1997-3-2 last update, 1996-9-15 first day
Robert Jasiek,
jasiek@berlin.snafu.de
The Ko Coupling Rules aim with a relatively short but precise text at easy determination of allowed moves, even if many ko positions are on the board. They do not distinguish ko types. Ko couplings reduce the number of ko positions on the board; not each ko mouth itself is a ko position. Between so called ko threats on the board that are not ko stones each player can become disturber only once in each ko position.
A move-sequence is a non-empty colour-alternating sequence of board plays or pass plays by both players. A cyclical move-sequence is a finite move-sequence with board plays only and the same board positions before and after it.
A ko string is a string for which a move-sequence that contains a cyclical move-sequence exists so that a move of the cyclical move-sequence recreates the board configuration before the move-sequence and a move of the cyclical move-sequence removes stones on all board points of the string. A ko string is complete if its stone number during a defining cyclical move-sequence is maximal. A ko stone is a stone of a ko string.
A ko stone move-sequence is a move-sequence of board plays, so that only ko stones are played.
A ko mouth of a ko string of one colour is the set of board points of the complete ko string of the ko string of the colour and of the complete ko string of a ko string of the other colour that captures the complete ko string of the one colour during a defining cyclical move-sequence.
Given a ko mouth and its adjacent strings. All of at least two ko mouths, that are adjacent to no empty board point, with all of the strings and none else being adjacent to each of the ko mouths have them as their ko coupling.
ko position : If a ko mouth is adjacent to all strings of a ko coupling and not adjacent to any other string or an empty board point, then the ko position of the ko mouth is the union of the board points of all ko mouths that are adjacent to all strings of the ko coupling and not adjacent to any other string or an empty board point. If a ko mouth is not adjacent to all strings of a ko coupling or adjacent to another string and not adjacent to an empty board point, then the board points of the ko mouth are its ko position.
basic ko : A single ko stone that has captured a single ko stone may not be recaptured immediately.
disturber : During a ko stone move-sequence in a ko position a player becomes the disturber of the ko position by playing a ko stone in it first. As soon as the ko position with the stones on it has been repeated since the moment just before the occurance of the current disturber he is not allowed to play a ko stone in the ko position. With the end of the ko stone move-sequence in the ko position a disturber ceases to exist. If the disturber is not allowed to play a ko stone in the ko position and the ko stone move-sequence in the ko position continues, then the disturber ceases to exist and the other player becomes the disturber.
prohibition : From all board positions with the same set of board points of all ko positions and with the same configuration of stones on the board without the set each player may only once become disturber of each ko position or play no ko stone on each board point.