Superko

Keywords: Ko, Rules

Superko rules prohibit recurrences of an earlier board position under certain circumstances. The recurrence of such positions could be caused by long cycles, such as triple ko, eternal life or round-robin ko.

Table of contents
Forms of superko rules

Main variants

Other variants and related rules

Example

The role of passes

See also

Test cases

Further information

Discussions

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Forms of superko rules

Superko rules come in various forms, depending on when they forbid recreating a board position, and their view on what constitutes a repeated game state. Possible factors include:

on whose turn the position was previously created
whether players have passed, immediately before or at some intervening time ^[1]
the type of move recreating the position (see Chinese Superko below)
prisoner balance change (some long cycle rules, probably Chinese Superko as well)

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Main variants

The main variants in use of the superko rule and other rules on repetitions are:

Superko rule variants
Name of variant	Meaning	Used in	Comments
Positional Superko	Forbids a board play to repeat a board position	Chinese rules (in theory) Tromp-Taylor Rules	See Positional Superko / Example
Chinese Superko	A play may not repeat a board position by means of basic ko or sending two, returning one	Chinese rules (in practice)	This, according to the sixth meeting of the International Go Rules Forum, is what the Chinese rules were intended to specify.
Situational Superko	Forbids a board play to repeat a board position with the same player to move (regardless of how it previously arose)	AGA rules New Zealand rules
Natural Situational Superko	Forbids a player’s board play to repeat a board position that they created with an earlier board play	BGA Rules 2009	Note that it could allow an immediate ko recapture if the first capture was preceded by a pass. BGA rules combine this with the basic ko rule to forbid immediate ko recapture. According to Terry Benson, AGA rules were meant to use Natural Situational Superko, but everybody else interprets them with Situational Superko.
No result	If a board position is repeated, the game has “no result”	Japanese rules Korean rules	This usually means the game must be replayed.
Long cycle rule	Repetition of a board position ends the game.	Computer Olympiad rules	(PJT: ¿used with basic ko rule? The game result depends only on the number of stones captured by either since the first occurrence of the position.
Threefold repetition	Third or later occurrence of a position is required to declare end of the game, the result is draw/loss/win depending on stones captured in the loop.	Renaissance rules	A single repetition of a position not necessarily means an endless cycle, see for example 1-eye-flaw. Further repetitions are also increasingly easier to recognize in practice.

Some of these reflect the traditional, lenient handling of repetition. See also generic long cycle rule.

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Other variants and related rules

Fixed ko rule: repeated positions may occur but you are not allowed to make the same move in them.
Short cycle rules?: The result depends on the number of moves between the repeats. If there are 3 or fewer moves between the repeats the game is a loss for the player who makes the repeat. If there are more moves between the repeats the game is a draw.
Long cycle seki rule: The groups involved in a long cycle are treated as alive in seki
Colour-blind superko: Ignore the colours, suggested as a ko-rule for multi-colour go.
Minimal superko: Forbids a board play to repeat the last position both players passed in successively.
Pair ko rule: Forbids repetition of pairs of moves rather than positions, which drastically reduces the amount of information that players need to remember from previous positions.

The following variants have also been used in theoretical discussions:

Active Superko (first description here by Rubilia): a player who makes the same play (including pass, in the same position) for the second time wins.
Sound Superko (term suggested by Robert Pauli): forbids “completing a cycle” (in his terminology) that does not include a pass.
Strict Superko (term suggested by Robert Pauli): forbids “completing a non-trivial cycle” (in his terminology).

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Example

The most commonly used example why a superko rule is necessary is triple ko. See below for a more simple case that also illustrates the rule:

This situation is a seki in the corner. Assume Black just passed, so that this position has occurred with either side to play. If White plays at a, Black plays b. With a superko rule in place, White cannot retake at white+circle , so Black can take the corner. Of course, this comes from a White initial mistake, but see Rules Beast 1 for a case where White breaks the seki and wins the fight...

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The role of passes

[1] Bill Spight: There are also versions of the superko rule that take passes into account, such as the earliest superko rule proposed, by Yasunaga Hajime in an article in Kido in 1929:

Article 7: The repetition of the same pattern shall be prohibited unless the right to an alternate move is disregarded.
( [ext]

http://harryfearnley.com/go/shimada/intro.html)

In modern terms, "disregarding the right to an alternate play" means passing. When a pass lifts a ko or superko ban, this is sometimes called "pass for ko threat". There are different versions of the superko rule in which an intervening pass allows a repetition. Yasunaga's seems to say that any intervening pass lifts the restriction on repetition, but it may mean a pass by the player who makes the repetition. The interaction with passes can pose problems with ending the game, but not taking passes into account can lead to strange results. My home page, when I get it up, will have a discussion, and my solution to the problem, based on Combinatorial Game Theory. Meanwhile, for my solution, see Spight Rules.

Yasunaga proposed a three-consecutive-pass rule, which is how my solution will usually work. Ing uses a four-pass rule.

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