Superko

    Keywords: Ko, Rules

This page is poorly organized and needs wiki master editing.


Introduction

Because stones can be captured it is possible to create positions that have appeared earlier in the game. A ko is the most basic form and every rule set has a rule that forbids it. But there are also recuring positions that are not covered by the ko rule? because the recreated position is more than one move away A triple ko is an example. The start position reappears after 6 moves.

A superko rule decides the game if this recreating or an earlier position appears. But not all rule sets have the same rule give the same decision. For example

  • The Japanese rules say that the game has no result sometimes this means that the game has to be replayed
  • The long cycle rule decides the result based on the captures made within the cycle.
  • Other rule sets say the move is illegal (and so the player who recreates a previous position loses by making an illegal move)
  • Some rule sets say nothing about superko and then it is possible to have non-ending games.

Forms of superko rules

There are two main versions of superko rules:

and

A less used rule is the 'natural situational superko' where a player may not use a board play to recreate a position if he has used one to create it.

Further information

Many rulesets have some form of superko rule (e.g., AGA rules and New Zealand rules), but other rulesets do not (e.g., Japanese rules, Korean rules and Ing rules[2]).

See also: [ext] http://home.snafu.de/jasiek/superko.html

/Discussion for a general discussion

Positional vs Situational Superko for discussion over which superko rule is best. (don't expect to find a definitive answer)

Long cycle rule for an alternative to the superko rule.

Table of contents Table of diagrams
Superko
Unremovable Ko Threat without Bent 4
SuperKo with score


Example

History

History in Japan

triple ko situational superko

History in China

Unending gamme Sending two, returning one positional Superko


DavidPeklak : Everybody says situations where this rule has to be applied hardly occur, but one occurred in one of my games recently, although I started playing Go only four months ago.

[Diagram]

Superko

The situation seemed to be seki. Probably attempting to kill the black group, White played at a. Black had to capture by playing at b. Now White played at white+circle again, which gave the original seki position again. This move would have been forbidden if the positional superko rule applies. In that case, Black could have played there after White elsewhere and kill the white stones. I think this is a nice example other than the triple ko situation.


You are right. Situations like these are quite common. Although the superko rule is often quoted when talking about double or triple kos, it can be applied in many other circumstances as well.

In this case, White has gained nothing and loses sente, and after the sequence, White has lost two stones, whereas Black has only lost one. A net loss of sente and a point - not very good.

However, the white move at a is an example of an unremovable ko threat - there is nothing Black can do to stop White from using it as a ko threat.

-- Morten Pahle

Morten, is that specifically because in this case it's bent four in the corner? -- Tim Brent

The prior diagram is not bent four in the corner. Albeit, it looks similar. It, the prior diagram, is related to bent 4 in the following way. Black has 2 moves to kill himself. Of these, one is significantly worse than the other. Both are self-atari, so if white takes, black dies in sente. But actually, both moves die in gote -- consider what happens if white passes, i.e., black plays a second move. The first variation becomes a ko for life, and the second variation leads to a bent 4 position. Which is essentially dead, unless black has an unremovable ko threat, returning to the original question.

The important thing about the first diagram is that it is a seki at the minimum number of common liberties (2 for eyeless strings, 1 for strings with an eye). Any such seki, including the following diagram, is an example of an unremovable ko threat. -- Will Cushing

[Diagram]

Unremovable Ko Threat without Bent 4

No, I don't think so. I think this situation works the same way in all aspects.

There is a small difference. In the first situation, both 'a' and 'c' are 'threats' to create ko fights for Black. Black could only play these if the other ko is extremely asymmetric in black's favor, black's ko threats are currently inferior to white's but would be superior after white finishes off the larger ko, and gote plays elsewhere on the board are significantly smaller than capturing these 3 white stones. Otherwise it would be better for black to leave the local situation as seki, rather than giving white the choice of ko/territory (if the first ko is smaller for white than capturing black locally). Since white gets to choose when the ko resulting from 'c' happens (since that becomes bent-4) the second condition is very unlikely after 'c', which makes 'c' the (much) worse threat for Black.

In the second situation, 'c' is a threat to make unconditional life. Still the ko fight would have to be extremely asymmetric in black's favor, and still gote plays elsewhere need to be significantly smaller than capturing the 4 white stones, but since the result isn't ko black doesn't need better ko threats after white finishes off the larger, asymmetric, ko. In this case 'c' is a far better threat than 'a' for Black.

