B 2
The game has ended. White claims that he can lock to lower side.
The proof would go like this:
2 passed
After 3, White can recapture the ko and Black would have nothing
better than to pass. White will capture again and proceed building
his 2-eye formation.
But the whole proof depends on the fact that after White's pass a
pass of Black won't end the game since the 2 passes are preceded
by a ko capture. White's pass wasn't intended to end progress but
to remove the temporary mark preventing ko recapture. So, it's not
a pass in the sense of doing nothing. But to avoid confusion, we'll
nevertheless continue to call it a "pass" and count it.
So again, the pass count must be -1 after the ko capture. LJRG
keeps things before and after the end equal. There are no special
rules that only apply after end.
An even smaller example [RGG281102]:
0 0 W 0
Originally designed for area scoring, it also works for territory
scoring (here a la LJRG). The game result depends on how game end
is defined:
area scoring territory scoring
--------------------------------------
two passes end | Black wins by 4 jigo
three passes end | Black wins by 10 Black wins by 7
The results in the first row seem unfair. The problem is that the
plain sequence
only makes sense for Black if he now can use a pass as a (trivial)
ko threat. (Note that 5 makes no sense under territory scoring
combined with "three passes end".)
But if two passes end, this isn't possible. He better had answered
1 at 4. After White answers at 2, we end in seki.
Answering 4, White can again choose 3. Black will now have to pass
to keep 2 as ko threat in reserve - a silly consequence of "two
passes end". This enables White to end the game with a pass:
0 0 B 2
Area scoring counts the same as in case of "normal seki": 6 - 2.
But why is it jigo under territory scoring? Doesn't Black control
the whole board? Well, not if two passes also end the proof of
control. In this case the trick for White is to start the proof
with a pass! As above it's fruitless for Black to connect in the
center, since after White takes the ko and Black passes, White
ends the proof with a pass - without Black having formed his two
eyes yet.
By now you should agree that "two passes end" (game or proof) just
is too simple. "Three passes end" is simpler than "two passes end,
provided the first removed no temporary marks", but the latter is
more accurate and fits perfectly to a "ko mark" (to come).
One argument against the need of 3 passes after a ko capture to
end the game is that a single double-ko seki could prevent the
game to end.
I myself was blocked for a long time by this argument, but I
changed my mind. Even if I hadn't invented cycle removal I would
now stick to this scheme: it's absolutely logical. You don't need
to play a stone to give your opponent a chance to fix a ko. He
gets it as well if you do "nothing". So, after his answer and
regardless if it was a pass or not, you are in a NEW situation
and should be allowed to recapture. A pass is a move - just like
zero is an integer.
Should I give up this logical scheme just to bar a few cycles from
the theater while a big, noisy crowd of them already took seat and
is waiting to disturb play? Add just one double-ko seki to the first
- all efforts to stop cycling by "two paasses end" were in vain.
Needless to say that double-ko sekis are no practical problem
If you know about a game where one occurred, please inform me.
We shouldn't take special measures to cope with them and, as a
side effect, corrupt something else. Instead we should let them
be what the are - potential cycles - and handle them like the
rest of the gang.
As already mentioned, the pass count of -1 has another advantage
in case we don't keep temporary marks in our minds: you can use
a single mark either to mark a ko or the current pass count.
(How about the cuplike base of an acorn? ;-)
If it's on the board (marking a ko), the pass count is -1. If
it's off the board, the pass count must be either 0, 1, or 2.
This suggests 3 fields labeled 0, 1, and 2 beside the board.
Since the whole board would stand for -1, field 0 would be
positioned nearest to the board and field 2 farthest away from
it:
If you now capture a ko, you would mark it. And after a pass you
would push the mark farther away from the board - getting nearer
to the end in a sense. In all other cases you would put the mark
back to field 0.
Another mark on either field B or W would indicate whose turn it is.
Of course, if a clock is used, it would replace this mark and cover
those fields. The minimal requirement for the clock is to always
give a clear visible sign to everyone about who has the turn - some
tiny dots pulsing on a digital display won't do, and neither should
it be necessary to take a certain angle to observe this sign.
The empty fields at the upper and lower side would be used to line
up captured stones - letting everyone see their number easily.
Ok, I admit this all being a bit eccentric - but isn't it also
pretty neat and logical? The idea should be clear: let everybody,
especially both players, visibly perceive the whole situation
without having them to refer back to the game's history (which,
remember, isn't part of the "situation").
Some cases where a professional captured in a ko prematurely already
were mentioned. There are even cases, where the pro didn't seem to
know who had the turn:
- Rin Kaiho lost the 3rd game of the 1987 Meijin (final) because
he made two moves in a row (first time ever in a title match).
There was a (evening) dinner break, and Rin sealed move 188
while in byoyomi. It was a forcing move, leaving only one
response to Kato Masao. The game seemed to be won by Rin.
After dinner referee Iwata restarted the game (by placing 188
and restarting the clock, I guess). One minute later Rin played
move 189, skipping Kato's obvious response.
[DGZ0687a] [RGG150293] [W-GB]
- Cho Chikun lost the 2nd game of the 50th Oza (final) by time
(first loss by time in a title match ever) because he kept
waiting while, as he believed, the byoyomi ("second reading")
was counted for his opponent, O Meien. But in fact it was being
counted for him. The game was his, and he already had decided
on move 145, but he missed O's 144 while staring into his lap.
When the time keeper said "ten" as the last second of the last
ten seconds elapsed, referee Sakaguchi Ryuzo declared with
Japanese "determination": "Black has run out of time, and so
we have to assume White wins". [DGZ0602b] [W-Cho]
I don't know how clocks and byoyomi are handled in Japan exactly,
only that pros there don't operate the clock themselfes. However,
according to LJRG there has to exist a visible sign that tells (at
least) both players whose turn it is. If a (reasonable) clock is
used, it naturally gives this sign. If one player is in byoyomi,
the clock still will be in use to time his opponent. But even if
both players are in byoyomi and are timed by two time keepers, each
using his private watch, for instance - the clock has to be operated
to preserve this sign!
I guess you won't object against wanting a computer screen to show
all the information making up a situation as defined by LJRG (and
additionally easing the task by marking the last stone), but you
might absolutely refuse to use marks in the real world. The only
compromise I'll offer is this:
The only aspect of the situation as defined by LJRG that may miss
is the information given by the ko mark. All other aspects have to
be visibly obvious, that's, how locations are colored, which are
marked permanently, which are marked temporarily (in the initial
situation), how many prisoners each side has made, and whose turn
it is. Otherwise the game isn't played according to LJRG.
If the game is played with a ko mark, it has to be used throughout.
If the game is played without one and it's your turn in a situation
other than the initial one, you may once ask your opponent (or a
designated person) which move was made last - with the right to get
an answer. He has to list all locations that changed their color
due to this move (for instance, by pointing to them one after the
other, or pointing beside the board for a pass). However, empty
(uncolored) locations that contact an already listed empty location
may be skipped (since they necessarily also changed their color).
Your right to ask does not depend on having been absent. Regardless
of using a ko mark or not, you may only leave the board if it's not
your turn, but if your opponent is absent and no answering person
is designated, you additionally have to leave behind the answer
about your last move (for instance, by writing down the algebraic
coordinates of the locations in question).
With a ko mark in use, you have to remember absolutely nothing
(missing a cycle removal isn't illegal). Without one, you have to
remember at most the last two moves when you return to the board.
Given the third, you're able to complete the situation in your mind.
(In the worst case, he has passed just after you did. To know if the
game is over and if you may stop the clock, you have to be certain
that his move before was no ko capture.)
Remember Cho asking the scorekeeper (in game 3 of the 1980 Meijin
final) if he may take the ko? Under LJRG either there's a ko mark
around or Cho would be allowed to ask the sorekeeper what exactly
the last move was - both serving his needs. And if the answer given
is wrong? To me it seems fairer to undo the illegal move instead of
nullifying the game.
The number of prisoners has to be visible, no matter if they are
placed directly on the table or, as usual, stored in the flipped
lids of the stone supplies. There's a funny photo in [DGZ0598],
showing one guy standing up, bending forward, and almost tipping
his nose on his opponent's forehead to check their number, hidden
by a 2-inch board. Apparently his opponent is in overtime and has
dumped the lid's contents in front of himself to shut the supply.
(Under the popular "Canadian" overtime, see [W-BGA2], a counted
number of stones has to be played in a certain period of time.
Not to accidentally increase or intentionally decrease their
number, one shuts the supply.) He should have shut it with the
lid still holding the prisoners or at least dumped them beside
the board (into his "prisoner zone" ;-).
And what if, more likely, rather the number of stones remaining to
be played in the period were to be checked? Neither overtime nor
overtime stones are covered by LJRG, but their number should be
visible too by analogy. One should keep them somewhere beside the
board if it's too thick.
At last it should be mentioned that if physical devices like board,
stones, marks, etc. are used, they ought to be uses in the rules'
sense.
For instance, if you push the ko mark over to "2", the game isn't
yet at an end - you also need to switch the turn (via mark or clock).
If you instead leave your clock running, you risk losing by time
since it's, technically, still your turn. If disputes aren't played
out, the game would now be over, but since the clock knows nothing
about that, your opponent should now stop both clocks. This may seem
strange, but it enables the simple rule that whose clock runs out of
time, loses by time. Otherwise it could happen that we had to decide
which was faster, the ko mark reaching "2" or the clock running out
of time - not very practical.
Or, if you forget to put the ko mark back onto "0" after making
your ko threat and then switch the turn, you committed an illegal
modification of the situation just as if you had removed one of
your stones to create a second eye. If we look at it strictly, you
would have lost in both cases, even it the latter obviously is more
intentionally than the former. Practical rules, LJRG isn't concerned
with, could try to soften this by letting your opponent undo your
illegal modification and continue the game as if you'd passed.
AFTER END
To prove control mathematically, we would have to go through all
possible move sequences that don't go beyond a final or repeated
situation and allow the claimant to cut off all but one branch in
each node he has the turn. If this tree then always ends in leafs
with the claimed set filled by a 2-eye formation of the claimant,
the claim would have been verified.
This certainly is of no practical use because it would take almost
forever. So, the two players would have to agree that a claim holds
instead. But what if a player doesn't agree? Maybe you think this
isn't a problem because we practice this agreement every time we
play go - without thinking much about it. But everyone designing
rules has to consider the worst case.
The simplest dispute breaker would be to designate one or more wise
referees who would have to rule those disputes - thereby bound to
keep as close as they can to the ideal solution explained above.
Another possibility would be to set up a test for each dispute.
If, for instance, Black didn't agree in White having control over
a location, White would have to identify a set he thinks he could
lock which includes the location in question and set up his worst
case for that set on a second board. Black would then start and
the test would continue until either White reaches his goal, the
pass count reaches 2, or the situation becomes repeated.
Black only refutes White - not in a mathematical sense, of course
- if the test ends without White having reached his goal. White's
goal is having build a 2-eye formation on his set. This can easily
be checked. To shorten the test, we would also let Black succeed as
soon as he extends his permanent stones into White's claim or covers
any part of it with a black 2-eye formation.
Not to give one player an edge, both would have to fix their claims
(write it down, for instance) of what they believe to control before
they exchange this information. To shorten this list (or the number
of clicks), one (empty) location for every "hole" one believes to
control is enough. Each such location is understood to identify the
claiming player's smallest bordered set that includes this location.
Each player then may mark - privately again - one location claimed
by his opponent in case he disagrees. If both agree, there's no
dispute (even if claims overlap) and normal count based on both
claims decides the score. But if not, each dispute is played out as
explained above and the player winning more disputes also wins the
game (if both win one, it's a tie).
In case there are 2 disputes and one player asks for, both disputes
should be played interlocked. Black starts in the first dispute (the
one he's the refuter in) after which both players, now starting with
White, alternately play in both disputes, each playing first in that
dispute his opponent has played in last:
B1, W1,W2, B2,B1, W1,W2, B2,B1, ...
This was my first version. Here's a maybe more practical second one:
After "game end" the players alternately either point to an empty
location or pass, starting with the player who didn't pass last.
To disagree, a player points to the same location his opponent just
has pointed to. In this case a dispute is played out and decides the
winner (of the dispute AND the game). In case of two passes in a row
there is no disagreement (even if claims overlap) and normal counting
based on both claims decides the score and the outcome.
Since at most one dispute is played out and passes don't give up the
right to claim later, the sequence and timing of claims now may play
a role - a (small) drawback of this unsymmetric scheme.
If there are lots of small territories, both schemes can take quite
a number of pointing. To reduce this, one could let the players
identify dead stones and neutrals instead. Both schemes could be
modified in this way. Let's modify the second:
After "game end" players alternately either point to an empty
location, point to one occupied by an opposing stone, or pass -
starting with the player who didn't pass last. Pointing to an empty
location claims that it is neutral. Pointing to an opposing stone
claims that it and all opposing stones sitting in the claimant's
smallest bordered set that includes the claimed stone are dead.
To disagree, a player points to the same location his opponent just
has pointed to. In this case a dispute is played out and decides the
winner (of the dispute AND the game). In case the location is empty,
the disagreeing player has to prove that he controls it. In case it
is occupied, the claimant (opponent of the disagreeing player) has
to prove that he controls it. The "proof" is done as usual.
In case of two passes in a row there is no disagreement and normal
counting decides the score and the outcome. This is done by treating
all locations that, suppose all claimed dead stones had disappeared,
are empty, neither are nor contact claimed neutral locations, and
contact only stones belonging to one player as being controlled by
this player.
The third scheme seems to be very practical (even if the control
claiming schemes mathematically appeal me more). It inherits the
unsymmetry from the second (no one wanting to point to dubious
locations first), but no overlapping can happen any more. Instead,
a new oddity pops up: it's possible to neutralize one's own
territory. The opponent can't disagree (because he can't prove
control), but he won't bother to do anyway. Claimed dead stones
in a neutralized territory don't count because, as defined above,
their locations are not controlled. Note that only neutrals in a
seki's eye actually have to be claimed. So if there are no sekis
with unbalanced eyes and no dead stones around, and no defect
elimination is missing, the claiming phase can end immediately
with two passes. Nice.
The third scheme is slightly gentler than the first two. If you
missed a defect eliminiation and your opponent claims neutrals
where you believed territory, you can reconsider and avoid losing
by a failed proof. Of course, this will only help you if your lead
is big enough and no dead stones are sitting in this "territory"
(which would let your opponent avoid to claim first).
Good rules always have to anticipate extremes. Obstructer will claim
whatever gets into his mind, regardless how unsound. Obstructer will
disagree with whatever you claim, regardless how sound. Not to drown
in disputes, each player at most can lodge one. To compensate this
restriction, the second principle is that whoever loses a dispute
can't win the game any more. This will prevent unsound claiming and
unsound disagreeing - with one exception: Obstructer will do so when
he's behind.
So, if disputes are played out, you better watch your claim since
rules have to treat you as a potential troublemaker. Try this one
[DGZ0502b]:
Disputes are played out. Control is claimed. The game is over. What
should White claim?
0 0 B 2
White certainly can claim control of 8 locations on each side,
giving him 4 points. Since this is enough to win, White should
refrain from claiming more. If he nevertheless does, that's,
if he claims the whole board, he could lose the game (if his
opponent decides to kick kihin and stick to the rules).
White may think that his proof will succeed via ko since he
starts the ko without any internal ko threats around:
7 passes, 8 connects, etc.
But Black can do better:
0 0 B 0
If White now expects Black to continue in the center, he'll
be quite surprised by Black's pass. Finished? Yes. Got it?
It's seki - the most astonishing seki I've ever seen!
As always, since I don't mention it in the rules, if a clock is used
and disputes are played out, actions after the "end" are to be done
while each clock is running. It should be obvious what this means in
each case.
I won't discuss this further - already went too far. I'm satisfied
having precisely defined what it means to "control" a location.
Nevertheless, if asked to choose a dispute breaker, I would prefer
a referee (or better three of them) because after game end no skill
on part of the two players should be asked for any more (ignoring
their skill in convincing the referee). Note that if disputes aren't
played out, disagreement (intentionally) risks nothing.
On the other hand, if the game is played via Internet, playing out
disputes recommends itself - at least as far as no program is able
to be the perfect referee. This also puts an end to disagreeing
escapers.
Under Yahoo, for instance, it's possible for the player who passed
last to force his opponent to play another stone by disagreeing to
game end - three passes in a row are prohibited (to prevent endless
resumptions I guess) [RGG090303]. This effectifely implements
no-pass go (or nim go - German "nimm" is "take!" ): who runs out of
legal moves loses. Some claim this to be "Mathematical Rules of Go"
[W-JCC], but we shouldn't regard it to be in the spirit of go.
Here's a nice example why [RGG010997]:
0 0 W 0
White wins by repeatedly sacrificing stones in Black's eye, despite
losing under every other rule set I know. This especially refutes a
claim that nim go is the same as stone scoring: it is NOT. In case
you want that, you additionally have to allow to return (or destroy)
a prisoner as a move (and treat jigos under stone scoring to be lost
by who passed first), as I believe. But the finish remains dull.
Preferable, Yahoo should either implement the perfect solution given
here or at least the simpler, but less perfect, "cleanup" phase
solution.
In this case disagreement starts a second phase, giving turn to the
player that didn't pass last. The cleanup phase ends in the same
way phase one did, but without permitting a further phase nor any
agreement about dead stones. Since only empty locations surrounded
by one color (i.e. contacting one color) are counted at the end,
all believed dead stones have to be captured explicitly.
Not to lose points in doing so, each stone played in phase two (no
matter if it gets caught or not) generates one extra point (draws
a prisoner) for the player having played it. (Equivalent ways to
put it: pass-stones plus even number of moves a la AGA, or prisoner
recycling plus balanced prisoner fill up [RGG090895]).
