____        ____   _________     _________
             /   /       /   /  /         \   /        /
            /   /       /   /  /   ___    /  /   _____/
           /   / ____  /   /  /   /__/   /  /   / _____
          /   / /   / /   /  /       ___/  /   / /_   /
         /   /_/__ /_/   /  /   /\   \    /   /___/  /
        /        /      /  /   /  \   \  /          /
       /________/______/  /___/    \___\ \_________/

                     Summer 2004
                   Robert M. Pauli

         all rights of the author are preserved
             according to international law

            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 - again taking
    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 (normal action).
    Each action may (occasionally must) be omitted, but if
    both are performed, it must happen in the given order.

 4. If a player neither adds nor removes stones in his turn, this
    is called a "pass" (and also is an action). 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 stone"), and
    - for each opposing stone that was removed (no
      matter by whom) during the game ("captive").
    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,
    - identify all opposing stones thereafter being
      without liberties, and, in case there are,
    - remove them from their locations ("capture").

 7. To "remove a cycle" means to remove all stones sitting on
    locations "used" by the cycle - which are those 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 would not 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 the new stone has none.

11. Putting a stone on an empty location makes "pseudo suicide"
    if after placement the new stone and all stones of opposite
    color still have liberties, but those of the new stone all
    are permanently prohibited.

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 the location it sits on contacts
    at least one empty location - each a "liberty" of the stone.
    A location "contacts" another if by starting from the former
    and repeatedly (including zero times) jumping to a neighboring
    location that, compared to the jump's origin, either also is
    empty or also occupied by a stone of same color, one can reach
    a location neighboring the other location. 

14. A player "controls" a location if it is member of a set
    of locations he has bordered and he cannot be prevented
    from building a two-eye formation on this set even if
    - each location outside this set is cleared and 
      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 and actions are forgotten, 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 "two-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 at least has one neighbor
      (possibly outside this set),
    - no empty location in this set ("eye") has an empty neighbor,
    - each stone sitting on a location in this set at least has
      two liberties in this set.

17. In case the game started with no referee(s) designated to
    decide disputes about control, the game continues after its
    normal end as follows: 

    Starting with the player who did not pass last, both players
    alternately either
    - point to an empty location that contacts opposing but no
      own stones,
    - point to an opposing stone, or
    - pass.
    Pointing to an empty location claims that it is neutral.
    Pointing to an opposing stone claims that it is dead,
    including all other opposing stones sitting in the claimant's
    smallest bordered set that includes the stone's location.

    In case of two passes in a row there is no disagreement and
    normal counting decides score and outcome. This soley depends
    on control, which is assigned as follows:
    Only for this purpose all claimed-as dead stones are treated
    as if gone. Then each location
    - that is empty,
    - that neither is nor contacts a claimed-as neutral location, 
    - that contacts at least one occupied location, and
    - that only has one player to whom all stones on such
      locations belong
    is treated as if controlled by this player.

    To disagree, a player points to a location or stone claimed by
    his opponent. In this case a dispute is played out, which
    decides the game. In case of an empty location, the disagreeing
    player is the "prover", otherwise his opponent. The prover has
    to prove that he controls the empty location or the location
    occupied by the stone by building a two-eye formation on a set
    of locations.

    This set initially includes the prover's smallest bordered set
    that includes the disputed location, but may be extended by him
    repeatedly: each time he points to an empty location not yet in
    the set, his smallest bordered set including this location is
    added to the set. As soon he passes or doesn't extend, the
    initial situation for him trying to build a two-eye formation
    on this set is set up as defined in the definition of control.
    Starting with the "refuter", that's the prover's opponent, 
    the game then continues until either
    - the refuter puts a stone on a location
      neighboring a location outside the set, 
    - the refuter builds a two-eye formation that
      includes at least one location in the set, 
    - a situation is similar to a former one, or
    - the prover has build a two-eye formation on the set
    (cases before the last two only to shorten disputes).
    In the last case the prover wins, otherwise the refuter.

bulky rationale (from 2003)

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