A game in which Black could use such ko threats would be pretty rare, but a game in which unremovable ko threats and superko rules are worth thinking about is a game where such ko threats might very well be useful. For example, if white has 'killed' a larger Black group via bent-4, then Black can (under AGA rules) force white to either let that group live (in seki), or make a few points by using the 'a' threat in the first situation or the 'c' threat in the second situation. The ko resulting from playing out a bent-4 is flower-viewing for Black in the sense that losing the ko isn't worse than allowing White to declare them unconditionally dead; Black risks nothing by forcing White to play it out.


mermeladeK: The example you put is not a Super Ko. It is not because there is one more black stone on the board after white plays again at white+circle .

Bill: Actually, it is. The Black stone is captured, not on the board.


[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.''

Quoted at [ext] http://www.goban.demon.co.uk/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.

[2] The Ing rules originally had a positional superko rule, but Ing decided that some of its implications were too counterintuitive, and revised his rules. Still, the Ing rule about fighting ko prevents many long cycles of play, and may be considered as a form of superko rule.


Jasonred : I have a suggested solution : No placing a stone or stones that repeat the exact same position on the board in general. Anything else goes! Of course, this would lead to chaos as people play through every single different variation possible, wasting much time.


Benjamin Geiger: Does the superko rule prevent (the extremely unlikely event of) rotations and reflections of the board?

tderz: No. A rotated or mirrored boardposition which results from a symmetry operation onto a previous boardposition is not identical only symmetrical. This is because a1 ≠ a19 ≠ t19 ≠ t1.

Tas: But it would prevent two consequent reflections though...

Charles Matthews: That isn't the intention of the rule. On very small boards this is more of a possibility.

John Tromp: On small boards the superko rule has peculiar consequences. For an example, see Rules Beast 1.

I don't see these strange consequences as an indication that there's something wrong with the superko rule. In fact it seems to fit right in with the other simply stated Go rules that yield a game so rich in strategy and subtleties.

blubb: Another illustration is given by Superko Puzzle 1.


[Diagram]

SuperKo with score

Just add a few stones to point out something that has not been mentioned. This position is a seki, i.e. the point at a9 counts for white, c9 & b7 do not count. If there are no prisoners and komi is 0.5, the score (after white b9) is: White: 0 prisoners + 0 dead + 21 territory points + 0.5 komi = 21.5; Black: 0 prisoners + 0 dead + 21 territory points = 21.0. White wins.

Rich: a9 does not count as white territory, as it is an eye in seki.

(Counting a9 or not does not change the superko discussion. I understand, according to the rules, that if white is alive, a9 is white territory because, unlike c9 and b7, it is surrounded by living stones of the same color.)

Rich: I agree; it merely changes the score and the subsequent result :) Quoting from the link below: "an intersection is black-territory / white-territory if it is a black-eye-point / white-eye-point that is not part of an in-seki black-region / white-region."

This subject is discussed in Seki with Eyes Question 1. Apparently, there are rulesets (e.g., IGS rules) where points in seki do count, and rulesets in which they don't.

To win the game as white in AGA rules (with japanese counting) white needs to play a9 after black passes. This forces black to pass again, giving up an extra pass stone. Then the score will be: White: 2 prisoners + 0 dead + 20 territory points + 0.5 komi = 22.5; Black: 1 prisoners + 0 dead + 21 territory points = 22.0.

After the moves described, the japanese score is: White: 1 prisoners + 0 dead + 20 territory points + 0.5 komi = 21.5; Black: 2 prisoners + 0 dead + 21 territory points = 23.0. Black wins!

Under chinese or AGA scoring (if the moves are played at the end of the game) the result would be unchanged, but a superko rule is still necessary to force White to allow the game to end.

In modern methodologically coherent rule sets as Japanese 2003 draft [ext] http://home.snafu.de/jasiek/j2003.html there is no SuperKo if the number of prisoners between both positions is uneven. SuperKo, if the score is maintained after the sequence repeating the board is a MUST. Any rule set ignoring this has a bug that could (potentially) be exploited by unfair players to avoid losing. But when the score is not repeated, there should be no need of a super ko rule, since one of the players is being damaged by the repetition and will avoid it or lose.


This is a copy of the living page "Superko" at Sensei's Library.
(OC) 2009 the Authors, published under the OpenContent License V1.0.
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