The diagram shows an example of a basic ko shape. The board point a and the board point right of it are together called basic ko. This shape consists of exactly two adjacent board points. It is the simplest and most frequently (more than 95%) occuring shape for which ko rules are necessary.
In a basic ko a single stone can capture a single stone, this could be recaptured immediately with an opponent's single stone, and the process could be repeated infinitely. This is to be prohibited:
basic ko rule: If a single stone captures a single stone, then no single stone may recapture it immediately.
The rule is sufficient for beginners. All other cases that require different treatment are rare. The following deals with the rarities.
Surprisingly, all ko rule sets at least partially deviate from the above purposes. Many do not even approach them. Instead further purposes may be included for maintainance of tradition being expressed by exceptions.
Some ko rule sets consider unions of ko points and call them "ko". E. g. in many rules the two board points of a basic ko are a ko. In practice, strings that could be captured during a cyclical move-sequence are often called "ko strings". E. g. in a basic ko single ko stones of each colour may occur one after another.
Since single ko stones are easy to detect, many ko rule sets restrict their consideration of kos to shapes in which only single ko stones are involved. Then bigger ko strings are treated by different rules. Double and triple ko stones are relatively easy to determine by assigning some cycles to them. Difficulties, however, may arise with very big strings. For ko strings of at least four stones no example with a "reasonable" (worth playing) cyclical move-sequence is known yet. With a definition of "reasonable" one might try to give a proof that no "reasonable" cyclical move-sequence for big ko strings exists. If a player claimed that a particular big string were a ko string and therefore an opponent's move were invalid according to some ko rule set, then he needed to prove that by presenting a proper cyclical move-sequence.
Often it is not worth fighting over single, double, or triple ko stones. Cyclical move-sequences for such ko strings can also be considered "unreasonable". A ko rule set may rule about types of ko strings, but it is left to the players to relinquish "unreasonable" cycles. In practice trouble can only occur if both players can only prohibit losing by playing through cycles and both cannot calculate in advance how to apply a rule set so that a win could be ensured with a short move-sequence instead of long cycles.
Partition of the board into two parts: cyclical and non-cyclical
B[ecadbacbde] is a cyclical move-sequence and shows that the three small marked strings near to letters are ko strings, one single ko string and two double ko strings. [See Conventions.] During the cyclical move-sequence all played stones are ko stones. 10 board points are involved in the repetition process: The letter and the marked points. Including single pass plays and with the aid of suicides other strings might be repeatedly captured during cycles. However, the essential part of the board as to repetition consists of the 10 board points. They may be called the "cyclical part" of the board. The rest of the board, 54 board points, shall be the "non-cyclical part" of the board. Another example is a board with a basic ko as the only ko on the board; there the cyclical part consists of two board points.
A set of voidness may lead to games with no outcome (void games), sets of repetition or prohibition produce an outcome for each game. A set of repetition evaluates the whole board and applies only one rule to it. Simply speaking, a set of prohibition divides board positions into a cyclical part and a non-cyclical part and applies rules to the parts.
In most cases - including all known "reasonable" - it is easy to detect a repetition of the non-cyclical part of the board by remembering the move-sequence of the played game. On the other hand, it may be hard to detect a repetition of the cyclical part due to a great variety of cyclical move-sequences in it.
With a played part of a cyclical move-sequence even with usage of a set of repetition players will analyse with the aid of a partition rather than referring to the whole board position. A repetition set has a very short text but allowes a high variety within cyclical parts of the board. Repetitions are forbidden.
Sets considering a partition of the board do so to severely restrict the complexity of possible move-sequences in a great number of cases. - In a set of prohibition repetition might occur, but then restriction applies for the next move.
A systematical analysis of many rule sets as to their ko rules is achieved by a classification.
basic ko rule: A board play which repeats a position two moves ago
game end rule: If positional repetition occurs, the players may agree to end the game.
Repetitions not restricted by the basic ko rule may lead by agreement of both players or intervention of a referee to a void game. In theory both players could neglect ending the game. In practice void games, e. g. caused by triple ko or double ko stones, are rare.
Positional Super Ko
repetition rule: No board play may repeat a position.
The rule, also called super ko rule, considers whole board positions. A repetition is not allowed to be reached. Besides repetitions no further restrictions apply. In theory in many positional classes extremely long move-sequences could be played. In practice in most cases "reasonable" move-sequences are comparatively short.
The Basic Ko Rules
ko definition: Two board points are a ko if on them a move of one
player followed by a move of the other player repeats the configuration
basic ko rule: A stone in a ko that has captured a stone in it must not be recaptured immediately.
prohibition rule: From all board positions with the same set of board points of all kos and with the same configuration of stones on the board without the set each player may only once play on each board point.
Only basic kos are considered kos by the Basic Ko Rules. For them the flavour of the game is kept by the basic ko rule. General repetition is dealt with the prohibition rule. It uses a partition of board positions that considers only all basic kos seperately. Thus a partition is easy to detect. With the same non-basic-ko part of board positions allowed play within the basic ko part is short and easy to detect. Only with very rarely occuring actual play of multiple ko stones analysis may be more difficult.
Complexity mainly occurs as linear or exponential in the number of board points. Since "unreasonable" cannot be suitably defined in practice, all ko rule sets at least allow in some "unreasonable" example classes move-sequences of exponential lengths. Sets only considering basic kos allow determination of all kos on the board in linear time. A simple rule set of the prohibition class, the Basic Ko Rules, achieve linear move-sequences in most "reasonable" cases.
To fairly end "unreasonable" long games a constant game end rule or a finite time limit is required.
A comparison analyses three often used sets: Japanese, Ing, super ko. See also Examples 6 and Complexity.
Modern rule sets like New Zealand and AGA rules use super ko. China 1988 uses super ko together with some traditionally maintained precendental exceptions. Modern Japanese style rules try to avoid exceptions and the latest invention of WWGo rules even uses the repetition concept. The Ing 1991 ko rules might be replaced by the simplest set of the prohibition class, the Basic Ko Rules, which would mean close resemblance to super ko.
Hence it is not far-fetched to predict a world-wide use of the simple concept of restriction due to repetition and a unified ko rule (set) for the whole world.