The cleanup phase solution isn't perfect because
- all neutrals will have to be filled in phase one (to avoid
counting if their number is even, to avoid defect elimination
for free, and to avoid giving a hint about defect elimination)
- potential kos have to be uncorked in the global context (e.g.,
bent four in the corner isn't unconditionally dead any more)
- some sekis produce extra points in phase two (those with
single-sided dame and - provided seki "territory" is ignored
in the case of agreement - those with an unbalanced number of
eyes)
Point one only means extra effort, and point two and three are
admittedly rare - but why settle with second best?
(Note that the reasons for filling neutrals can't be overcome by
both players' good will to agree on game end and dead stones.)
What annoys me about cleanup phase solutions is that most of them
just don't treat seki as it should be treated and that they give
no real reason for their peculiarities. Take the one above, for
instance. After a while you ask yourself, "Why don't we skip phase
one and start with phase two immediately?" since, as it turns out,
this is equivalent to area scoring, which then can be explained
far more simpler.
We already saw this position above:
2 0 B 0
The question was if Black should pass. If he, eager to win, does,
he missed to remove the aji that crops up when all outer liberties
would be filled, spoiling his control.
What if White doesn't recognize this aji and accepts a 1-point loss
after both passed? For me this is comparable to any other error
during counting. It's a practical matter LJRG doesn't address.
LJRG neither deals with dropped stones, shifted stones, manipulated
captive counts, graphically recording in advance (I can't share van
Diepen's opinion to tolerate one move [P-Prag93]) clicking fans
(Rin Kaiho's bad habit [GR-Su74]), rattling stones, humming (Cho
Hunhyun's bad habit [DGZ0794b]), talking ("It's over!?"), eating,
smoking, etc.
A practical solution could be that the result is fixed after
both players agreed to it.
Would a 3rd person be allowed to correct an error before the
result is fixed?
In the second week of the 1969 European Go Championship Juergen
Mattern and Anthony Goddard agreed to end their game and stopped
the clock. Mutabzija, watching the game, intervened and showed
that there was a sente-point for Goddard, a gote-point for Mattern,
still on the board. Mattern would win with this point. Without it
the game would be a jigo. I don't know the game record, so I made
up an example:
0 0 W 0
The rule committee decided to play a second game: Goddard getting
jigo in case he wouldn't lose. Goddard won by 9 points and got a
jigo. Mutabzija was first punished with losing 1 point. Later this
was converted into a fine [DGZ0669].
The sad thing isn't that both player overlooked that 1-point play
- mishaps remain - the sad thing is thatt both had to play a second
game. Since I'm not sure how 1949 rules, effective at that time,
define game end, I can't comment on this decision. We only can
learn from it that the end of the game must be defined in an
unambiguous way. If the (absolute) end wasn't reached by stopping
the clock, Mutabzija's intervening would be as if commenting on the
game loudly while it's still in progress, but I hardly can imagine
that this was his intention.
How to handle this, again, is a practical matter LJRG doesn't cover.
According to it the game would have reached its end. Everybody would
then be invited to take part in monitoring the discussion of control
and the counting process. This can't do any harm - can only help to
reach the correct result.
So, if a 3rd person witnessed counting in our first example, he
could, without feeling bad, inform White that Black has missed
to add a stone and isn't entitled to count any territory there
- in fact, he should inform White.
If, of course, disputes are played out, nobody may intervene - as
long as it concerns the question of control - till dispute breaking
is over! In this case White would have to recognize the aji and
find the correct sequence by himself.
The example also demonstrates that simply counting everything
that's surrounded by a single color after dead stone removal
wouldn't always be correct. In practice one could fill all
uncontrolled empty locations before counting, but remember that
this isn't part of the game any more. If, for instance, Black
has missed to add a stone, as in the situation below:
0 0 B 2
then he can't make up for it after game end. Black controls not
one location above. Under LJRG Black should have added a stone
either above or below the center before end. If uncontrolled empty
locations are filled to ease counting, ALL 5 locations at the left
would have to be filled - no matter with what color.
Here's another (funny) example [DGZ0502a]:
x y W 0
White suspected there to be aji and continued at A. Black "oh"ed
and took his time. Then, with lots of "oh"s from both sides, it
went on like this:
After the end Black happily started taking out the white stones
- without White opening his mouth. They seemed to agree. But some
spectators, of course, raised their eyebrows.
I don't know it for sure, but it seems that they counted the game
as if the white stones on the lower side would be dead. (The only
clue the source gives is that "White nevertheless won" - on a 19x19
board, of course.)
If the game is played with play-it-out dispute breaking, spectators
ought to keep their mouths shut till the players agree on who
controls what - after which they may then burst out in laughing.
But if this isn't the case, the spectators should notify the players
that Black lacks control on the lower side. The players can't insist
on their wrong counting (even if it wouldn't matter) - tough luck
for Black. LJRG not even grants him the option to continue and to
squeeze out 3 white captives: the game is over.
How should one count?
After determination of who controls what, the score must be counted.
Traditionally each player removes dead stones from his territory and
fills them together with captured stones of the same color into his
opponent's territories. Each player additionally moves stones around
to shape his opponent's territories into plain forms, of course
without affecting their total area.
If the only drawbacks of this method were tangled arms and not
being able to monitor what one's opponent is doing, this method
weren't that bad. To overcome: just let the players take turns.
But its main drawback is that the final situation is massacred.
This is very unpleasant, especially if the game is close.
After counting out game 3 of the 40th Oza, 1992, both players
appeared quite surprised to learn that Black (Fijisawa Shuko) had
won by half a point. Kobayashi Koichi requested a replay, which is
very uncommon, and poor game recorder Endo Yohifumi had to replay
the whole game to confirm the result - 230 moves. [RGG100702]
Needless to say that the normal folk enjoys no game recorder, and
that it either doesn't bother to record at all, or omits to record
at least the final stage. A complete game record is the exception.
Therefore I recommend not to modify the final situation at all.
Instead, both players should count both scores and then compare.
To enable comparison, both have to agree on how to treat dead and
captured stones. I suggest to avoid subtraction (and negative
numbers), contrary to what was done above, and to add those
numbers to the score of the reverse color.
For instance, one could use following (score) chart:
TB DW PW | SB
TW DB PB K | SW
with T for territory, D for dead, P for prisoner, K for komi,
and S for score (and B and W for black and white, of course).
Needless to say that SB and SW each is the sum of what's to
its left.
If the number of moves (M) (including handicap, so it's actually
the number of stones) are known and one additionally counts the
neutrals (N), one can extend the chart to make it self-checking:
TB DW PW | SB
TW DB PB K | SW
M L
N
-- -------
X X
with L being the number of locations. Needless to say that each X
is the sum of what's above it, and that those sums have to match.
In case opposing controls overlap (which I don't believe can happen,
but anyway), those locations have to be accounted for twice in L,
and stones on them twice in M.
Here's the (simple) proof that both X match:
kind of location increase on
control occupied alive left side right side
-------------------------------------------------
0 0 N L
0 1 M L
1 0 T L
1 1 0 T M D L
1 1 1 M L
2 0 TB TW L L
2 1 T M M D L L
and, of course, each increase in P is matched by one in M.
To all who prefer to play things out:
This certainly leads to simpler rules, but I don't think they
then deserve to be called "Japanese" rules because they will fail
to treat the question of life and death locally. If, for instance,
there's a bent four in the corner on one part of the board and a
double-ko seki on another, then playing things out will only
result in the unconditional death of the bent four if you modify
the ko rule - for instance, prohibit ko recapture till a pass was
invested in this ko, but this rules out internal ko threats.
Playing things out will also fail to naturally treat sekis as
neutral - a characteristic of Japanese rules. The argument that
this is a strange exception anyway that should be removed no
longer holds: LJRG proves the opposite!
I don't have any big problem with playing things out at all. For
instance, it would be pretty easy to convert to rules that "punish"
passing with a prisoner to be given and to end the game after two
passes in a row - provided no location was temporarily prohibited
when the first pass was made and White passed last. This would
guarantee an equal number of stones used by both sides, and we could
count in the Japanese or in the Chinese style - both giving the same
result.
Now, wouldn't this be a good candidate for international go rules?
An existing proposal [W-RJ2] takes this view (see [RGG140998] for
announcement and discussion). It includes above's pass-stone method
as an optional scoring rule. Since this produces the same outcome
as area scoring, it was called "Equivalence Scoring" (which is a
poor choice since it's a method of counting - it should be called
"territory counting for area scoring").
It differs only slightly from what was said above in that the
first stop (double pass) only ends the game if an agreement about
dead stones can be made. If not, the game continues (of course,
with that player that didn't pass last) and ends as soon as the
second stop was made (and all stones left being alive). An equal
number of stones is reached by forcing White to add an extra pass
(stone) just before scoring if Black passed last.
The whole thing is practically equivalent to AGA rules [W-FH2].
AGA rules also use pass-stones (but not as an option). As above
a stop followed by an agreement ends the game, and as above White
must add his extra pass after game end if Black passed last. But
different from above the game doesn't end with the second stop
after a failed agreement. Instead, each further stop again gives
agreement a chance. In case agreement always fails, a double stop
(four consecutive passes) ends the game without agreement (and all
stones left being alive, of course).
Since the proposed "International Rules" and AGA rules both use
super-ko (positional the former, situational the latter), neither
allows passes as (trivial) ko threats: after a double pass the ko
still is taboo. (However, if the "Basic Ko and Exceptional Game
Ends" option of "International Rules" is in effect, one's first
pass could be a (trivial) ko threat.)
Before you now vote for one of the three alternatives given above
(zero, one, or multiple chances for agreement - to coin them),
please be aware that they all share one property - they are area
scoring effectively. Is this the simplest rule set possible?
I don't think so. There's another "play things out" candidate out
there - called "stone scoring" (or "stone counting", but I like
Robert Jasiek's idea to reserve "counting" for counting methods)
- and every child will instantly grasp wwhat's the game about:
To get more stones of your color
onto this board than your opponent
Stone scoring rules seem to be the most natural thing on earth. Why
not make THEM the candidate for international go rules? Ok, under
the various equivalent counting methods applicable to area scoring
everybody finds one he's used to - more or less - but for someone
unbiased, stone scoring is absolutely plain (and has the older
rights anyway - see below). The scoring rule couldn't be plainer:
A player's score is the number
of locations that have his color
If you look at it this way, it's not very convincing to additionally
count eyes. You surrounded one? So what. If you can't occupy it with
one of your stones, it doesn't seem to be yours - any toddler will
understand that, and Sesame Street's Count von Count would create
quite some confusion if he mixed stones and holes in one count.
In this text I try to make Japanese-style rules plain. If my aim
were to propose an international rule set, logic would sleepwalk me
to rules of the "stone scoring" type. And somehow I have the feeling
that if the big global rule election would be made, and children
(unbiased as they are) would participate (and why shouldn't they?),
the vote would be a clear "stone scoring". Maybe they're right.
Whatever the current rules are, when introducing the game to kids or
beginners, stone scoring would certainly be my favorite rule type
(example rule set at the very top). In my opinion, beginners should
play lots of games on SMALL boards (say 9x9 or even 5x5) right from
the start, and not be taught tactics or elaborated concepts at all.
Why not even keep our mouths shut and let them detect the "trick"
with the territory ("filling can wait") or that with the two eyes
("don't fill too much") on their own? Japanese-style rules
(including LJRG of course - I'm not blind) are spoilers in this
respect and absolutely unsuitable for beginners: to let them depend
on a referee when questions like "Is the game over?" (without some
"two passes end" rule) or "Is this dead?" arise is ridiculous.
They should be able to walk off and play with each other.
Therefore I have mixed feelings about the "greatest" go event on
German TV in the year 2002: our child program "Die Sendung mit der
Maus" - famous for bringing things down to simple terms - explained
go! That's the good news, but the bad one is that they did it via
Japanese rules.
They explained capture (but neither suicide nor the case when it
just looks like one), territory (empty "crosses" surrounded by
one color, but ignoring the symmetry between inside and outside),
and that each prisoner and each empty cross in one's territory
counts for one point, but ko was never explained (nor distinguished
from suicide in an eye).
Then a 9x9 game was played and ended as "no more" moves were
available (leaving the impression that entering an already
surrounded area isn't allowed). Stones surrounded by opposite
color were removed (too bad that those stones themselves never
surrounded some "territory" - we would have experienced their
first rule debate). To top it, they managed to count 6 points
in a 3x2-shaped corner.
After 66 moves White had won by 24 - 13 = 11 points:
5 2 (66 filled 17) (B sat at the right)
No one depending solely on that information will really know the
rules. Worse, he'll think he knows them, but probably got'em wrong.
Ok, it was a good appetizer and it seemed simple - but it just was
incomplete and misleading. I'd tolerate this if go rules couldn't
be squeezed appropriately, but this definitely isn't true as, for
instance, stone scoring rules given above prove - in less than 25
lines and without any "abstract nonsense". It's better to start
with rules that are simple as well as complete than to start with
the real thing and omit to define ending or scoring only to
simplify or because oneself lacks a complete understanding. I
neither recommend crippled rules like "atari" (first-capture-wins)
go. Whether the initial rules actually are used anywhere on earth
or not is irrelevant - as long as they preserve the spirit of go.
But before you now vote for stone scoring, let's look for something
else to be considered. There seem to be two conflicting goals:
- simple rules (like stone scoring) on one end, and
- simple practice (like Japanese-style) on the other.
Both, stone and area scoring, have in common that they "play things
out". Very appealing - especially when introducing go to beginners.
But playing things out also has its disadvantages - especially for
experienced players (which one happens to be for the longer time).
Experienced players are dealing with the practical consequences
of the rules, not with the rules themselves. They want an early
end - without any fuss. They don't want to
- count groups to see who will need more eyes
- make superfluous connections to avoid some eyes
(this two drawbacks, of course, only come with stone scoring)
- count neutrals to check if having the turn got meaningless
(we have to fill'em anyway? - not under LJRG)
- let the outcome of a ko or the game depend on the number of
neutrals
- start silly kos about one neutral more or less (see below)
- uncork potential kos (like bent four) in the global context
- be forced (by a disagreeing obstructer) to capture dead stones
All this would only prolong the game without making it much more
interesting - just fussier. Of course it's a matter of taste, but
if you prefer the fussy style then consider being consistent and
also divide shared spaces in sekis minutely (as Ing rules once did
[P-Ing86], but seemed to have dropped). If not, you naturally end
up with territory scoring (which is more than just a method of
counting). This has nothing to do with stubbornly sticking to some
weird tradition. It just shows that once in a while there's a grain
truth in tradition - if not a boulder here.
The non-fussy practice lets this
0 0 W 2
(suppose the center was prohibited in the first turn)
be a jigo, instead to count Black's eyes in the seki.
Counting points in sekis wouldn't prolong the game and might not
bother anybody - that's why I excluded it from above's list - but
nevertheless I like how LJRG treats seki: no control - no points.
The non-fussy practice doesn't care about neutrals. You need a
definition? I'll try one. Look at board extensions of this kind
(LJRG nowhere excludes boards that fall apart, by the way):
plain neutral
Black's silly ko
White's neutral
If the main board's "orbit" could be extended by whatever finite
collection of such "satellites" (including their color-reversed
variants) without changing the game's outcome, we can qualify the
underlying rules as being neutral-indifferent (which LJRG is).
Some words about the silly ko:
0 0 B 0 (5 stones each)
Under Japanese rules both players would now pass and the score
would be even, but under stone or area scoring Black will start
a ko at A, exploit his ko threat below the single white stone,
and win by 2 points.
Normally there are "neutrals" around, like here:
0 0 B 0 (16 stones each)
Black has to be armed with enough ko threats to keep the ko alive
till all neutrals are filled, investing one threat after each pair
got filled. He has enough here, and he wins by 2 points (under area
or stone scoring) if he starts the silly ko. If not, White ties.
In the situation below Black doesn't have enough ko threats to keep
the ko alive this long:
0 0 B 0 (14 stones each)
But Black wins anyway because the number of neutrals is odd. He'll
take the last one even without going through the silly ko. However,
Black risks nothing starting it. As soon as he notices that he has
exhausted all his ko threats, he can return to the plain sequence
by filling the ko.
There's a variation of area scoring that deprives Black from the
extra point [W-IT]:
If the [very] first pass was made by White [...], 1/2 point
is subtracted from Black's score and added to White's score
[to] eliminate the one-point difference between area and
territory rules that arises about half of the time in even
games from Black's having played an extra stone.
An alternative but more symmetric way to eliminate the one-point
difference is to allow a single half-point button beside the board
to be taken as a move and additionally to increase komi by half a
point [RGG170101]. Either Black takes the last neutral, but his
extra point is compensated by button and increase, or White takes
it, and Black makes up for the increase by taking the button.
Again, if the number of neutrals is odd it makes no sense to
fight the silly ko, but in the even number (neck-to-neck) case
Black still fights it, even if now "only" for a 1-point win.
So, the deprivation amendment fails to make neutrals meaningless
in all cases.
By the way, it's not "if the last pass was made by Black..."
because this invites pass fights. For instance, Black would tie
0 0 B 0
after he filled the last neutral by answering White's pass not with
a pass, but with a throw-in (in White's 2-point eye). White can't
help but to capture (under any play-it-out rules), letting Black
avoid the last pass.
For a hyper-complicated treatment of a silly ko see [GW71b]. I'm far
from being sure, but it seems that Japanese rules don't enable such
a fuss.
Above, the ko was fought as soon it was set up. Is this always
right? Choose Black's move below (area scoring):
0 0 B 0 (12 stones each)
If Black takes the (center) ko, it ends in a tie:
Sly White doesn't atari (error), but fills the (bottom) neutral,
Black fills the center ko, White ataris, Black fills at the top,
White takes the corner ko, Black passes, White fills the corner ko
(works in all ending schemes), and both pass. Both captured one
stone, and Black's territory is one point larger, but Black suffered
from an extra pass.
