Keywords: Theory

A 1-eye-flaw is a group of 1 eye and 1 ko that cannot be removed by the opponent because a pass is his only useful legal move.


W1 has just captured the ko, and Black must pass. Now if White passes and if the game ends with 2 successive passes, then Black cannot remove White by continued alternate play.

AGA rules and Tromp-Taylor rules permit the game to end in such a way. Ing rules, Chinese rules, Korean rules, and Japanese rules do not permit the game to end in this way.

tderz: What do the rules say about passing stones to White while passing?
If Black passes and hands over a stone (or more), his pass would be quite different from previous or future normal PASSes which do/did not involve such a transfer of stones (known as pass stones).
Hence, the game would not stop (not two subsequent, identical passes), White could not do anything, and black would capture.

RobertJasiek: This depends on the rules themselves. If they associate passes with stones as situational change, then this aspect becomes part of the restriction rules. However, usually rules do not say such.

Karl Knechtel: Rulesets which allow the game to end this way should also require more than two passes to end, yes? I understand that AGA requires White to pass last, but otherwise the game would end here (i.e. 2 or 3 passes end the game depending who starts) - and if I'm reading this right, that means White is permitted to count his stones as alive here? That can't be right. (I guess in normal situations Black could fill a dame or point of territory, and then retake the ko, but...)

Velobici: The 1-Eye-Flaw is due to certain rulesets. We perceive it as a flaw because the White stone can't be captured and so the White group lives with only one eye! In normal situations the board would be larger and this would not be an all-dominating ko from its inception. On a larger board, we would expect that Black would have captured White when the value of a move falls to the value of the ko. Nonetheless, the flaw seems to arise from the combination of several rules and conditions:

  • a rule that one must either place a stone on the board or pass (no third option....being pedantic here),
  • a rule that two consecutive passes end the game and,
  • the condition that White captures capture first when there are no other legal moves that do not reduce Black's own territory by more than the value of capturing the White group. (11 points for the White group?)

I may be misunderstanding or may have missed stated the rules/conditions.

Bill: Hmmm. I interpreted flaw simply to refer to the false eye. I do disagree with the two pass rule, but obviously opinions differ on that. ;)

RobertJasiek, but afterwards contents changed by others trying to "correct" language only: "1-eye-flaw" is just the traditional name. It is not a particularly bad choice of a name though because normally we are used to stones remaining on the board if they can be transformed to a two-eye-formation or if they coexist with opposing stones that also cannot be transformed to a two-eye-formation.

Bill: I thought the traditional name was Moonshine Life, although traditional Moonshine Life depended upon also having a double ko seki on the board. The one eye flaw can only occur under rules where passes end the game. That is a modern development.

Herman Hiddema: I think both this and moonshine life are in a similar set of situations that are related to "Local-Global relations". Many people feel that it is more logical that a local situation resolves the same regardless of the global position, so they feel that eg this white group:

locally dead  

should be dead, regardless of the position on the rest of the board. Both moonshine life and this 1-eye-flaw involve a global situation in which this group is "alive" (under some rules) due to unusual global circumstances. This local/global conflict is, as I understand it, the reason that Ing chose not to use superko in his rules.

RobertJasiek: There is also a different, broader, informal usage of the term in the sense of moonshine life. The latter is sometimes used to refer to a 1-eye-flaw group only, sometimes used to refer to the combination of a 1-eye-flaw and a double-ko-seki elsewhere.

Karl Knechtel, why "can't" this be right? Here is what I wrote to the mailing list computer-go in response to a critism on the superko rule's effect on 1-eye-flaw:

Why would you be disgusted?

The so called 1-eye-flaw occurs in much less than 1 of 10,000,000 games on the 19x19 board. In the entire history of go, it is reported to have occurred exactly once on the 9x9 board. Why do you dislike rules that enable something possible in theory but never occurring in practice?

What do you have against 1-eye-flaw staying on the board at the game end?

  • a) That it is a group with only 1 eye,
  • b) that it is a group with only 1 ko, or
  • c) that there is a string with only 1 liberty?

Discussion of (a), (b), and (c):

All rulesets used by humans allow games to end with groups with only 1 liberty.


This example shows two stable anti-sekis. By symmetry, it would be superfluous to prolong the game to dissolve either.

If you are disgusted by the 1-eye-flaw, then you should be even more disgusted by anti-sekis; i.e., you are disgusted by all rulesets currently used by humans.

Strings with 1 liberty at the game end can also occur in hane-sekis, double ko sekis, quadruple kos, etc.

Maybe you would like human rules to be changed by a so called greedy rule like "A player may not pass if there is at least one string with exactly 1 liberty on the board." Such would dissolve all those disgusting things. One can even be more brutal in rules design like dissolving all those disgusting ordinary sekis, too. :)

If you want to criticise positional superko, then state your first order aims! Which are they? "I hate 1-eye-flaw!"? Why should one particular shape be that all-important while we do not know some 100^500 other shapes yet? List them all, and then tell us what makes 1-eye-flaw so special :)

More importantly, why are you worried about a shape at all? Shapes are the consequences of move-sequences and strategic decisions, see [ext] http://home.snafu.de/jasiek/j2003.html for a basis with that I defined "eye" formally. Write down your disgusting rules with such a design to enable yourself to define particular shapes in the first place so that you won't overlook any of your potentially hated disgusting shapes...

By the way, positional superko is accepted in some human rulesets like Chinese, Simplified Ing, or World Mind Sports Games 2008.

All restriction rules (about suicide, cyclic repetition, successions of passes) contribute to the goal of preventing games from not ending (Such games are ruled no-result). Ko rules do so by restricting cycles, succession of pass rules do so to avoid very long encores.

In principle, everything can be expressed by rules; e.g., both 1-eye-flaw and long-cycle shapes like triple ko can be avoided by the following, not overly restrictive restriction rules combination:

  • the basic ko rule as the 2 move rule (i.e., passes serve as ko threats)
  • the fixed ko rule ("A play may not leave position A and create position B if any earlier play has left position A and created position B.")
  • 3 ending passes

The effect is that 1-eye-flaws can be removed, triple-kos are not fought, and triple-kos can be removed (one side is dead!).

For the purpose of letting triple-kos and other non-abusive long cycles lead to a tie, one can use yet different rules:

  • 2 or 3 play rule (applies to basic ko and sending-2-returning-1)
  • pass lifts 2-move cycle ko ban rule
  • long-cycle-tie rule
  • 3 ending passes

But then, agreeing on a world-wide accepted ko rule is more important and we get the positional superko rule because that is well known and simple as a rule. Living with an extremely rare frequency of strange strategic consequences should be tolerated (or even welcome) in exchange.

1-Eye-Flaw last edited by asmobia on May 20, 2011 - 05:07
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