If Black instead fills the neutral, he'll win by 2 points:
White ataris, Black fills at the top, and - since both kos cancel
out each other - White passes, Black passes, and White passes again
(for an even number of moves). Black's territory still is one point
larger, but now White suffered from an extra pass.
This example is a shrunken version of a game between Seto Taiki
and Liu Fan, played in the 2003 National Weiqi B League. Ironically
the Chinese (Liu) took the ko and lost by half a point instead to
win by 1.5 [RGG040403].
Note that, to be fair, taking the ko isn't wrong per se. If Black
had enough ko threats (somewhere else), he could win by 4 instead
of by 2 (and overcome komi, for instance):
White fills the neutral, Black fills the center ko, White ataris,
Black fills at the top, White takes the corner ko, Black retakes it
after threat and defense, White passes, Black fills the corner ko,
White passes again, and both pass once more. Black is ahead by one
point territory, one prisoner, and two white extra passes.
Now to the obstructer (plus a rule debate under play-it-out rules -
you wouldn't believe it):
In the second round of the 46th European Go Championship (Zagreb,
July 20 - August 4, 2002) the Hungarian 6 dan Csaba Mero (White)
was pitted against the German 5 dan Robert Jasiek (Black). The
game was played under Ing rules (area scoring). At the end of the
game, Robert was behind with about 25 points. Both passed in
succession (first "stop"), but no agreement about dead stones was
made (no idea if one was tried - Robert continued). The game went
on with Robert capturing "dead" white stones while Csaba kept on
passing (and maybe smiling).
After having removed all "dead" white stones, Robert finally
passed too, leading to the second stop (since Csaba must have
passed before). After a third stop, immediately following the
second one, the game was over. [DGZ0402]
The real "fun" started now - they didn't agree about the "dead"
black stones: Csaba wanting to take them off, Robert insisting
that the game was over and those stones thus had to stay (giving
him the win).
The referee decided against Robert. The appeals commission agreed
(deciding that "the game is in a pause", but failing to underpin
this with rules). Weeks later Matti Siivola, president of the
Finnish Go Association and chairman of the RRC (EGF's rules and
ratings commission), wrote Robert that the RRC "agreed that the
decision of the appeals commission will not be changed" (six
members out of seven took part - Robert, of course, not) - with
"slightly varying reasons", but not giving the slightest hint
[RGG120902].
The Ing Foundation itself didn't answer any of Robert's queries.
In an org-e-mail Christoph Gerlach, German 6-dan, also agreed to
the appeals commission's decision, arguing that the game doesn't
end in case there still are dead stones around.
I honestly was stunned. Aren't Ing rules [W-Ing91] of play-it-out
type? Or am I mixing up Ing rules with AGA rules [W-FH2]?
Under AGA rules (area scoring as Ing rules) the game either ends
with a stop followed by an agreement about dead stones or with
two stops in succession (making it impossible to block game end
by endlessly disagreeing). This would clearly support Robert's
opinion.
I guess Christoph draws his opinion from [W-Ing91], quote,
Article 1
[...]
After the neutral points have been filled, both players pass
and play pauses. After the dead stones have been taken away,
both players pass again and play ends.
When you first read this, it doesn't seem to fit to, quote,
Terminology
[...]
19 "Play ends" when each side passes twice, making four
consecutive pass plays. Play cannot resume for any
reason, so that game ends.
Didn't the former let the game end after one stop, not two? But
then you realize that "taken away" refers to agreement and not to
capture, and that therefore taking stones away doesn't insert any
moves between both stops.
For me Article 1 is an example where a rule of practice gets
confused with a legal rule: "stop, agreement, stop" might be the
normal case (adding a superfluous trailing stop, compared to AGA
rules), but of course "stop, no agreement, stop" is also a game
end - else we could forget the whole idea of the trailing stop.
But nevertheless Christoph wants to think that the game ending
stop only qualifies as one if it not only immediately follows
another stop, but if additionally all dead stones are "taken away"
between both stops. Obviously Christoph (and who not?) disapproves
Robert's conduct and tries to interpret the rules in his way.
If he is right, he would have to define what "dead stones" are
- because depending on agreement will ceertainly not do. This
definition must also be independent from their capture in the
"cleanup" phase (after the first stop) to avoid a vicious circle.
Suppose we would use "stones are dead if they can't avoid capture
(even if they start)" to accomplish this. Of course, this doesn't
mean that "dead" stones can simply be taken off after a stop - as
"one slips" (beast 4) demonstrates. In its case the game would
have to continue (since both groups are "dead"), one group would
have to be captured, and the other would be allowed to make life
- fine.
But rule design is a delicate job. What if the opponent is behind,
refuses to capture, and blocks the game from ending? (Not very
thankful of him - he's the one we actually wanted to help not to
forget his capture.) We could additionally prohibit passing if
there are opposing dead stones around (and define "end" without
referring to dead stones again), but counter-examples remain:
First, the stones in a double-ko seki's kos are "dead" according
to the definition, but there's no way to get rid of them: the game
would never end (and neither before).
Second, it's sometimes wiser not to capture:
0 0 B 0
Each side has 21 stones on the board. 10 locations are empty
(21+21+10 = 52 = 13x4) - of which Black has surrounded 3 and
White 2. The other 5 are neutral - 4 of them in seki. If Black
just takes the last neutral not in seki, he'll win by 2 points.
But according to our definition the white stones at the left side
are dead (of course not because of bent four) and Black would have
to continue after White's pass. After Black starts the ko in the
bent four, White will make a ko threat in the seki and, whatever
Black does (ignoring the threat or answering it), it will end in
a tie (under area scoring).
Considering this, we may now come up with the idea that a player
is allowed to pass even when opposing dead stones are around, if he
only renounces to capture them - but, guess what, now we're almost
back to where we started from. We only have to let the renunciation
be understood with passing to reach home plate again.
I don't think that it's worth the effort to prevent games to end
"too soon". If both players know that the game ends with two stops
in succession, they should have no problem to capture whatever they
feel can be captured before this happens (since this costs nothing
but time under area scoring). It's of course the organizer's
responsibility to make all players fully aware of this ruling.
We should learn this: Either we use play-it-out rules, benefit
from their simplicity (though Ing rules aren't the best example),
but suffer from having to play it out in case an agreement fails;
or we use Japanese-style rules, swallow their complexity, but are
able to humiliate our opponent with passes in case he stupidly
keeps on going - it's as simple as that.
Do I think the decision was wrong? It was absolutely wrong. Csaba
should have swallowed his pride and "kicked" Robert's stones off
the board (if he knew the rules). But Robert Jasiek shouldn't feel
too well either: If he's a proponent of play-it-out rules, as
e-mails and posts suggest, he ironically hasn't done them a big
favor, and, even worse, he missed a chance to demonstrate kihin.
It's true that under area scoring of Ing-type approaching "dead"
stones doesn't waste time because you have to fill in for counting
anyway, but under the AGA-type it would be extremely unpolite to
disagree if things are clear - and neither is it good style to let
clocks run longer than necessary, under whatever rules.
Robert should ask himself why he passed as soon he had removed the
"dead" stones. Why didn't he continue with filling his territory?
Doesn't he has to do this anyway too under Ing rules? This wouldn't
change the score? Come on, this argument backfires twice. First,
should one start to drop a "dead" stone into each opposed territory
just to let it technically ceases to be territory for the moment?
Second, capturing clearly "dead" stones neither changes the score,
at least not if we assume both players to behave well and to agree
on them. But one gets the impression that he wants to play the game
without agreement, that he wants to take "play it out" to its
extreme. (For a tiring discussion about all this see [RGG250902].)
A slight chance for his excuse might be that Article 1 (Pass Play)
says nothing about agreement (the only hint is using "taken away"
instead of "removed"). One has to spot it in the Preface (3):
"After play pauses, if there are no disagreements when the dead
stones are taken away, both players make one more pass play each
to end the game." So maybe he honestly wasn't aware of this option.
Another try for excuse would be to deny the concept of "dead" stones
to exist under "play it out" (that's why it's put in quotes in this
context). I could try to define it ("clearly dead" is dead in LJRG's
sense even if each worst case is worsened by adding a double-ko seki
satellite which must survive successfull proofs), but it's simpler
to say that if we could agree on some stones to be "dead" without
changing the expected score, then it's polite to do so.
However, Robert certainly had to become aware of Csaba's lack of
rule knowledge as Csaba allowed him to end the game "too soon". To
exploit this isn't good style. Better warn your opponent and add a
stone to the board just to give him the chance to make up for his
technical error - even if you now lose. What's kihin worth if it
always were for free?
But again, technically Robert had won. As ridiculous it is that
the EGF forces European go players to play under area scoring or,
worse, Ing rules each time they meet for two weeks annually, when
in fact they play under Japanese-style rules in the remaining 50
weeks of the year - as ridiculous it is when the EGF pockets Ing's
money and equipment (including those silly measuring bowls, worth
being smashed against the wall), but doesn't apply his rules in
exchange. It's not the RRC's business to judge kihin (and maybe
it didn't). Its business is to make clear what the rules are and
how they should be applied in the future, but it failed to do so.
If you want to make fun about Ing rules or protest against them,
how about exploiting following garbage, quote,
Article 8 Penalties
[...]
Unpenalized mistakes: The following are not penalized.
(1) Mistaken pass: If a player makes a pass play when a point
could still be made by a board play, thus failing to make a
possible board play, he loses his turn, but is not penalized.
[...]
If you're behind and don't want to lose, the only thing you need
are some "dead" stones somewhere in your potential territory.
Since only their removal will convert it into territory, clearly
"a [...] point still [can] be made by a board play". Now, every
time you pass this is no pass, but just a lost turn. Since the
game only is over if "BOTH players pass again" after a stop,
you've made it: Ing's odd fill-in procedure is waiting in vain.
You may disagree and point to Article 8's continuation, quote,
If both players overlook the final neutral point and it is
discovered during the fill-in procedure, since the game has
ended and play cannot resume, the point is left as a shared
space. There is no penalty.
This only can happen if passes stay passes, no matter what. Fine
with me. In this case you must agree that the "mistaken pass" rule
indeed is garbage (likewise not recording passes when no board play
follows - Article 10).
The last quote also is another blow to Christoph's opinion:
If neutrals may be overlooked - why not "dead" stones too?
I still owe you the fact that, besides being unbeatable simple
and logical, stone scoring also seems to be the origin. Here's an
analysis of four old game results supporting this. I don't think
that this in question at all, but anyway (if only to show that
one scoring definition can lead to several counting methods).
[GW71a] presents this four ancient games (sorry for omitting
game records and final diagrams - I just was too lazy):
Game 1 "Four Fairies" (Song Dynasty, 920 - 1279 A.D.)
Game 2 "Ranka" (Jin Dynasty, 265 - 420 A.D.)
Game 3 "Golden Flowerpot" (Tang Dynasty, 618 - 907 A.D.)
Game 4 "Jia Xuan" (Song Dynasty, as above)
But Ing Chang-Ki misses to expressively point out to the reader
that those four games were played under stone-scoring rules! He
seems to be misled by scores reporting of captured stones and lu's
(empty locations) each side managed to count. But the numbers of
lu's given only make sense after you also consider the eyes and
"unpaired" stones - as you would if a game under stone scoring
isn't played out to its full length.
In this case you can't use the natural counting method of simply
counting your stones on the board. One way out is to count your
area and subtract the number of eyes you need:
Score = Area - Eyes (area style 1)
The other avoids counting your stones by only counting your empty
area - after filling in dead and captured stones - and again
subtracting your number of eyes. But this depends on both players
having used the same number of stones. If not, the number of extra
(unpaired) stones must be added to the score of the player who
played them:
Score = Terr. - Dead - Eyes + Unpaired (territory style)
= Area - Paired - Eyes (area style 2)
with
Terr. = Number of locations you surrounded after dead stone
removal
Dead = Number of captured or dead stones of your color
Eyes = Number of eyes you would need to keep open
Unpaired = Number of stones you played more than your opponent
Paired = Number of stones used by a player who didn't use more
(just to make both styles comparable)
Area = Size of your territory plus number of your stones on
the board - after dead stone removal
Here are the figures. Those in column "Dead" and "lu's" quote
the article. The rest was deduced by me from the final diagrams.
Game Color Terr. Dead Eyes Unpaired Paired Area Score lu's
----
1 Black* 55 9 4 1 132 179 | 43 | 42
White 57 7 8 0 132 182 | 42 | 43
| |
2 Black 37 9 10 0 155 183 | 18 | 18
White* 45 22 6 0 155 178 | 17 | 17
| |
3 Black 52 6 6 0 135 181 | 40 | 40
White* 51 6 6 0 135 180 | 39 | 39
| |
4 Black* 76 21 4 1 127 183 | 52 | 51
White 58 9 6 0 127 176 | 43 | 43
Seki 2 ----
The * indicates who started the game. In all 4 games each color
occupied 2 diagonal corner hoshis before the first free move was
made - a custom in those days. For instance, game 1 lasted for
132 + 132 + 1 - 4 = 261 (free) moves. All games were played till
all "neutral" locations - besides those in seki, of course - were
occupied. Dead stones seemed to have been removed by agreement.
Comparing my scores with the lu's given in the article seems to
reveal two errors in the article:
1. It mixed up the lu's in game 1.
2. It dropped 1 black lu in game 4.
Since game 2 and 3 had no unpaired stones, it could also be that
the number of unpaired stones was subtracted from the score of the
player having played less stones instead of added to the score of
their owner. This would lead to a similar error in game 4 - a score
of 51 to 42 in contrast to 51 to 43 lu's, as reported - but the
error in game 1 wouldn't be that "nice" any more - a score of 42
to 41 in contrast to 42 to 43 lu's. However, it seems pretty likely
that stone scoring was also used in those two games - and there's
no doubt about this for game 2 and 3.
JRG89 IN DEPTH
This chapter takes a critical look at the 1989 rules and suggests
interpretations and fixes. It's a complicated mess because JRG89
is very ambiguous and incomplete. I hope its last section about
the erring rule masters makes up for it.
I'll include the English translation of JRG89 below, but for the
comments and examples that accompany them see [P-ARS90] or [W-FH1]
(or the Go Players Almanac).
Figures labeled C-nn are from JRG89's commentary section. Those
labeled LD-nn are from its life and death example section (and
correspond to beast nn). All outer stones in JRG89's examples are
assumed to be alive and not in seki.
The Japanese Rules of Go
April 10, 1989 (Effective May 15, 1989)
Translated by James Davies
The Nihon Kiin and Kansai Kiin hereby revise the Nihon Kiin's
Rules of Go formulated in October 1949 and establish the
Japanese Rules of Go. These rules must be applied in a spirit
of good sense and mutual trust between the players.
Article 1. The game of go
Go is a game in which two players compete in skill on a board,
from the beginning of the game until the game stops according
to Article 9, to see which can take more territory. A "game"
refers to the moves played until the "end of the game."
Article 2. Play
The players can alternately play one move at a time, one player
playing the black stones, his opponent the white stones.
Article 3. Point of play
The board is a grid of 19 horizontal and 19 vertical lines
forming 361 intersections. A stone can be played on any unoccupied
intersection (called an "empty point") on which Article 4 permits
it to exist. The point on which a stone is played is called its
"point of play."
Article 4. Stones that may exist on the board
After a move is completed, a group of one or more stones belonging
to one player exists on its points of play on the board as long as
it has a horizontally or vertically adjacent empty point, called a
"liberty." No group of stones without a liberty can exist on the
board.
Article 5. Capture
If, due to a player's move, one or more of his opponent's stones
cannot exist on the board according to the preceding article, the
player must remove all these opposing stones, which are called
"prisoners." In this case, the move is completed when the stones
have been removed.
Article 6. Ko
A shape in which the players can alternately capture and recapture
one opposing stone is called a "ko." A player whose stone has been
captured in a ko cannot recapture in that ko on the next move.
Article 7. Life and death
1. Stones are said to be "alive" if they cannot be captured by
the opponent, or if capturing them would enable a new stone
to be played that the opponent could not capture. Stones which
are not alive are said to be "dead."
2. In the confirmation of life and death after the game stops
in Article 9, recapturing in the same ko is prohibited. A
player whose stone has been captured in a ko may, however,
capture in that ko again after passing once for that
particular ko capture.
Article 8. Territory
Empty points surrounded by the live stones of just one player are
called "eye points." Other empty points are called "dame." Stones
which are alive but possess dame are said to be in "seki."
Eye points surrounded by stones that are alive but not in seki
are called "territory," each eye point counting as one point of
territory.
Article 9. End of the game
1. When a player passes his move and his opponent passes in
succession, the game stops.
2. After stopping, the game ends through confirmation and
agreement by the two players about the life and death of
stones and territory. This is called "the end of the game."
3. If a player requests resumption of a stopped game, his
opponent must oblige and has the right to play first.
Article 10. Determining the result
1. After agreement that the game has ended, each player removes
any opposing dead stones from his territory as is, and adds
them to his prisoners.
2. Prisoners are then filled into the opponent's territory, and
the points of territory are counted and compared. The player
with more territory wins. If both players have the same amount
the game is a draw, which is called a "jigo."
3. If one player lodges an objection to the result, both players
must reconfirm the result by, for example, replaying the game.
4. After both players have confirmed the result, the result cannot
be changed under any circumstances.
Article 11. Resignation
During a game, a player may end the game by admitting defeat.
This is called "resigning." The opponent is said to "win by
resignation."
Article 12. No result
When the same whole-board position is repeated during a game, if
the players agree, the game ends without result.
Article 13. Both players lose
1. After the game stops according to Article 9, if the players
find an effective move, which would affect the result of the
game, and therefore cannot agree to end the game, both players
lose.
2. If a stone on the board has been moved during the game and the
game has proceeded, the game continues with the stone returned
to its original point of play. If the players cannot agree,
both players lose.
Article 14. Forfeit
Violation of the above rules causes immediate loss of the game,
provided the result has not yet been confirmed by both players.
In defining dead and alive, JRG89 concentrates on stones. All rule
sets that take this path have the disadvantage that seki has to be
covered by extra rules.
If you ask someone knowing the game to teach it to you, it's very
likely that you're told something about stones that can be removed
at the end because they could be captured or because they can't
avoid capture. It's less likely being told the opposite - that
stones may stay on the board because the can be defended.
If you nevertheless investigate it systematically, you might come
up with
C1 = capturable if their opponent has first turn
C2 = capturable even if their opponent has second turn
D1 = defendable if their owner has first turn
D2 = defendable even if their owner has second turn
detect these four relations
C2 implies C1 C1 = not D2
D2 implies D1 D1 = not C2
and draw following picture
with the areas surrounding the three small squares (C2,X,D2)
being empty (follows from the is-not relations above).
It seems obvious to take C2 as dead and D2 as alive. But what
about X, the intersection of C1 with D1? If you consider snap
back, the only choice that makes sense is to treat shaky X as
alive.
So you finally reach
C2 is dead D1 is alive (each implying the other)
This is a very popular definition. Many books introducing the game
(carelessly) use it, including [P-IK] and [P-JDRB]. To quote the
latter
At the end of the game, any stones that cannot
avoid being captured are removed as prisoners
without actually being captured.
This translates to "C2 is dead" (the stones may act first - their
opponent only second). Note that the almost similar "stones that
can be captured are dead" would be closer to "C1 is dead", which
was rejected.
"C2 is dead" isn't that bad at all. For instance, it covers "bent
four in the corner is dead". Ironically the authors of above books
don't seem to trust their own definition. Both include an extra
rule for bent four. But if you follow the definition strictly, it's
obvious that ko threats can be ignored because the only thing that
matters is the question if those stones can be captured or not.
This isn't a continuation of the game - just a (hypothetical!) test.
([W-RJ3] seems to have problems with the plural in statements of
the kind "dogs that bark are alive". Of course this doesn't try
to define if a group of dogs is alive - it simply means the same
as that "one dog that barks is alive".)
On the other side, "C2 is dead"
- doesn't cover the seki exception
- ignores defects (e.g. 3x2 in the corner would be territory)
- treats "one slips" (beast 4) unfair (both groups are called
dead because they can't avoid capture, ignoring the fact that
capturing one enables the other to live)
Neither LJRG nor JRG89 takes this path. LJRG instead defines who
controls an area - live and death just follows. JRG89 still sticks
to categorizing stones, but X isn't treated as alive - it's dead.
Since this alone makes no sense (snap back), JRG89 has to define
the strange exception class "capturable alive".
Let's see what this means.
C-7b
JRG89: 1 dead white stone in black territory.
According to JRG89's Article 7, the two black stones are alive -
not because they couldn't be captured by White, but because this
enables Black to play a new stone his opponent can't capture (on
the corner location or above it). Recall Article 7:
Article 7 (life and death)
1. Stones are said to be "alive" if they cannot be captured by
the opponent or if capturing them would enable a new stone to
be played that the opponent could not capture. Stones which
are not alive are said to be "dead".
2. In the confirmation of life and death after the game stops in
Article 9, recapturing in the same ko is prohibited. A player
whose stones have been captured in a ko may, however, capture
in that ko again after passing once for that particular ko
capture.
Article 7.2, to start with the pass-for-ko rule, seems to be
understood in the following way:
The normal ko rule is sharpened. It's now harder to recapture in
a ko. It doesn't help to play elsewhere after a ko capture - you
still can't recapture. First you have to pass once after the ko
capture for this ko. And certainly you have to inform your opponent
which ko your pass was intended for because now several "hot" kos
could be around at the same time.
Robert Jasiek asks the good question if a recapture would be
possible "if after the last opponent's capture in a ko the ko
temporarily ceases to be a ko and then occurs again" [W-RJ3].
For instance, suppose White just has taken the ko at the right
in a hypothetical line of play. Black then takes the center ko,
and White passes for it. It should be out of question that there's
no need for Black to pass himself for the "ko" at the right because
at this moment it is no ko - he could capture two stones. Ok, but
what if he passes instead and lets White recapture in the center
(coming back to above's configuration). Would Black now still be
allowed to capture in the ko at the right (now being one again)?
The question is what Article 7.2 means with "same ko". The empty
location in the right ko and all its neighboring locations didn't
change color during the capture and recapture in the center ko.
But is it still the same ko?
This is a typical question that comes up when rule texts are not
formal. Instead of giving a direct answer, I'll translate my
interpretation into the parlance of LJRG (without really getting
formal) and let you figure out:
1. A location is "in ko" if it is empty (uncolored), all its
neighbors are not, all its neighboring stones have the same
color, and exactly one stone in atari contacts it.
2. If your capture in a hypothetical line of play produces a new
location in ko, you have to put a "semi-permanent" mark on it.
3. You only may put a stone on a semi-permanently marked location
if this stone has the same color as the stones neighboring
this location. In this case you have to remove the mark.
4. If your turn adds no new stone to the board, you may remove
exactly one semi-permanent mark ("pass for a ko").
5. You must remove all semi-permanent marks sitting on locations
no longer in ko at the end of your turn.
Note that allowing to remove marks produced by oneself does no harm.
Note further that it's impossible that a location in ko changes the
location of its stone in atari without going through a state in
which it's not in ko.
Now to the heart of Article 7 - its definition of life and death.
Article 7.1 seems to be interpreted as follows:
I1. The capturing player has the first turn.
JRG89 uses C-7b and other snapbacks as examples of, quote,
stones that are alive because capturing them would enable a
new stone to be played that the opponent could not capture.
Since Black could certainly avoid capture in C-7b if he started,
the capturing player - here White - must have the first turn.
I2. The new stone doesn't has to be played
immediately after the capture.
The stone Black plays after White captures in C-7b sets up a second
snapback - it can be captured again, it isn't yet the uncapturable
new stone. This will be played by Black's second capture, regardless
if White passes or captures again.
[W-FH1] takes another point of view: it understands Article 7.1 as
a recursive definition. But then you would have to change the rule
text of 7.1 from
...enable a new stone to be played that
the opponent could not capture...
to
...enable a new stone to be played that
is alive...
and this sounds like a cyclic definition. We could avoid this with
some notion of degree, reformulating Article 7 like this:
7.1. Stones are said to be "alive" if they're alive in degree N >= 0.
7.2. Stones are said to be "alive in degree 0" if they cannot be
captured by the opponent (who takes the first turn).
7.3. Stones are said to be "alive in degree N+1" if capturing them
would enable a new stone to be played that is alive in degree M,
with M in 0..N.
But I don't believe this was the intention of JRG89.
I3. The new stone doesn't always has
to be played on the same location.
I don't have an example for this (C-7b is none: a new uncapturable
stone can always be produced on the corner location), but I can't
rule out the possibility that the capturing player could at least
influence where the new uncapturable stone will sit at the end even
if he can't avoid it, and Article 7 doesn't seem to care about this
case.
I4. The new stone doesn't has to be played
on locations cleared by the capture.
For instance:
LD-2
JRG89: Both are alive in seki.
Black clearly can't capture White, so the white stones are alive.
But couldn't White capture the 2 black stones in the corner? Yes,
but this would enable Black to capture 2 white stones by playing
2 new black stones at A and B which White couldn't capture any more.
Notice that White, even taking the second turn, could prevent this 2
new black stones if he is released from the commitment to capture
the 2 black stones in the corner: after Black plays A, White
captures with B. This justifies the term "enabled" (for the moment).
Therefore the 2 black stones in the corner are also alive.
I5. The new stone doesn't has to be uncapturable
in the very moment of its staging.
See beast 12 for an example where it matters.
But even interpreted as above, there remains the problem of how to
formalize "enable". Notice that if the new stone pops up underneath
the captured stones (on one of their locations after they have been
removed) there is no question that it indeed was enabled by the
capture - simply because not capturing prevents a new stone there.
But unfortunately this isn't the only case. Wrecking my brain, I
came to following conclusion:
I6. An uncapturable stone is enabled to a set of locations
by a capture only if the capturing player
1. - taking the first turn -
can't perform the capture without permitting an
uncapturable new stone of his opponent taking place
on one of the locations in that set, but
2. - taking the second turn and restricting himself
to a fixed number of stones of his choice -
could prevent all locations in that set of getting
occupied by an uncapturable new stone of his opponent.
The first part is more or less what Article 7 told us already. The
phrase "set of locations" makes explicit that the new stone doesn't
has to pop up on the same location in all variations.
The second part misses in Article 7. Here's why we need it:
The capturing player certainly must be able to prevent the enabled
stone in some circumstances because otherwise it would make no sense
to talk of "capturing them would enable".
But this also can't be in all circumstances for the following
reason. Imagine two dead-or-alive groups of your opponent in your
believed territory. Each could be brought to life or to death
depending on who starts. Both groups don't depend on each other.
The game has ended - silly, but may happen. If you now declare both
dead, your opponent could say no, arguing: if you capture one, I'll
save the other - with the new stone.
And indeed, the stone would be enabled by this capture because you
could prevent it with your first move! Therefore both groups would
be alive: not what JRG89 wants, I guess. So, this is the reason for
the "second turn" restriction.
Explaining the need for the "fixed number of stones" restriction
will take a bit longer:
LD-11 "false eye and double-ko seki" (or "moonshine life and...")
JRG89: The 7 white stones at the left are dead in territory.
Certainly, White's false-eye group can't prevent being captured
because of the pass-for-ko rule in effect. This is shown by JRG89,
and it concludes that the white group is dead. But to show that a
group is dead one also has to show the non-existence of the enabled
new uncapturable stone.
Well, there don't seem to be some around? But sly White will argue
as follows (discovered by me independently from James Davies):
If you (Black) are committed to capture my false-eye group, you
will start to capture in its ko. Then I'll start a nasty cycling
attack in the double-ko seki (Ing would call "disturbing"). If you
at any time capture my false-eye group, I'll capture your group in
the double-ko seki (either because it's in atari or you missed a
ko-opening pass) and thereby play my uncapturable new stone - which
you could prevent taking second turn and relieved from the capture
commitment.
So how about that! In fact, everyone could now exploit a double-ko
seki with the same argument and reanimate each of his believed dead
groups if it at least has 2 liberties.
How could we fix this? I'll include the already mentioned "fixed
number of stones" restriction in the interpretation of Article 7.
Now White can't argue any more as above because Black would need
an infinite number of stones to prevent White's uncapturable stone.
It seems this fixes the problem, but let's face it:
JRG89 is getting increasingly uglier.
I7. A hypothetical proof doesn't end by two passes
in succession if on of them is a pass for a ko.
As LJRG understands passes after a ko capture not as intention to
end, passes for a ko shouldn't be interpreted so neither. See beast
12 for an example where it matters (slightly).
Now let's see how our "enable" definition would work in C-7b:
The capturing player is White. Black wants to prove that his two
stones are alive despite the fact that White can capture them.
So he claims that an uncapturable stone is enabled to the corner
location by a capture of his two stones. If White captures, Black
will easily produce an uncapturable stone there (no matter if White
captures his throw-in or not). This was the first part.
White accepts this and tries to refute the second part. He argues
that the uncapturable stone Black plays in the corner after the
capture is not enabled by it. Could White prove that he - taking
second turn and restricting himself to a fixed number of stones -
could not prevent this uncapturable stone in the corner?
No, in fact he can: simply by doing nothing (that's, passing).
Then Black won't be able to clear the corner location nor put a
new uncapturable stone on it.
This was the second part. The 2 black stones are alive.
Let's see how the definition works in LD-2:
The capturing player again is White. Black wants to prove that his
2 stones in the corner are alive, despite the fact that White could
capture them. So he claims that an uncapturable stone is enabled to
the 2 empty location labeled A and B by a capture of his two stones.
Indeed, White can't prevent this when he is committed to approach
the 2 black stones, for if he approaches, Black gives atari at A
or B, and White can't capture this stone, due to lack of liberties,
but must capture the 2 black stones instead, giving Black the time
to capture the 2 white stones and produce his uncapturable stone at
A or B. This was the first part.
Now again, White denies that this was enabled by his capture. He
then has to prove that he - taking second turn and restricting
himself to a fixed number of stones - could not prevent an
uncapturable white stone at A or B. But, in fact, he can. If Black
enters at A, for instance, White captures with B. Now White only
has to have another 2 stones in his hand: one to answer Black's
approach from inside the corner, and the other to connect the just
played corner stone with his group. From then on he doesn't need to
play any further stone, but still manages to prevent an uncapturable
black stone at A or B.
This was the second part. The 2 black stones are alive.
Now let's take a look at how the game ends under JRG89.
C-19a
JRG89 would have to rule 7 points territory for Black because the
black stones are alive. They certainly can't be captured because
the most White can get is seki (at 2-2).
But this only holds if the players managed to end the game. If
both players pass in a row and can't agree to end the game nor
one of them requests resumption to avoid giving his opponent the
first turn - both lose. Recall Article 9 and 13:
Article 9 (end of the game)
1. When a player passes his move and his opponent passes in
succession, the game stops.
2. After stopping, the game ends through confirmation and
agreement by the two players about the life and death of
stones and territory. This is called "the end of the game".
3. If a player requests resumption of a stopped game, his
opponent must oblige and has the right to play first.
Article 13 (both players lose)
1. After the game stops according to Article 9, if the players
find an effective move, which would affect the result of the
game, and therefore cannot agree to end the game, both players
lose.
2. If a stone on the board has been moved during the game and the
game has proceeded, the game continues with the stone returned
to its original point of play. If the players cannot agree,
both players lose.
(13.2 is only of practical matter and should be shifted over to
tournament rules. I'll therefore ignore it here.)
Wait a moment. They have to "agree" to life and death? But didn't
our painful discussion above just has shown us that life and death
is defined objectively? A game can be "resumed"? And what if this
happens endlessly? What exactly is an "effective move"? We saw an
example above, ok, but wouldn't filling my second eye also be one?
They also have to "agree" to the end? And if not? Oh yes, both lose
- wow. Anyone another cup sake?
If this was too cynical for you, sorry, but I really get mad when
I read stuff like this. Let's go through the points I don't agree
to one by one:
First, game end seems to rest on agreement. "The game is over
when both players agree to end it" is the more popular version,
to quote [P-JIE]. I can't hear it any more. This may fit to
Japanese or East Asian mentality, where consensus is of high
value, but not to a strategic board game. The definition of game
end shouldn't depend on the good will of any of the two players
because the one behind has no interest in ending ("Agree having
lost?" "NO!") - it must be defined objectively (which also will
take care of an endless number of resumptions).
Second, neither should life and death rest on agreement ("Agree
being dead?" "NO!"), and, since life and death already are defined
objectively by JRG89, there is no need anyway. Agreement would
additionally open the door to attempts to trick one's opponent
without any risk:
0 0 W 0
If both pass above, White should try for an agreement in which all
neutrals are filled (to get rid of seki) AND his stones being alive.
In this case he'd win by 1 point. Viewed objectively, of course,
his stones would be called dead by JRG89's standards. But even if
someone would inform Black before counting, Black would have to
stick to the agreement - otherwise agreement would be meaningless.
White risks nothing. If Black disagrees and tells him why, White
will smile (or pretend being surprised), add a stone (he couldn't
avoid being forced by Black anyway) and accept jigo.
But couldn't "confirmation" mean that both players work out the
objective life and death status of all stones before game end? It
could, but I'm also against this. In the example above, if White
wouldn't be aware of his defect, Black would have to inform him
that his stones would be dead after neutrals are filled: silly.
Third, permitting the game to be resumed isn't necessary at all.
Even "the BGA [British Go Association] Council [, which adopts
JRG89,] makes the comment that restarting the game has never been
the custom in the UK" [W-BGA1], and, I guess, nowhere else as
well. Unfortunately the BGA lacks the guts to go further and
"stipulates that all requests to restart the game after both
players have passed be made only through the Event Organiser
or Referee". But actually JRG89 works fine without resumption.
For instance, we could let the game be over after the first stop.
Since life and death are defined objectively, the players could
step aside and let a referee count it. Ok, they now had to fill
neutrals (to avoid seki) and eliminate (some) defects before
they "stop", but so what? Don't they have to do this anyway?
If we want to stick to tradition and separate both phases, we
could also let the game go on until the second stop is made - the
first stop to be made when turn possession becomes meaningless.
But I hesitate strongly to punish someone who misses this point.
How about this instead: After (again) the first stop, both players
step aside and let the referee compute the perfect result for each
in case each had the second turn. If BSW means "Black's score if
White starts" and BR means "Black's result" etc., this could be
expressed as:
BR = BSW - WSW
WR = WSB - BSB
This also would give us a definition for "effective move" (without
needing it here, however). None is around if
BR = - WR
which is the normal case. In the example C-19a above, if White had
a territory of, say, 5 points (and no komi), this would lead to
BR = 0 - 5 = - 5
WR = 5 - 6 = - 1
and both would have lost - the same as if no one requested
resumption. If White had a territory of 7 points
BR = 0 - 7 = - 7
WR = 7 - 6 = + 1
Black would still have lost, but White would have won - the same
as if White had requested resumption. The interesting case is when
White's territory would amount to 6 points
BR = 0 - 6 = - 6
WR = 6 - 6 = 0
Again Black would have lost, but White at least would have got
jigo. Not so with the resumption scheme: either both would lose
or both would get jigo (since Black won't call for resumption).
The last case shows that the "two results" scheme is fairer than
the "resumption" scheme because nobody gets more than his worst
case, but at least he gets that. If no effective move is around,
both schemes meet and produce what we're used to.
But since JRG89 tells us a different story and I'm no longer eager
to cure it (this whole chapter is now more or less to show how
deuced things are), I'll let it keep its resumption.
Another reason is that resumption enables (by accident?) passes
to be (trivial) ko threats, which was missing in the schemes above
for simplicity.
Fourth, if we could do without having to define "effective move",
we should. It can be questioned anyway if referring to it wasn't
more an example than a rule.
Fifth, nobody should have the feeling that he requested resumption
too early, that he should have waited a bit longer.
Sixth, rules shouldn't depend on the commentary. For instance, you
have to read JRG89's commentary on Article 9 to be told that moves
after the stop are "no moves as defined by the rules and need not
be played according to the rules" "if the players agree" and that
"if a game is resumed, any moves played not in accordance with the
rules during the period when the game was stopped are invalid". In
the extreme: "Go is a game - look up the rest in the commentary".
So, after considering all this, I'd like to (re)interpret Article
9 and 13 in this way:
After each stop (two passes in succession) players get a chance
to agree to an arbitrary final configuration (includes prisoners).
If they do, this configuration is counted in accordance with
JRG89's objectively defined terms (life, death, seki, territory).
If no agreement is reached, both privately fix their answer to
the question if they would like to resume (e.g. write it down).
If both refuse resumption, both lose. If just one refuses, he
starts in the resumption. If nobody refuses, the one to start
in the resumption is chosen randomly. Each resumption starts,
of course, with the configuration after the last stop.
To come to an end, there's only one further (final) resumption
allowed in case they dare to annoy us with an "empty" resumption
(one that consists just of passes). Should this final resumption
stop, its configuration is counted as if agreed upon.
First, this scheme will certainly come to an end if at least one
of the players wants to and no (balanced) cycles are around.
Why? Because if your opponent keeps on playing stones this will
eventually lead to a configuration consisting just of (1-point)
eyes and live stones of your color. Then:
He has to pass. You pass too. Stop. No agreement. You call for
resumption. He starts with a pass. You pass too. Empty resumption.
No agreement. You call for a (final) resumption...
An unbalanced cycle won't "help" your opponent either. After you
have piled up enough prisoners, you stick to passing. Since we
play without suicide, he again can't play stones forever and will
be caught by the final resumption.
The only way for him to go one forever is to use a balanced cycle.
But then he already could have prevented the first stop and forced
you to agree to no outcome - so this scheme is out of charge.
Note that allowing a final resumption isn't really necessary, but
it would be annoying if the player starting in a resumption would
have to play a neutral just to make sure that his opponent doesn't
end the game too soon. You only have to keep an eye on this in the
final resumption.
Second, this scheme allows passes as (trivial) ko threats.
For instance,
0 0 B 0
wont be won by Black:
Black captures. White passes. Black passes. Stop. White calls for
resumption. Black fills false eye. White recaptures. Black passes.
White fills ko. Black passes. White passes. Stop...
But what if Black passes instead to fill his false eye? Would White
be allowed to recapture after three passes? Very good question!
This is exactly one of this little annoying questions rule texts
are there to answer us. Back to the rule book:
Article 6 (ko)
A shape in which the players can alternately capture and
recapture one opposing stone is called a "ko". A player whose
stone has been captured in a ko cannot recapture in that ko on
the next move.
The question is if a pass is a "move". If not, the three passes
wouldn't count as moves, the recapture would be the "next" move,
and White wouldn't be allowed to do so. But JRG89 doesn't make this
clear. If you read the comment, you get the impression that a pass
isn't a (trivial) ko threat:
[...] White cannot [...] recapture unless he first plays
at least once elsewhere [... ,] called a "ko threat".
If a player recaptures on the next move without making a
ko threat, he forfeits the game [...].
This could even mean that White wouldn't be allowed to recapture
in the case where Black has filled his false eye because White
himself hasn't yet made a "ko threat". JRG89's text isn't of much
help. By now you should appreciate formal rule texts - undisturbed
by comments that don't address every case and thereby make things
worse.
But since I don't trust this comment and favor passes to be moves
as well as (trivial) ko threats anyway, I'll feel free to reject
this interpretation. This has consequences:
The nice one of passes being (trivial) ko threats, but also that of
a single double-ko seki leading to no outcome - what I think is
logical, because it exploits a weakness one can't get rid of, but
may not be Japanese tradition. In case you don't like this, you may
be happier with "there's at most ONE resumption".
(By the way, "no resumption may be empty" isn't a good idea. The
one behind will disagree without calling for resumption, but the
other neither wants to because he doesn't wants to be force to add
a stone when his opponent passes: both lose. And fixing this with
"neither calls for resumption is agreement" would produce garbage
in case of a forgotten effective move.)
Third, all complex questions that ask for an objective answer like
those concerning life and death or those about the existence of an
effective move aren't part of the ending scheme any more. This only
makes things unnecessarily complicated.
[W-RJ3] is of this sort, quote,
Hypothetical play is to be applied after the game stop and
before the game end for determination of allowed dame and
necessary defensive moves inside territory [...].
This intentionally restricts what can be done after the stop. Now,
after each post-stop move a re-evaluation of what is dame and what
is territory would have to be made.
Besides being a nightmare for all referees, this wouldn't work as
expected. In the second example above, White couldn't defend his
3x2 "territory" after Black takes one neutral because it still is
in seki via the other neutral - it's technically not yet territory.
White would have to resort to resumption - silly. Of course, this
could be corrected by replacing "territory" by "eye points", but
why bother at all? Why not instead let players agree to whatever
they want to? Each of them will certainly watch for himself
(safeguarded by the no-agreement path).
Unfortunately, above's re-interpretation still leaves a chance to
silently avoid defect elimination without any risk:
0 0 B 0
If they stop, agree to fill the neutral, and then let the referee
count, White will win by 1 point - despite having seki aji (Black
enters at A). It's a shortcoming of JRG89 that it only focuses on
the status of stones, not on that of area. Since the possible seki
doesn't harm the white stones' status of being alive, they surround
territory according to JRG89.
But if Black is aware, calls for resumption, and after White's
pass fills the neutral, he gives White (who may be unaware) a
hint and destroys his last chance to win.
So, there's a tension between, on one hand, always to fill all
neutrals before stop to avoid hints and, on the other hand, to
leave them empty as tradition calls for. (This tension also exists
under LJRG, but to a lesser degree because all defects, including
seki aji, spoil territory. In most cases spoiled territory is a
good enough compensation for unexploited aji. In the case above
it's even better: Black spares a throw-in.)
Inevitably, I already used the term "territory" above. Let's now
take a look how it actually is defined by JRG89.
LD-9
JRG89: All stones inside are dead, but not in territory.
Each player starting can capture the other without enabling a new
uncapturable stone, so all stones inside are dead.
By the way, this example shows clearly that the confirmation about
life and death, Article 7 is talking about, is meant hypothetical
because under normal play, with or without the pass-for-ko rule,
of course only one group would die, never both.
But what about the second part "not in territory"? What if sly
White claims that the corner is his territory? Didn't he surround
all these dead stones? Here's how JRG89 defines territory:
Article 8 (territory)
Empty points surrounded by live stones of just one player are
called "eye points". Other empty points are called "dame".
Stones which are alive but which posses dame are said to be in
"seki". Eye points surrounded by stones that are alive but not
in seki are called "territory", each eye point counting as one
point of territory.
And later JRG89 explains:
Article 10 (determining the result)
1. After agreement that the game has ended, each player removes
any opposing dead stones from his territory as is, and adds
them to his prisoners.
[...]
But weren't we just told that territorial points (or locations) are
special eye points and that eye points are empty? There never would
be anything to be removed from them.
And what's the exact meaning of "surrounded"? Is, for instance,
Tokyo surrounded by water? Japan is, and Tokyo is a part of it. On
the other hand, not every step crossing Tokyo's border will be wet.
To solve the last problem I'll interpret "X is surrounded by S" as
"S is the set of all locations that X has contact to but that don't
share X's color". If you recall the definition of "contact", this
means the same as that S is the set of all locations that can be
reached from X by repeatedly moving to neighbors that all share
X's color (including the case of staying on X) before finally
moving to one that does not (empty is a "color" in this sense).
Furthermore, I'll interpret "X posses Y" as "X has contact to Y".
But this only makes sense if we clear the paths, that's, remove
dead stones - which also solves our first problem that territory
can be underneath dead stones. But if we remove ALL dead stones
above, the corner indeed would become white territory. It seems
that this isn't JRG89's intention, quote,
If the game ends like this [LD-9], Black and White are both
dead [their stones, of course] but none of the stones can be
removed. According to Article 8 there is no territory.
Therefore I'll guess only dead OPPOSING stones are removed when we
check for territory of one side. Article 8 would then have to be
fixed like this (adding the [...] and trying to delete nothing of
the English translation of the "sacred" original text):
Article 8 (territory)
Empty [or with dead stones occupied] points [that are and
only are] surrounded by live stones of just one player
[if but not necessary only if his opponent's dead stones
would be removed] are called [this player's] "eye points".
[...]
The additions also try to fight three ambiguities:
1. One could believe that it's also fine if not one live stone
is surrounding, enabling shared territory.
2. One could believe that all live stones that surround have to
belong to the same player without excluding the possibility
that other things that aren't live stones also may surround.
3. One could believe that the condition on the points should only
hold if opposing dead stones are removed but not if they stay.
All three beliefs are wrong.
The single dead white stone in LD-9 would now spoil White's ambition
for territory.
Don't confuse the abnormal not-played-out situation above with a
"normal" one like this:
The white stones are dead. But couldn't White declare the single
black stone to be dead too, spoiling Black's territory at the left?
No. It can't avoid capture, that's right, but Black can produce a
new uncapturable black stone (on the same spot) if White captures.
The single black stone is of this odd "capturable alive" kind.
It seems that JRG89 is now producing reasonable results also in,
admittedly, silly cases - but look at this comparison:
In both diagrams the chain of 4 black stones is alive and all other
stones are dead. In the left diagram Black wins by 15 points. The
right diagram is pretty similar - just two dead stones added - but
the effect under JRG89 is enormous: jigo. This is because the dead
black stone at the left (it's dead now, contrary to above's example,
because White could now live - capturing AND preventing Black's
uncapturable stone) permits no eye points there (if we stick to
above's quote). But then the 4 empty points at the left are dame,
which puts Black in seki. (The single white one just for balance.)
LJRG won't follow this nonsense even if it faces this silly cases:
in neither diagram Black may claim territory at the board's left
side - Black wins by 4 in the first, and by 5 in the second case.
Here's another example of the both-dead type:
The four black stones at the right side are the only ones alive.
Removing the white stones produces no eye points for Black at the
left because of the two dead black stones. Since the empty point
at the left is no eye point, it's dame. But now lucky Black is
not in seki because the dead white stones on non-eye points shield
him from dame (see LD-24 - beast 24 - for the same shielding effect
- Black is shielded there from dame B byy a dead white stone sitting
on a non-eye point):
Black wins by 2 points. LJRG agrees, but would also come to this
result if the white stone on the lower edge wouldn't be there (in
which case JRG89, as understood here, would rule jigo).
Now that we seem to understand "eye point" and "dame", only one
hurdle is left to understand "territory" - that's "in seki".
Shouldn't be a problem - but look at this:
All stones are alive because they can't be captured. Black has two
eye points (at the bottom) and White has one (at the left), but
White's eye point isn't territory because the neighboring white
group possesses dame (in the "center"). For the same reason Black's
eye point in the corner isn't territory: the 4 black stones at the
right posses (or contact) the same dame.
What about Black's other eye point? The 6 black stones surrounding
it don't possess any dame. Therefore sly Black will claim the point
enclosed by them to be his territory (and White will hurry for the
referee).
Well, this certainly isn't the intention of JRG89. The whole thing
is a seki, and Japanese count nothing in sekis (even dead stones
remain in them). To fix this, Article 8 needs a further improvement
(again avoiding deletions):
Article 8 (territory)
[...]
Other empty points are called "dame".
Stones which are alive but which posses dame
[or eye points in seki] are said to be in "seki".
A Player's eye points that are surrounded by stones that are
alive but not in seki are called "territory", each eye point
counting as one point of territory.
[Non-territorial eye points are called "eye points in seki".]
The addition is that not only dame but also eye points that fail
to qualify as territory put stones in seki, and that these eye
points are to be called "eye points in seki".
The (missing) first part removes dead stones hypothetically, but
this shouldn't mislead you to believe that points dead stones are
sitting on could ever be dame (else there would be no shielding
effect like that in LD-24 or beast 24 - this isn't essential, but
I'm bound by JRG89's examples).
Now Black's non-territorial eye point in the corner - an eye point
in seki - also puts the 6 black stones into seki and prevents Black
from claiming territory.
Seki can be viewed as an epidemic that jumps between empty points
and stones: dame (the initial source) infect stones contacting them,
infected stones infect empty locations contacting them, infected
empty locations infect stones contacting them, and so on.
Everything infected is then in seki and doesn't count. (Note that,
because "contact" isn't symmetric, those contacting a sick one are
not necessary the same as those the sick one itself has contact to.)
Finished? Wait a moment - look at this:
The 3 black stones in the corner and the single white stone are
dead. Alternately removing dead stones of one color reveals that
White has 5 eye points (at the left) and Black has 4 (at the
right). Therefore the empty point on the upper edge is dame (his
right neighbor is not). If we now start our seki infection, it
will infect all white stones in the first step (they all contact
that dame), infect the empty point in the upper left corner in
the second step, but will then stop, leaving White's 4 eye points
in the lower left corner unharmed.
To fix this too, the check for infected eye points has to happen
after dead stones have been (hypothetically) removed. So finally,
we reach this version of Article 8:
Article 8 (territory)
Empty [or with dead stones occupied] points [that are and
only are] surrounded by live stones of just one player
[if but not necessary only if his opponent's dead stones
would be removed] are called [this player's] "eye points".
Other empty points are called "dame".
Stones which are alive but which posses dame
[or eye points in seki] are said to be in "seki".
A Player's eye points that [only] are surrounded by stones that
are alive but not in seki [if but not necessary only if all dead
stones would be removed from eye points] are called [his]
"territory", each eye point counting as one point of territory.
[Non-territorial eye points are called "eye points in seki".]
Note that a check for territory only makes sense, after the seki
infection has had enough time to do its job and infect as much
stones as possible.
If you now think that dame has to be filled during the game under
JRG89 to avoid seki, then you're wrong. The (dirty) trick is that
the players stop after 2 passes in a row and check if they agree
about life and death. During this agreement they don't just nod
their heads, but may also add stones to the position without
regarding them as moves obeying the rules. In this sense these
stones - mostly filling dame, some fixing defects - are not played
during the game. Only after this confirmation phase has ended, the
game ends too.
So, in the end, to identify territory under JRG89 you "only" have
to do this:
1. Identify all stones that are alive - the others are dead.
Your stone is alive if you either could prevent your opponent
from capturing it - even if he starts and plays perfect - or you
could identify some points that you couldn't manage to get a
new uncapturable stone onto - even if you start and play perfect
but he only is allowed a fixed number of stones of his choice -
but he isn't able to prevent this if he is committed to capture
your stone - even if he starts and plays perfect. (Got it? ;-)
2. Pretend all dead black stones are gone, and identify all white
eye points: those empty points that have and only have contact
to white stones alive.
3. Pretend all dead white stones are gone, and identify all black
eye points: those empty points that have and only have contact
to black stones alive.
4. Identify all dame: those empty points that aren't eye points.
5. Pretend all dead stones on eye points are gone, and perform the
seki infection: first infect all dame, and then infect stones
contacting infected empty points and empty points contacting
infected stones repeatedly until nothing new gets infected.
All eye points not infected are territory (belonging to the side
the eye point belongs to) - the others are eye points in seki.
(JRG89's examples don't suggest it, but a simpler procedure to
identify territory would be to remove ALL dead stones at once, to
identify eye points of both colors, to call remaining empty points
dame, to perform the seki infection, to call all eye points not in
seki territory, and finally to put all dead stones back.
I guess this matches the result above for all games that end
sensibly, that's, the number of dame is minimized and no dead
stones are left on eye points of the same color.)
After all there are 15 categories of points under JRG89:
empty black white
- alive dead alive dead
---------------------------------
no eye in seki | 0 5 9 6 10
no seki | - 7 - 8 -
bl eye in seki | 1 - - - 12
no seki | 3 - - - 14 (=> bl terr)
wh eye in seki | 2 - 11 - -
no seki | 4 - 13 - - (=> wh terr)
(Half of the combinations don't exist. Proofs are trivial, except
for dead stones on non-eyes not in seki, but I'll skip this here.)
Here's an example:
Now compare this with just 9 categories under LJRG
(provided nothing can be controlled by both):
empty black white
--------------------------
nobody controls | 0 3 4
Black controls | 1 5 8
White controls | 2 7 6
It's obvious that JRG89 is a mess compared to LJRG, and I think
you'll also agree that the proofs concerning life and death (or
control), inevitable under don't-play-it-out rules, are much
closer to what really goes on in our minds under LJRG than under
JRG89 - or can you remember having ever searched for a new
uncapturable stone enabled by a capture in one of your games?
Note that stone scoring has an unbeatable minimal set of categories.
Small as a haiku, I'll spare all tables and diagrams and just list
it:
empty, black, white
Before you now leave this chapter, enjoy the erring rule masters.
Proving stones to be alive is a hairy job under JRG89. If they can
not be captured, they're alive. This is the simple case. But if they
can be captured, you're confronted with the problem to prove that
one can't do so without enabling a new uncapturable stone. And if
you think you found one, don't miss to check that it really is
ENABLED by the capture. This last check is likely to be forgotten
- as we'll see.
Since "dead" is defined as not being alive, its proof is as hairy.
You always have to prove not only that those stones can be captured,
but also that one can do so without enabling a new uncapturable
stone.
In both cases the delicate part is to prove if the capture enables
the new uncapturable stone or not. Here's an example where even the
creators of JRG89 failed:
LD-1
JRG89: Seki - no territory. [?]
JRG89's original comment:
Black and White are both alive because if either side plays A,
a cut or snapback follows, resulting in new stones that cannot be
captured by the opponent. Since A is a dame point, the position is
a seki.
But it's wrong. Certainly, new uncapturable stones will pop up after
a capture, but they must be ENABLED by the capture to qualify the
captured stones as being alive.
If White captures the 4 black stones, Black will produce a new
uncapturable stone at B. Since White could prevent this simply by
doing nothing, this stone was enabled in the sense of the rules.
So, the 4 black stones are indeed alive.
But now, what if Black captures the single white stone? White can
recapture and will also produce some new uncapturable stones -
underneath the 3 black stones neighboring B. Couldn't Black argue
that this isn't enabled by his capture because he
- taking the second turn
- and restricting himself to a fixed number of stones
couldn't prevent any of those new uncapturable stones?
Yes indeed, he can. Here's the simple sequence:
Black did his best, but couldn't prevent the three new uncapturable
white stones. Actually, Black can't even prevent them with his first
turn and an infinite number of black stones, so we don't depend on
my interpretation of "enable" in Article 7 above.
Thus White managed to produce his uncapturable stones even without
committing Black to capture the single white stone. Therefore this
stone is capturable without enabling a new uncapturable white stone.
According to Article 7 we must conclude:
The single white stone is DEAD under JRG89 !
Then according to Article 8 this is 1 dead white stone in Black's
territory. Would you believe it? Ironically this position is called
"three points without capturing" because 1949 rules counted 3 points
for - guess whom - White (see [GW05] for a motivation - and no idea
why the same author tells you a couple of years later that it has to
be played out [P-JDRB]). If now 1989 rules have to count 3 points
for Black - how will LJRG deal with it? It cuts the nonsense, simply
treats it as seki, and counts nothing at all (beast 1).
Robert Jasiek, despite I don't know how many hundreds of hours
spent on JRG89, doesn't do better either. He "proves" the single
white stone to be alive [W-RJ3]. First, here's his interpretation
of "capturable living", quote,
- Let Ae, Ab, Aw be the sets of all empty, black, white
intersections of the board before any hypothetical play.
- Let x be an arbitrarily chosen but fixed player.
- Let Px be for each player x all intersections of Ae for that
x cannot play an uncapturable stone on one of them before any
hypothetical play.
- Let Sx be the union of Ab, Aw, and Px.
- Let before any hypothetical play Cx be the set of all
intersections of the board with stones that are of player
x and that do not belong to all uncapturable stones.
- A string of Cx is a "capturable living string" if in each
alternating play, that starts with the opponent of x, that
captures the string, and for which the player x cannot prohibit
the capture, x can choose plays, that are moves or passes for
kos, so that x can play an uncapturable stone on an intersection
of Sx, and if such an alternating play exists.
Got it? I'll try to repeat it in my words:
If the question arises if one of my stones is alive, and I can't
prevent you from capturing it if you start, but whenever this
happens you can't prevent now me from producing a new uncapturable
stone in a special area, then my stone in question is said to be
"capturable alive" - provided this special area (Sx) is the set of
all those intersections that, at the time the question arises, are
occupied with a stone or suffer from the property that I can't force
an uncapturable stone onto them [even if I start and you're limited
to a fixed number of stones of your choice].
So he lets Black capture the single white stone and lets White
produce a new uncapturable stone to the right of A, underneath
the removed black block. And since this location was occupied,
it's certainly in Sx for whatever color x - fanfare.
Too bad that this is plain nonsense: give me, for instance, a
2-point eye with a dead stone inside that I can afford to fill,
and I'll prove that all of my capturable stones are alive. To
allow my new uncapturable stone to pop up underneath stones of
my opponent isn't necessarily avoidable by him, and - if not -
the demonstration that I can do so is worth NOTHING. (For another
error in [W-RJ3] see beast 32.)
The obvious correction is to define my Sx as the set of all those
intersections that at the time the question arises suffer from the
property that I can't force an uncapturable stone onto them [even
if I start and you're limited to a fixed number of stones of your
choice] - no matter if they're empty or not. As shown above, all
intersections beneath the black block other than B would then not
qualify to be in White's Sx, and those that qualify won't be
exploitable by White: the single white stone is (still) dead.
The same argument used for LD-1 applies to LD-5 (beast 5):
JRG89: Black and White are both alive. [?]
By Article 8, the position is a seki.
All stones are alive - except the single white stone. It's dead.
But in this case that's of no use for Black because his stones are
in seki - 2 dame on the upper side. Therefore the dead white stone
is not in territory and will not be counted.
BESTIARY
This chapter shows how diverse positions would be counted after
the game ended. The first 25 beasts are the 25 life and death
examples of JRG89. It should be mentioned that we don't care how
the players have gone through JRG89's odd ending procedure. We'll
just judge what they show us as their final position on board -
prior to any removal of dead stones.
Therefore I completed the examples by adding outer stones and eyes,
and erasing irrelevant locations. So don't mind if a grid is shaped
like a L or U. I checked not to erase too much, triggering play
"underneath" stones or enabling sekis, but if any flaws slipped
through: please inform me.
The comments only mention and count those locations that are not
obviously part of 2-eyed groups. Please keep this in mind when
reading something like "Black controls nothing".
The official rules of 1989 are called "JRG89" (see [P-ARS90] or
[W-FH1] for an English translation of the full rule set and all
accompanying examples) and this new rules "LJRG".
For the purpose of easing comparison, I'll use following terms of
JRG89 also in the context of LJRG. Here's their translation:
1. Locations belong to a player's "territory" only if he
controls them and they aren't colored with his color.
2. Stones are in "seki" only if they sit on locations
controlled by nobody.
3. Stones are "dead" only if they sit on locations controlled
by their opposite color.
4. Stones are "alive" only if they are not dead.
Under JRG89 it's possible that dead stones sit in neither sides
territory and don't count. This never is the case under LJRG.
The beasts of JRG89 - in their corrected version - that LJRG
doesn't agree with are 1, 6, 8, 14, 15, 16, 17, and 24.
The beasts of JRG89 I've dared to correct JRG89's result are
1, 5 (marginally), and 23. 18 was corrected by Robert Jasiek.
Beast 1 "three points without capturing" or "torazu san-moku"
JRG89: Seki in lower left corner. [wrong original version]
JRG89: 1 dead white stone in black territory. [my corrected version]
LJRG: Seki in lower left corner.
We already went through this beast above. I agreed that under JRG89
the block of four black stones is capturable alive, but I disagreed
on this for the single white stone - it is dead: It can be captured,
and it can't claim a new uncapturable white stone to be ENABLED by
this because all new white stones that would pop up (underneath the
black block except 2-2) couldn't be prevented by Black anyway.
LJRG won't give anyone control of the 6 locations in the corner
because every claim that includes them can't lock them all, and
only including some of them isn't possible because the claim
wouldn't be bordered.
White should have captured. He would gain two points and win by 1
instead to lose by 4 (JRG89) respectively 1 (LJRG) - provided Black
isn't two ko threats ahead, letting him save a jigo.
Beast 2
JRG89: Seki - no territory.
LJRG: Seki - no territory.
LJRG: Neither side can lock anything taking the second turn.
Beast 3 "hane-seki"
According to [W-Ing91], hane seki was discovered by Kaise Takaaki.
JRG89: Seki - no territory.
LJRG: Seki - no territory.
Whoever captures three stones will lose everything in this fight
after his opponent occupies the center of the cleared area.
Neither does it make sense for White to capture the single black
(hane) stone because Black gains too much liberties by snap-back.
Under JRG89 all stones are therefore alive. The three big groups
are uncapturable alive. The three short ones are capturable alive.
Under LJRG Black controls nothing because he can't lock anything.
White only controls the obvious nine locations at the left side.
He can't lock the whole board, and, even if he can't be prevented
from extending his 2-eye formation on the left side as far as to
the center stone of his 3-stone group, he can't extend his claim
this far because it wouldn't be bordered any more.
Beast 4 "one slips"
JRG89: Seki - no territory.
LJRG: Seki - no territory.
This may not look familiar. Normally "one slips" is set up on two
joining sides of a bigger board, having the eye in the corner, but
let me spare as much as possible.
Black can't claim the whole board under LJRG because he can't
capture both white groups:
3 at A
3 at A prevented 2 eyes on the left side, but after 4 Black can't
again prevent 2 eyes on the right side - he has to hurry on the
left. Therefore he can't claim the whole thing. But couldn't he
just claim, say, the left one? No, because his worst case would
then look like this:
0 0 W 0
Now Black has lost his precious liberty on the right side and
won't be able to capture the five white stones at the left nor
fill his (smaller) claim with a 2-eye formation: it was not
independent from the context!
Black should have continued to gain 5 points (both capture 6
stones, but Black ends up with a 7-point territory compared
to only 2 points in White's territory).
Beast 5
JRG89: Seki. The enclosed black and [wrong original version]
white stones are all alive
JRG89: Seki. The single white stone [my corrected version]
is dead, but in no territory.
LJRG: Seki - no territory.
In analogy to beast 1, I explained above that the single white stone
is dead under JRG89 because it certainly can be captured, but it
can't claim a new uncapturable white stone to be enabled by its own
capture. But since the 5 black stones left of it posses dame, this
stone is in no territory and won't be counted.
If under LJRG Black doesn't claim the 6 corner locations, he
won't have the liberties gained there to capture the 3 white stones.
But if he extends his claim by those 6 locations, he won't be able
to fulfill it totally: White will intrude permanently after the
removal of the 4 black stones. White, on the other side, could also
try to extend his claim by the 6 locations in the corner, but now
Black will refute this claim by a play underneath the stones.
Beast 6 "long life"
JRG89: Dead black stones in a white territory.
LJRG: No territory.
LJRG: White doesn't control the left side because Black will start
and prevent 2 eyes with A again and again. Since White has to fulfill
his claim without going beyond a repeated situation, he fails.
Black can't lock anything either because White would use his right
to move first to make "knife five" at A.
Beast 7 "bent four in the corner"
JRG89: Dead white stones in black territory.
LJRG: Dead white stones in black territory.
LJRG: Black can't be prevented from locking the whole board
because he'll win the ko due to White's lack of ko threats -
not to speak of an internal one.
(If you wonder, it's called "bent four" because this form has
to be scrificed by Black in a proof. See beast 31 for a variant.)
Beast 8 "stable triple ko" or "moonshine double-ko seki"
JRG89: Dead black stones in white territory.
LJRG: No territory.
JRG89: If White starts, he can capture all black stones inside
using the pass-for-ko rule. Therefore they are dead. Black can't
capture the white stones at the right because White defends by
cycling. Therefore they are alive.
You may ask if the single white stone at the right isn't dead.
This would spoil the territory. The answer is no: this stone is
capturable alive because White will produce a new uncapturable
stone underneath it - which Black could prevent by passing.
LJRG: Black can't lock anything, but White neither. Black doesn't
even has to take the first turn. If White takes the left ko, Black
flips the double ko and recaptures, since in the hypothetical proof
the normal ko rule is still in use under LJRG. White can't ignore
the flip because this area also belongs to his claim and he has to
fill up the whole claim with a 2-eye formation.
By the way, a triple ko of exactly this type appeared between
Leszek Soldan (6d, Poland) and Christoph Gerlach (6d, Germany) in
round 6 of the EGC 1999 - with Christoph enjoying the eye. Since
Ing 1991 rules were in use, an expert had to be consulted (guess
who). Far from being impressed by his expertise, only the presence
of a similar position in the rule booklet finally convinced them:
Leszek's stones being "disturbing dead" (indeed, VERY disturbing),
prohibiting him to repeat and losing him the game and the day.
[RGG100899] [DGZ0799]
Beast 9 "resolving a direct ko"
JRG89: All stones at the right are dead, but in no territory.
LJRG: No territory.
LJRG: Nobody can lock anything. In case White claims, Black captures
and lives in White's claim. In case Black claims, White takes the ko
and wins it.
Beast 10 "approach-move ko"
JRG89: Dead white stone in black territory.
LJRG: Dead white stone in black territory.
JRG89: The difference to LD-9 is that, after White has captured the
single black stone, Black will use the pass-for-ko rule to win the
ko - the extra liberty gives him time for a ko-opening pass - and
produce the new uncapturable stone: the single black stone is
capturable alive, and the single white stone is dead.
LJRG: White can't claim being able to lock anything since Black
simply captures him. But Black can claim being able to lock the
corner because the extra liberty gives him the time he needs to
win the ko: he uses a pass as a (trivial) ko threat. After White
ataris, Black recaptures and succeeds.
Beast 11 "false eye and double-ko seki" or
"moonshine life and double-ko seki"
JRG89: The white stones in the left position are dead in territory.
LJRG: The white stones in the left position are dead in territory.
LJRG: LJRG has no problems here at all. Since Black can't and
doesn't claim anything in the double-ko seki, it is removed and
filled up with permanent white stones when proving Black's claim
for control at the left. And since no internal ko threats on the
left side exist for White either, nothing can annoy Black.
There was a centuries lasting debate in Japan on how to decide this
situation, starting with monk Nyobutsu's decision in the 13th century
that the false-eye group is not dead. This is the global view. The
rivaling local view called it dead. The decision flipped back and
forth over the time. The rules of 1949 as well as those of 1989 apply
the local view and call it dead. LJRG agrees in this case, but not
when the attacking group depends on the double ko (see beast 8). It
has to be mentioned that the exact position Nyobutsu was confronted
with is lost - it was only assumed to be of the independent type.
[W-MSO1]
Beast 12 "ten thousand year ko" or "mannen ko"
JRG89: Seki - no territory. All stones alive.
LJRG: Seki - no territory.
LJRG: Neither side can lock anything. If Black claims he could
lock the board, White simply connects (to pass would also work).
Should Black then sacrifice his stones, White will live. And if
instead White claims he could lock the board, Black passes until
White approached. Then he takes the ko, captures the remaining
white stones after White's pass, and builds two eyes in White's
claim.
JRG89: Black can't capture White by taking the ko and approaching
because White would have time to pass for the ko, but White can't
capture Black either because after his approach Black takes the
ko, and passing for it is now too slow.
But what about the single white stone? Is it dead or alive?
JRG89's official commentary states that all stones are alive.
Since the single white stones is certainly not uncapturable, it
must be capturable alive. Black could try to refute this: Black
captures it, White passes for the ko, and now Black passes too
(instead to approach as told in [W-RJ3]).
Where will White now produce his new uncapturable stone? Of course,
he recaptures the ko, but after Black passes again for this ko we
have the same situation: the (new) single white stone is still
capturable.
The solution is that White connects the ko and thereby makes the
former stone uncapturable. Note that the connecting stone itself
doesn't qualify to be the new uncapturable stone because Black
never could have prevented it anyway.
Note that this example suggests that JRG89's new uncapturable stone
doesn't has to be uncapturable in the very moment of its staging.
It further suggests that passes for a ko don't take part in ending
JRG89's hypothetical play.
Note that if the ko is in a state as if Black captured last, White
can't be prevented from gaining a point before the end by capturing
and connecting (under either of the two rule sets).
Now imagine that sly White is behind and rufuses to do so, just for
the purpose of not to let the game end. This is possible if passing
is unrestricted and game end is defined in a complex way like "the
game is over if neither player can gain anything more".
This definition is quite popular in go introductions and at least
is better than "the game is over if both players agree", but it
leads to an impasse. Black could only overcome White's tactics if
he can afford to let his group die by filling the ko. Very strange.
If you now think this is just the mad fantasy of a rule addict like
me, you'll be surprised to hear that exactly this once happened. In
round 2 of the 1928 Autumn Oteai, Takahashi Shigeyuki pulled this
trick against Segoe Kensaku. Segoe was clearly ahead, despite giving
two handicap stones. After Takahashi made move 302, there were only
12 neutrals and one mannen ko left. Takahashi had the option in it:
rest omitted
Segoe went on and filled the first neutral, expecting Takahashi to
take the ko and to connect it subsequently since neither side had
reasonable ko threats, but Takahashi filled the second neutral
instead. They continued in this manner until Takahashi eventually
filled the last neutral.
Segoe, having no more left to play, laughed and expressed his
bewilderment. Referee Iwasa Kei told Takahashi that he should
have made seki long before since the game already was over. But
Kubomatsu came over and claimed it to be a void game because no
game can be over with a ko still pending. Segoe expected the
mannen ko to be treated as seki since there were no reasonable
ko threats around, but Takahashi just didn't believe that it was
a mere seki and wanted the game to be treated as finished - but
without having achieved a result (which isn't far from saying
that it hasn't ended).
Wow, what a mess. All other games were suspended because the
outcome of the whole East-West match was affected. The dispute
raged for a month, without any agreement. The final ruling of
the referees was
We declare that in the position up to move 302
White [Segoe] is adjudged to have won.
However, this decision is limited to this game.
Additionally, Takahashi was said to haven't lost because the
fundamental problem still was waiting to be solved. [W-MSO2]
"Just" 21 years later, 1949, Japan created its first written go
rules.
Beast 13
JRG89: Seki - no territory. All stones alive.
LJRG: Seki - no territory.
LJRG: Surely White can't claim to be able to lock anything because
Black, getting the first turn, simply passes, letting it stay a seki
and preventing White from building a 2-eye formation. If Black
claims the whole board, White passes too. He can't prevent Black
from sacrificing 3 stones and start a ko in the lower left corner,
but since White captures first in this ko and there are no internal
ko threats for Black, this is useless for Black.
Beast 14
JRG89: Dead white stones in black territory.
LJRG: Seki - no territory.
JRG89: Black can capture White if he has the first turn. White,
on the other side, can "only" produce a seki with the first turn.
White should have made seki by throw-in before the end and accept
losing a point (if Black doesn't forget to capture before end).
LJRG: Both sides can make a seki if they get the first turn. White
throws in a stone. Black just passes. So nobody can lock anything
because the claiming player has to do with the second turn.
Notice that under LJRG White can avoid losing a point by throw-in
if the ko threats favor him. A claiming player can never base his
claim on (non-trivial) ko threats (regardless if internal or
external), but, as this example shows, the refuting player CAN -
provided getting first turn compensates for losing external ko
threats (in the proof).
Beast 15
JRG89: Dead white stones in black territory.
LJRG: No territory.
LJRG: Black can't lock anything because White starts a ko in the
upper right corner and then ataris the single black stone with A.
Black can't exclude this ko threat because he has to include this
stone in his claim for the purpose of bordering - in this sense
the ko threat is "internal" to the upper right corner.
White neither controls anything because each of his claims will
suffer from white stones in atari - Black starts, captures them,
and intrudes.
If Black wants to avoid above's disaster, he has to connect at A
before the game ends. White can then gain another point by starting
the ko - even if he lacks ko threats. After Black captured in it,
White simply passes. Since a direct ko would prevent his lock, Black
can't allow the game to end without filling it. By playing one stone
more than White inside his territory he loses a second point.
The same would happen under JRG89, except that Black could omit A:
Black loses only one point.
Beast 16
JRG89: Dead white stones in black territory.
LJRG: Seki - no territory.
LJRG: Similar to LD-8. If Black wants to declare the white stones
on the lower side dead, he has to include his 7-stone group at the
right to close the border. But this group needs 2 liberties. So
Black has to extend his claim over its eye and the lower ko.
Bordering is ok, but one stone in the border again is in atari.
Black is forced to add the rest of the right side to his claim, but
then White will exploit the double ko for ko threats and refute the
claim by cycling.
Beast 17
JRG89: Dead white stones in black territory.
LJRG: Seki - no territory.
LJRG: Again Black can't declare White's corner group to be dead
because of the double ko he has to include in his claim. White
will exploit it to defend the liberty in ko on the right side.
If Black tries to bring White down to 1 liberty in the corner to
make the ko threats worthless, a further ko in the corner will
start. Black captures first in it, but since White still enjoys
his outer liberty, he has time to flip the double ko, recapture,
and win this ko.
Beast 18 "bent four i.t.c. with irremovable internal threat"
JRG89: Dead black stones in white territory. [wrong original version]
JRG89: Seki. [RJ's corrected version]
Stones in the double ko are dead,
but in no territory.
LJRG: Seki - no territory.
JRG89: For the longest time I took JRG89's example for granted. I
had to stumbled over [RGG151199] to get it. Of course, Robert Jasiek
is right. White has no chance to capture black stones under pass-for-
ko, except those in ko. This is because he has to omit a pass in the
double ko to make atari via bent four. His stones are caught and he
has to throw a stone into the cleared area to prevent two eyes. Now
Black doesn't setup the ko as usual (and maybe I did), but simply
captures in the double ko since White isn't yet allowed to do alike.
It's not a matter of ko threats, it's just a lack of liberties.
(By the way, Robert Jasiek's suggestion to solve this problem by
letting passes unlock ALL kos wouldn't work. Imagine two approach-
move kos (beast 10) hanging around. You start one and approach when
your opponent passes. He recaptures. You do the same in the second.
Then you pass, unlocking both kos simultaneously. Either you save
your stone, or you produce a new uncapturable one: not JRG89's
intention.)
LJRG: The bent four isn't dead here because White can't ignore the
threats in the double ko. If he does, capturing the black stones on
the right side, Black would capture in the second-step ko and build
two eyes in White's claim. Of course, White can't exclude the double
ko from his claim because the big white group needs these liberties.
So under LJRG bent four isn't dead in every case any more - but it
wasn't anyway (see beast 31).
Notice that in this special situation White can't enhance his proof
by removing the internal ko threats during the proof before starting
the ko, because he needs the liberties. In most other cases he will
be able to do so because he can hold back the ko. Therefore bent
four in the corner still is dead in most cases under LJRG - except
when INTERNAL ko threats are irremovable, like here.
Whoever invented this example: THANK you - and I hope you're
pleased by LJRG's ruling (even if this isn't such a big deal any
more since I realized that JRG89 in fact rules in the same way).
(Also included in [W-ST] - chapter VI, diag. 11.)
Beast 19
JRG89: Dead black stones in white territory. [unchecked by me]
LJRG: Dead black stones in white territory.
Under LJRG White will claim that he can lock the whole board.
One path of the proof would go like this:
3 passed
Now White captures first in the ko and wins.
Beast 20
JRG89: Both are alive. Seki. [unchecked by me]
LJRG: Both are alive. Seki.
Under LJRG White's claim of being able to lock the whole board
will be refuted like this:
3 passed
Black is faster.
But Black can't claim control of the whole board either:
1 passed
17 passed
Black's claim failed.
Notice that Black must avoid giving White the chance of ko in the
upper right corner in all cases where White could then capture the
second ko on the upper side with atari or - in case he already has -
give atari by extending his stone in that ko. This would be a ko
threat Black couldn't ignore.
Beast 21
JRG89: Dead white stones in black territory. [unchecked by me]
LJRG: Dead white stones in black territory.
Under LJRG Black claims that he can lock the whole board.
If White starts with a pass, things could continue like this:
1 passed
White will win the ko. Black failed. This illustrates how internal
ko threats under LJRG help the refuting player.
But Black can do better:
1 passed
13 passed
24 passed
Black succeeds finally.
This beast shows the drawback of all go rules that don't play
things out, including LJRG: the proof that something is dead can
be very complex. And if one avoids going through all possible
paths, one could err. Intuition is certainly at its limit here.
Beast 22
JRG89: Dead white stones in black territory.
LJRG: Dead white stones in black territory.
LJRG: Black claims the whole board. White starts but finds nothing
better than to pass. Black captures 3 stones and conquers the right
side, fueled by the liberties he has gained.
Beast 23
JRG89: Dead white stones in black territory. [wrong original version]
JRG89: Seki. All stones alive, except 2 [my corrected version]
dead white stones in the upper right
corner and 3 dead white stones in the
lower right corner - but all 5 not in territory.
LJRG: Seki. No territory.
White certainly can't capture the black stones. Could Black capture
the white stones in the mid? No. The proof below holds for both rule
sets.
Under LJRG Black claims the whole board and White gets the first
turn. But since White passes, we'll label black stones with odd
numbers in this case too. Under LJRG we could use the internal ko
threats in the seki at the left, but (again to unify) we'll do
without them here:
9 passed (for ko under '89)
The situation after 10 is the same as the one after 4. Black won't
ever capture the white stones in the mid and, therefore, under JRG89
these stones are alive, and under LJRG Black's claim to be able to
lock the whole board has failed.
Notice that JRG89 will call the 3 white stones in the lower right
corner dead, but won't count them because the surrounding black
group is in seki (see discussion of Article 8 above).
You may ask what the purpose of the seki at the left is. Good
question. It prevents Black to start the same cyclic attack as above
BEFORE game end. In case he tries - hoping to continue till he had
piled up enough white prisoners to retire - White uses his 2 ko
threats in this seki to win the ko. (Remember that under JRG89
these ko threats are worthless AFTER the end.) Instead to connect
the ko with 4, as above, White continues like this:
When White recaptures the ko with 14, Black's disaster is complete.
So, proving life this easily, why does JRG89's original comment
(below) declares them to be dead?
From Article 7 clauses 1 and 2 and the purpose of the game
stated in Article 1, Black is alive and White is dead. If
White plays A [upper right corner location] before the end
of the game, the position becomes a seki, but Black can
capture 9 white stones while White captures 1 black stone.
The mentioned Article 7 defines life and death, we've gone through
it in detail above, and Article 1 reads like this:
Article 1 (The game of go)
Go is a game in which two players compete in skill
on a board, from the beginning of the game until the
game stops according to Article 9, to see which can
take more territory. A "game" refers to the moves
played until the "end of the game."
It reminds you about your aim or purpose to play in case you have
forgotten it: taking more territory. Neither convinces me nor
should convince you. Cloudy arguments won't do. At least we can
guess what was meant. The problem with White's defense above is
that White loses stones at a higher rate than Black. But nowhere
in Article 7 this affects the definition of being alive. Period.
And don't tell me that the stones played in the confirmation of
life and death belong to the game because the "end of the game"
hasn't been reached. Because if this confirmation isn't just
hypothetical play in our minds, then an equal number of black
and white stones would have to be used, and then Black's pass
would also cost him something.
Another reason for the hypothetical-play interpretation is beast 9:
the starting player could save his stones - breaking symmetry.
But to understand the comment, let's pretend it's right. This would
mean that White's cyclic defense, unbalanced in Black's favor, would
be useless, and that the white stones would be declared dead after
the end. Being aware of this, it would be wise for White to connect
in the corner before end because then White wouldn't depend on a
cyclic defense any more after the end:
Now Black is in atari but can't recapture the ko: he didn't yet pass
for this ko as the pass-for-ko rule, effective after the end, asks
for. So, White's defense is much cheaper now and seems to convince
the 1989 rule committee: White is (uncapturable) alive - seki.
That's the reason for White connecting in the corner - forced by the
rigid 1989 rule committee, not by their rules! Now the time has come
for Black to change plans. Instead to end and gain nothing from this
seki, he squeezes as much out of it as possible before end:
0 3 W 0
0 6 W 0
1 8 W 0 (8 passed)
1 9 W 0
Black managed to capture 9 white stones and only gave one black.
Notice that Black again can't risk the ko in the corner because
of White's 2 ko threats in the seki on the left side, and that
White has to avoid the second-step ko to start because his ko
threats would then be worthless.
That's the background for JRG89's comment. But since an unbalanced
cyclic defense after the end is nowhere punished in JRG89, I have
to disagree and allow White to have seki according to JRG89 without
filling the upper right corner location.
A very interesting beast.
Beast 24 "filling dame to obtain territory - two-stage ko"
JRG89: Seki - provided game ended. White should fill A, B, C
to get 2 points. Black should fill A to get 3 points.
LJRG: 2 points for White and 3 for Black - without filling.
JRG89's Article 8 punishes contacting dame with seki. In the
confirmation phase both players must therefore fill up dame
before they end the game. There's no doubt that A is dame. It
has contact to live stones of both colors. What about B and C?
(In the following I use my interpretation of Article 8 above.)
The white stone below B is dead. The one left of B is alive. If
we remove dead white stones, B wouldn't qualify as eye point.
Neither would it if we remove dead black stones.
In both cases not only live stones of just one player surround
B - it's dame. The same test shows that C is a white eye point.
Since B is dame, stones alive contacting it are in seki. This is
the case for the white stone left of B. This prevents the white eye
point C from becoming (white) territory: not all of its surrounding
stones (after removal of dead black stones) are alive and not in
seki. And since C is a non-territorial eye point or eye point in
seki, the stones contacting it are in seki too. And this finally
also prevents the 2 remaining white eye points to become territory.
White has to get rid of dame and eye points in seki if he wants to
convert these 2 eye points into territory - he has to fill B and C.
LJRG doesn't care about dame. Sekis are where nobody controls
something. White certainly controls the 2 empty locations and the
stones bordering them on the upper side, as does Black control
the 3 empty locations and the stones bordering them on the lower
side. Nobody certainly controls A. And B and C aren't controlled
by White, even if he bordered them, because, depending on how far
White extends his claim, one of the single white stones will end
up as a border stone. Proof setup will atari this stone by the
permanent black stones on the outside, letting Black capture,
connect, and refute Whites claim.
Beast 25 "double-ko seki"
JRG89: Seki. The single stones are dead, but in no territory.
LJRG: Seki - no territory.
LJRG: Nobody can claim anything here because nobody will be able
to fill the board with a 2-eye formation - even if he were allowed
to start. Since not one location is controlled by anyone, there
certainly are no dead stones around.
Beast 26 "rattlesnake - ends colored alike"
JRG89: Dead white stones in black territory.
LJRG: Everything except the ends is a seki.
JRG89 would argue as follows: Black ataris the, let's say, left
white group by approaching. A flip in the double ko follows, but
after the flip the white group is still in atari and both kos are
waiting for their pass each. Nothing else will open them.
Therefore Black has time to defend whatever White tries on the rest
of the board, preventing any uncapturable new stones if needed, and
eventually captures all white stones at the left. This proved that
they are dead. Similar on the right.
LJRG is more sensible. If Black claims to be able to lock the
whole board, White will refute this by starting an endless cyclic
attack, flipping the double kos. Black must keep up in those kos
because he may not lose anything of his claim. Technically the
proof - or better each path in it - will stop at the first repeated
situation.
And if Black tries to claim only one white group? His own center
stones will be ataried by the permanent white stones filling up
the rest. White will capture some and extend into Black's claim.
I invented this beast to bring down one of my former rules.
The false eyes aren't essential any more, but at that time their
purpose was to force the rules to treat the double kos separately.
As we've seen: LJRG does not.
Notice that the rattlesnake can grow:
Both arguments above still hold: JRG89 piling up dead white stones,
and LJRG only counting the ends for Black.
Why kill'em? Let'em rattle.
Beast 27 "rattlesnake - ends colored opposite"
JRG89: I guess the 5 white stones at the left and the 5 black ones
at the right are dead in territory, and the 2 stones in the center
double ko are dead in no territory - but don't nail me down.
I didn't check for the uncapturable new stone.
LJRG: Only the ends count - 2 points for each.
Beast 28 "bent four with large internal ko threat"
[0 3 B 2]
JRG89: Dead white stones at the right and lower side
in territory - Black wins by 25 points.
LJRG: Seki - Black wins by 1 point.
This example is taken from [P-Ing86].
Under JRG89 Black will never touch the bent four till game end.
After end, ko threats are worthless due to the pass-for-ko rule.
Therefore Black can capture the bent four and the seki collapses,
demonstrating that they are dead.
Under LJRG Black won't start the ko either because he'll lose
16 - 14 = 2 points, and after the end Black can't separate the ko
threat from the bent four because his stones surrounding it would
only keep 1 liberty in the lower right corner - not enough to lock
the right side. And if he includes the lower left corner in his
claim, the ko threat will make locking the whole claim impossible.
Since empty locations only count if they are controlled, Black
- controlling nothing - can't count the 2 corners he has surrounded
on the lower edge.
If the threat were worth 3 points less, Black should start the ko
before game end.
Beast 29 "bent four with small external ko threat"
[0 0 B 2]
JRG89: Dead white stones on the left side
in territory - Black wins by 15 points.
LJRG: Dead white stones on the left side
- Black wins by 15 points.
This example is taken from [P-Ing86].
Under JRG89 the ko threat is worthless after the end due to the
pass-for-ko rule. Therefore Black can hypothetically capture the
bent four without giving White compensation, proving that it's
dead.
Under LJRG Black can separate the ko threat from the bent four
because his stones surrounding the bent four don't depend on it
- are independent from outer liberties. He therefore controls
the left side, agreeing with JRG89.
Beast 30 "double bent four"
[0 1 B 2]
JRG89: Dead stones on the upper side, but not
in territory - Black wins by 11 points.
LJRG: Nobody controls the upper side
- Black wins by 11 points.
This example is taken from [P-Ing86].
If the game ended like this, JRG89 would declare all stones on the
upper side to be dead but in no territory. The starting player can
capture all - without allowing a new uncapturable stone. Note that
both sides will avoid the ko in their proof because their opponent
would capture first - a big advantage under the pass-for-ko rule.
But all these dead stones aren't in territory because taking out
dead stones of just one color won't produce eye points - always
some surrounding dead stones remain to spoil it. Note that ignoring
dead stones of BOTH colors would produce black territory.
Since the advantage of having the first turn is lost after the
end, Black would have done better if he had extended his 3 stones
to form the bent four before game end. White will pass because
he'll lose the semeai anyway. Black passes too, the game stops,
and according to Article 7 all white stones are dead for the same
reason as above. But the black stones now no more because, even if
White starts, Black is still ahead in the capture race.
The argument under LJRG is almost the same. If ended, nobody
would control the upper side because the refuting player starts.
Therefore Black continues the semeai by forming the bent four.
White drops his hopes and passes. Black passes too. Since no ko
capture preceded the 2 passes, the game has ended. Now Black
claims to be able to lock the whole board. He's right because,
even if White starts in his effort to refute Black's claim, Black
still is ahead in the semeai. And a ko won't help White either
because Black captures first and there's no internal ko threat.
White, on the other side, can't claim anything because Black would
then be ahead by 2 moves.
The count then proceeds as under JRG89.
Beast 31 "bent four in the corner on 3x3"
This is the smallest bent four in the corner on rectangular
boards and - watch it - it is not of the common dead type.
JRG89: Seki.
LJRG: Seki.
Since nobody can make 2 eyes, nobody controls anything under LJRG.
Under JRG89 White proves that he is capturable alive as follows:
2 and 4 passed
12 at 10
Despite Black trying hard to prevent it, finally White's new
uncapturable stone emerged (fanfare).
Note that it won't help Black to pass at any time because White
will continue and nevertheless produce his new uncapturable stone.
Since all these new white stones pop up underneath the white stones
in question, they are trivially "enabled" by the capture.
(Prove for yourself that the black stones are uncapturable.)
Beast 32 "bent four in the corner on 4x3"
Here's another minimization of bent four in the corner that's not
of the common dead type (as Robert Jasiek falsely claims [W-RJ3]):
JRG89: Seki.
LJRG: Seki.
If Black approaches (after the end), White won't capture (even
if this would work too) but simply pass:
2 passed
White's 4 prevents Black from making 2 eyes and is uncapturable,
for instance:
8,10 passed
18,20 passed
JRG89 and LJRG both judge this mini bent four as a seki:
LJRG simply because nobody is able to build 2 eyes, and JRG89
because the 3 black stones are uncapturable (prove it yourself)
and the 7 white ones are capturable alive as sketched above -
their capture enables the new uncapturable white stone at 4.
Beast 33 "Unsound pass-for-ko rule"
JRG89: Black wins by 15 (jigo if resumed).
LJRG: White wins by 1.
This beast is essentially that from James Davies [RGG150696].
I just shrank it and swapped colors (to avoid White being a
move ahead).
JRG89 would not only call the black stones at the right dead, but
also the white ones. Why? Because Black can capture them using the
pass-for-ko rule: Black takes the upper ko and - after White defends
his upper eye - also the lower ko. If White now wants to retake one
of them, he first has to (identify it and) pass. But this lets Black
take the third ko and White is lost.
Since all those dead stones are in no territory, Black wins by 15.
For this reason White will add a stone and a jigo will result.
Note that White risks nothing by requesting resumption here
because Black can't make any use of the first turn (without the
pass-for-ko rule).
LJRG will give White a 1-point win (16-15) because he controls
the right side - as everyone would expect. There's no peculiar
pass-for-ko rule that prevents him from retaking the older ko,
saving his second eye, and eventually filling the whole right
side with a 2-eye formation.
Beast 34 "Cyclops on 9x9"
JRG89: Black wins by 1 (if not resumed).
LJRG: Seki.
JRG89 calls the black stones (capturable) alive because their
capture enables new uncapturable black stones (on san-san, for
instance). Therefore the eye in the center is territory.
LJRG only laughs at this judgement and, of course, gives no one
control of any location because neither side can lock the whole
board (and Black neither can lock the whole board exclusive its
center, of course).
According to [W-RJ3] this is John Tromp's joke. Hope he likes how
I named his baby. Here's how it may have looked right after birth:
Area scoring: Black wins by 3.
Stone scoring: Black wins by 2.
JRG89: Black wins by 1.
LJRG: Both score 0 - jigo.
CONCLUSION
This text presented precise rules to capture the essence of the
Japanese Rules of Go, added some new ideas, and took a critical
view on the official Japanese rules of 1989.
The focus in this text was to give Japanese rules a solid base,
not to prove that they're better than playing things out. Since
I prefer diversity over global unification, I hope having done
my best to save them from extinction.
If, for instance, we would use pass stones as suggested above, we
would effectively convert to area (or Chinese) scoring through
the backdoor - be aware of this.
One man's clinker is another man's nugget. Many of us got used to
Japanese rules, many books explain the game in their terms, and,
as was certainly shown here, they're not illogical at all - even
if their opponents don't get tired telling us.
Of course, the official rules of 1989 are no big help in this
discussion - or do you want to defend that seki is an exception,
that life and death is defined bizarrely, that the game may end
with no outcome or even with both losing, that a game that seemed
ended can be resumed, that unfilled neutrals enable the riskless
avoidance of defect elimination, and, finally, that dependencies
with internal ko threats are completely ignored (external ones
have to be ignored if we don't want to play it out) ?
Compare it with physics: if a theory explains things well, it stays
in use, but if it fails to explain only a single phenomena, it has
to be revised or be replaced by a new theory.
Could it be that LJRG are the logical,
loop-hole-free, unimpeachable,
and formal territory rules
most doubt could ever
be formulated, but
nevertheless
eagerly are
waiting
for
?
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REF's
At this point many thanks to Georg Nassiokas for providing me with
some of the material below.
The references aren't sorted by author but by "channel":
DGZxx Deutsche Go Zeitung (German Go Journal, 7+8'94=0794)
GMRxx Go Monthly Review
GR-xx Go Review (winter starts year)
GWxx Go World
P-xx paper, book, copy, or the kind
RGGxx news://rec.games.go (sometimes meaning the whole thread)
or groups.google.com/groups?group=rec.games.go (formerly www.deja.com)
(xx = ddmmyy = day month year)
SL-xx http://senseis.xmp.net/?FrontPage
W-xx WWW (http://...)
[DGZ0669] "Gedanken zu einem seltsamen Unentschieden"
Horst Hausa
Deutsche Go Zeitung ("DGoZ"), 1969, No. 6,
pp. 1.1.326-1.1.328, pp. 8.1.11-8.1.14
[DGZ0687a] "Der Meijin Titelkampf 1987 - 3. Runde - Der Alptraum"
DGoZ, 1987, No. 6, pp. 46-47
[DGZ0687b] "Der Meijin Titelkampf 1987 - 4. Runde"
DGoZ, 1987, No. 6, pp. 47-48
[DGZ0490] "Verbesserungvorschlaege zum Einstufungsystem
von koreanischen Berufsspielern"
Kang Chol-Min
DGoZ, 1990, No. 4, pp. 38-40
[DGZ1093] "Honinbo-Partie: Ewiges Leben"
James Davies (transl. Klaus Blumberg)
DGoZ, 1993, No. 10, p. 16
[DGZ1293] "Kommentar zum 'Ewiges Leben'..."
Werner Fabry
DGoZ, 1993, No. 12, p. 13
[DGZ0794a] "Japans staerkster Amateur"
Klaus Blumberg (transl.)
DGoZ, 1994, No. 7+8, p. 8
[DGZ0794b] "Tong-Yang Secuirities Cup"
Klaus Blumberg (transl.)
DGoZ, 1994, No. 7+8, p. 8
[DGZ0994] "Hoefliche Eroeffnung"
Christoph Gerlach
DGoZ, 1994, No. 9+10, p. 14
[DGZ0395] "Rui - Feng (2)"
DGoZ, 1995, No. 3+4, pp. 22-23
[DGZ0595] "Kato - Cho (1)"
DGoZ, 1995, No. 5+6, p. 16
[DGZ0796] "Go auf dem runden Brett"
Harald Schwarz
DGoZ, 1996, No. 7+8, pp. 50-51
[DGZ0198a] "23. Tengen, Game 3"
Klaus Blumberg (transl.)
DGoZ, 1998, No. 1+2, p. 12
[DGZ0198b] "Go-Probleme"
Andreas Fecke
DGoZ, 1998, No. 1+2, p. 36, problem 1
[DGZ0598] "Die Benimmecke der DGoZ"
DGoZ, 1998, No. 5+6, p. 41
[DGZ0799] "43. Go-Europameisterschaft in Podbanske/Slowakei"
Christoph Gerlach
DGoZ, 1999, No. 7+8, pp. 15-16
[DGZ1099] "24. Meijin"
Klaus Blumberg (transl.)
DGoZ, 1999, No. 9+10, p. 8
[DGZ0102] "Regeldisput am Ende der 5. Kisei-Partie"
N.N.
DGoZ, 2002, No. 1, pp. 24-27
[DGZ0202a] "26. Kisei"
Thomas Rolle
DGoZ, 2002, No. 2, pp. 32-33
[DGZ0202b] "Problemgo"
Andreas Fecke
DGoZ, 2002, No. 2, p. 44, problem 4
[DGZ0402] "46. Go-Europameisterschaft in Zagreb"
Guido Tautorat
DGoZ, 2002, No. 4, p. 14
[DGZ0502a] "Kiel"
Juergen Beetz
DGoZ, 2002, No. 5, p. 7
[DGZ0502b] "Bochum"
Andreas Fecke
DGoZ, 2002, No. 5, p. 9 + 32
[DGZ0502c] "6,5 Komi"
Thomas Rolle
DGoZ, 2002, No. 5, p. 23
[DGZ0602a] "40. Ama/Pro Honinbo"
Thomas Rolle (transl.)
DGoZ, 2002, No. 6, p. 21
[DGZ0602b] "50. Oza"
Thomas Rolle (transl.)
DGoZ, 2002, No. 6, p. 22
[DGZ0602c] "Karl-Ernst Paech zum 80. Geburtstag (3)"
Karl Scheitler
DGoZ, 2002, No. 6, pp. 35-38 (37)
[DGZ0103a] "Abschaffung des Oteai"
DGoZ, 2003, No. 1, p. 31
[DGZ0103b] "Ausschreibung der Vereins-DM"
DGoZ, 2003, No. 1, p. 38
[GMR0469] "Famous Games [...] XII"
Go Monthly Review, No. 4, 1969, p. 53
[GMR1069] "Takagawa beats Go Seigen by a rule"
Go Monthly Review, No. 10, 1969, pp. 17-23
["No komi" is wrong: it's 4.5]
[GR-Au73] "The 1973 Honinbo Tournament"
Go Review, Autumn 1973, 4th game, p. 17
[GR-Sp74] "From Iwamotos sensei's One Page Lesson"
Iwamoto [Kaoru]
Go Review, Spring 1974, p. 78
[GR-Su74] "Rin Kaiho's Fan"
Seichi Ezaki
Go Review, Summer 1974, pp. 31-36
[GR-Wi75] "Meijin Title Match: 5th Game"
Go Review, Winter 1975, pp. 8-19
[GR-Au75] "Honinbo Title Match: 7th Game"
Go Review, Autumn 1975, pp. 16-22
[GR-Sp76] "14th Meijin Title - 7th Game"
Go Review, Spring 1976, pp. 29-37
[GW05] "The Chinese Rules of Go"
James Davies
Go World No. 5, Jan-Feb 1978, pp. 30-40
[GW45a] "When Is a Ko Not a Ko?"
Bob Terry
Go World No. 45, Autumn 1986, pp. 58-60
[GW45b] "Why Not Eliminate the Irrational in Go?"
Kudo Norio, O Meien, Murakami Akira
Go World No. 45, Autumn 1986, pp. 60-64
[GW50a] "Strange and Wonderful Shapes"
Haruyama Isamu
Go World No. 50, Winter 1987/88, pp. 16-22
[GW50b] "The Professional Rating Tournament"
John Power
Go World No. 50, Winter 1987/88, pp. 47-52
[GW50c] "The Suspicious Jigos"
Nakayama Noriyuki
Go World No. 50, Winter 1987/88, p. 53
[GW60] "Monster Go"
John Fairbairn
Go World No. 60, Summer 1990, pp. 46-48
[GW71a] "A Commemoration of Dr. Yang Liansheng's
Contribution to Goe Rules, Part One"
Ing Chang-Ki
Go World No. 71 [no season], pp. 7-13
[GW71b] "Where Is the '$1,000 Ko'?"
Elwyn Berlekamp & Yonghoan Kim
Go World No. 71 [no season], pp. 65-80
[GW72] "History of Codification of Goe Rules"
Ing Chang-Ki
Go World No. 72, Spring 1995, pp. 12-13
[I've no idea why Ing calls it "Goe"]
[P-ARS90] "The Japanese Rules of Go"
Anton Steiniger (ed.)
ARS electronica brochure, 1990, pp. 97-117
[P-BZHZ] "Spielklassenberechnung nach der Karlsruher Methode"
Bodo Zinser & Hans Zschintzsch
paper copy
[P-DB] "Live in the Game of Go"
David B. Benson
Computer Games II, D.N.L. Levy (ed.), 1988, pp. 203-213
or www.cs.ualberta.ca/~games/go/notes/020717/benson.pdf
[P-IK] "Go - Das faszinierende Brettspiel aus China"
Kaoru Iwamoto [family name given last]
1984, p. 150, dia. 4
[P-JDRB] "An Introduction to Go"
James Davies & Richard Bozulich
1984, pp. 10-11
[P-JIE] "Go: Battle in Black and White"
James Davies
Japan - An Illustrated Encyclopedia, pp. 460-461
[P-MK] "Go - Die Mitte des Himmels"
Michael Koulen
1994, p.31, p. 127
[P-Prag93] "Strange Dispute"
Brian Timmings, George ? (ed.), Niek van Diepen
Newsletters 3 and 5, European Go Congress, 1993, Prague
[P-Ing86] "The SST Laws of Wei-Ch'i"
(1986 version)
Ing Chang-Ki
[P-WD] "Das japanische Brettspiel Go"
Winfried Doerholt
1978, Falken-Verlag, p. 12
[RGG150293] "Re: Sealed moves and morality"
Wilfred Hansen
[RGG011093] "Re: How strong is a professional?"
Niek van Diepen
[RGG090595] "A fun thing...the PHINWHEEL KO"
Bill Taylor
[RGG090895] "Lasker-Maas rules for the game of Go..."
Robert Elton Maas
or www-2.cs.cmu.edu/~wjh/go/tmp/rules/Lasker.html
(By the way, it's Edward Lasker, not the famous Emanuel)
[RGG300196] "Re: A question about territory"
Eric Osman
[RGG150696] "Problem in Japanese rules"
James Davies
[RGG010997] "Re: Simple Rules, was: ~20 kyu question"
John Rickard
[RGG110997] "Re: The worst practical case, was: In remembrance ..."
Denis Feldmann
[RGG120997] "Re: The worst practical case, was: In remembrance ..."
Louise Bremner
[RGG140998] "International Rules"
Robert Jasiek
[RGG090299] "Komi?"
John Fairbairn
[RGG100899] "EGC Triple Ko"
Robert Jasiek [was consulted]
[RGG151199] "Reinterpretation of official Pass for Ko Rule"
Robert Jasiek
[RGG170101] "Re: Japanese rules - Article 9.2"
Bill Spight
[RGG190202] "Re: Point to pass?"
Hans F. Zschintzsch [played White]
[RGG220202a] "Video Clarification of Kisei result"
Louise Bremner
[RGG220202b] "Re: Ryu's mistake"
T. Mark Hall
[RGG220202c] "Rules glitches"
John Fairbairn
[RGG100702] "Area vs Territory"
"Planar"
[RGG120902] "Decision about Robert's protest"
Matti Siivola
[RGG250902] "Game End Under Ing 1991 Rules"
Robert Jasiek
[RGG281102] "Re: Komi for non 19x19 games"
Bill Taylor
[RGG090303] "Why is play forced when the end [...] is disputed?"
Tim Martin
[RGG040403] "Rules incident" [well, not really]
John Fairbairn
[SL1] "Amateur Honinbo vs Pro Honinbo 2002"
Dave Sigaty
senseis.xmp.net/?AmateurHoninboVsProHoninbo2002
[SW0902] "Der Kampf um die Sechsecke"
Ian Steward
Spektrum der Wissenschaft, September 2002
[W-BGA1] "British Championship Rules"
www.britgo.org/bchamp/chrules.html
[W-BGA2] "BGA Rules of Go"
www.britgo.org/rules/approved.html
[W-Cho] "The Second Game of the 50th Oza Title Match"
John Fairbairn
www.xs4all.nl/~rongen17/Cho/Stories/story002.html
[W-FH1] "The Japanese Rules of Go"
Fred Hansen (ed.)
www.cs.cmu.edu/~wjh/go/rules/Japanese.html
[Where's the (darn) official nihonkiin.or.jp/... link ??]
[W-FH2] "A Precise and Nearly Complete Description
of the SST Ko Rules"
Fred Hansen
www.cs.cmu.edu/~wjh/go/rules/Precise.html
[W-FH3] "The American Go Association Rules of Go"
Fred Hansen
www-2.cs.cmu.edu/~wjh/go/rules/AGA.html
(former www.cs.cmu.edu/afs/cs/user/whj/public/go/Rules.AGA.html)
[W-GB] "Meijin 12"
gobase.org/games/japan/titles/meijin/12
[W-Ing91] "Ing's SST Laws of Wei-Chi 1991"
Ing Chang-Ki (transl. James Davies)
www-2.cs.cmu.edu/~wjh/go/rules/SST.html
or www.usgo.org/resources/SST.asp
[W-IT] "Proposed Rules of Go"
Ikeda Toshio
www.fujitsu.co.jp/hypertext/igo/e_rules.html
[W-JCC] "Mathematical Rules of Go"
Jean-Claude Chetrit
brooklyngoclub.org/jc/rulesgo.html
[W-MK] "The Milton Keynes Go Board"
www.britgo.org/clubs/mk/mkboard.html
[W-MSO1] "Nyobutsu's Judgement"
John Fairbairn
14 March 2000
www.msoworld.com/mindzine/news/orient/go/history/nyobutsu.html
[W-MSO2] "Early Oteai (2)"
John Fairbairn
4 July 2000
www.msoworld.com/mindzine/news/orient/go/history/oteai2.html
[W-NK0902] "First game played with new komi"
14 November 2002
www.nihonkiin.or.jp/topics2002/oldtopics2002-e/oldtopics2002-e.htm
[W-PS] "The swapping rule"
www.playsite.com/t/games/board/hex/rules.html
[W-RJ1] "New Ko Rules"
Robert Jasiek
home.snafu.de/jasiek/newko.html
(former www.inx.de/~jasiek/newko.html)
[W-RJ2] "International Rules"
Robert Jasiek (ed.?)
home.snafu.de/jasiek/int.html
[via home.snafu.de/jasiek/rules.html]
[W-RJ3] "Commentary on the Nihon Kiin 1989 Rules"
Robert Jasiek
home.snafu.de/jasiek/j1989com.html
[W-ST] "Igo no suri"
Shimada Takuya
I'm referring to translated parts that can be found here:
www.goban.demon.co.uk/go/shimada/intro.html
If you find any errors or want to criticize - please inform me.
I certainly didn't master grammar, spelling, and punctuation,
but following "errors" are none:
- favoring AE over BE ("color" = "colour",
"center" = "centre", ...)
- favoring contractions ("can't" = "cannot", ...)
- favoring logic (my quotes don't swallow a trailing
comma or period - ridiculous;
my dashes don't glue words together
- "...word--word..." hurts my eyes)
Using "I" instead of "we" is just meant to be honest, and last but
not least she may forgive me for preferring "his" over "his or her"
etc. (and this "he is Black" and "she is White" doesn't attract
me either - and should be the other way around anyway).
