Triple Ko

(It is said that the Chinese rules include a superko rule that settles all complicated repetitions, so that there would be nothing special about triple/quadruple ko and the like under Chinese rules. In practice however, it seems the Chinese follow the Japanese and declare a game "Void", "No Result", when such repetitions occur.)

See also Quadruple Ko and Eternal Life.

Contents

Additions and corrections are welcome. Mail to aeb@cwi.nl

One dead group and a group with three false eyes

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It is Black's turn. As soon as White has a free move, she will play C19 and capture the Black group. So Black is forced to take one of the three kos, and then White takes another and a cycle is forced.

Another example:

Lee Sedol vs. Lee Hyung-ro, 1997-04-15

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It is White's turn. As soon as White has two free moves, she will play K10 and G4 and capture the Black group. After one free move, a cycle is forced.

Two groups with a common ko and a further false eye each

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Here Black has just captured at O19. White has no choice but to capture at S19. If Black connects, or plays tenuki, White takes at N19 and captures the Black group. So, probably Black has to capture at L15, White at N19, Black at R19, White at L16, Black at O19 and after six moves the situation repeats.

Both players have the option of using external ko threats, and giving up their group in return for two unanswered moves elsewhere.

Another example:

Li Zhe vs. Gu Li, 2011-09-04

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Here White has just captured at G19. The situation is similar to the previous one, but the groups are bigger, so it will be more expensive to break out of the cycle.

Yet another example (which inspired the Hikaru-no-go episode shown next to it):

Nagano Kaizen vs. Inoue Shunseki, 1724-04-27

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Note that the Hikaru version has a quadruple ko.

Two 1-eye groups with a common ko and a further false eye each

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Here White has just captured at J19. If both players are happy with the outcome, they can take the three kos in turn and get a Void result. Black has no choice, but White can deviate, if he wants.

Suppose that at some point after White has captured at T17, he fills at T16. A fight between two groups, each with one eye and a common ko, where one has an additional outside ko is always won by the group with outside ko - that group can always maintain two liberties by taking one of the kos, while the other needs infinitely many external ko threats.

That means that at the moment White fills at T16, Black must make sure to destroy White's eye by capturing at L18. That again means that Black K16, White T17, Black P19, White T16 is lost for Black, and also Black L18 loses, so that Black has to play P19. After White T17, Black K19, White can choose to fill at T16. Now Black captures at L18, White at Q19, and White wins unless Black has two threats that cannot be ignored and ignores two White threats himself.

In the present game that was a real possibility and White (Cho Chikun) chose the Triple Ko outcome.

Another example:

Yanagawa Hiromasa vs. Matsuoka Akira, 1980-05-28

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Here Black has just captured at A7. White has an outside liberty and can win (by filling at F1) if he is able to ignore two Black threats. Black has no choice.

Another example:

Yoda Norimoto vs. Hikosaka Naoto, 2002-05-09

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Here White has just captured at S1. There are no outside liberties, and neither player has a choice.

Three further examples:

Takashio Kenji vs. Yamaki Chinpei, 1849-09-18
Gao Xing vs. Pan Yang, 2009-05-14
Chen Yaoye vs. Gu Li, 2013-11-02

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On the left Black has to capture a ko, for otherwise White fills at A1 and Black loses. Neither player can escape from the cycle. In the middle Black must not have time to fill at F8, so White captures at A15. On the right Black has no choice but White could fill at T5 and start a real ko. It is good for him since Black needs three approach moves (N5, O4, J1) so Black has to ignore three White threats.

Two groups with two common kos and one further ko

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It is White's turn. If White wants, he can keep capturing one of the three kos adjacent to the black group, and Black, being reduced to a single liberty, is forced to reply and capture another one of these three kos. On the other hand, White can play elsewhere. Black cannot fill a ko. Black can take a ko, and then White replies by taking the other, and then Black has to play elsewhere as well. So it is White's choice: a Void game because of a cycle in the triple ko, or a continuation. If White chooses the continuation, then details of what happens afterwards depend on the rules for the end of the game. White will have the disadvantage of not being able to win any kofight since Black has an unending supply of threats.

Kaji Kazutame vs. Watanabe Hideo, 1953-08

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It is Black's turn. If he captures at A10, White is forced to capture at C7 and then Black is forced to capture at A8. If now White takes a Black liberty with G8, then Black C8, White A11, Black B9 and White loses. So, G8 is no good, and White has to play A11, Black C8, White A7 and the cycle repeats. The same cycle occurs if Black starts at A8 instead of A10.

Another example:

Kim Yoonyoung vs. Yoshida Mika, 2010-11-23

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It is White's turn. Again a cycle is forced.

And another:

Another - it might be called a quadruple ko, but the result was given as "Void, due to triple ko":

Liu Jianchang vs. Chen Qingyu, 2012-04-16

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White can play elsewhere and allow Black to fill the ko at L19 or P15. Afterwards it is a triple ko, and a cycle is forced.

Yet another:

anon. vs. anon., 2006-10-20

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Two 1-eye groups with two common kos and one further ko

Lee Wondo vs. Lin Shuyang, 2010-08-05

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It is Black's turn. If Black keeps playing the three kos in turn, White has no chance to connect a ko, and we cycle. Black can choose to deviate by capturing at T19, getting himself an additional liberty. But White has one eye and three false eyes, and Black needs to fill two of these false eyes, and would die himself. So, neither player has a choice here.

Double-ko seki and one additional ko

Park Taehee vs. Kim Dayoung, 2017-03-07

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Need to win a ko fight

Cho Chikun vs. O Rissei, 1998-10-15

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the players cycled through the three kos at A10, C10, and L17. The aim was to win the unimportant ko at L17. Threats at A10 and C10 suffice: both players threaten to continue to the next ko, with higher stakes. This infinite source of ko threats means that neither player needs to give up the ko at L17.

Another example:

Kim Hyeongwoo vs. Heo Yeongho, 2009-11-23

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The last move was a White capture at O7. The game is close. White could have made two eyes with T7, but could perhaps not afford a Black capture at P9, and prefers a Void result.

Another example:

So Yokoku vs. Zhu Songli, 2006-04-17

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Here the players fight a ko at Q13, and find infinitely many ko threats at A12 and C12. A mistake? Black is ahead, so White is interested in a Void result. The Black group around M9 has no eyes and needs a connection to the outside world. It is Black's turn. I think S14 suffices. Then White needs to prevent the loss of four stones at K18, and Black plays at R12 and P15 and wins.

Filling a ko

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Similarly, in

Yamashita Keigo vs. Kono Rin, 2013-09-27

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white can fill a ko and turn the triple ko into an ordinary ko. However, black would win since he has the threat at A.

Unfavorable ko

O Rissei vs. Mimura Tomoyasu, 2003-03-23

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Black (O Rissei) played T11 instead of T16, turning the triple ko into an ordinary ko that is very favorable for White. Black would have to find two threats that White reacts to, and ignore three White ko threats. Quickly afterwards he resigned.

Success

Choi Cheolhan vs. Luo Xihe, 2005-12-16

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White (Luo Xihe) filled at K14, turning the triple ko into an ordinary ko that provided him with a single threat that had to be ignored by Black. His threat P10 was sufficiently large, and he won by 7.5 points in spite of the loss of the big white group.

Pass

Wang Lei vs. Zhou Heyang, 2001-04-23

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Long ko-fight

Cho U vs. Gu Li, 2006-05-01

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Quintuple ko

Yang Hui vs. Chen Linxin, 1992-07-04

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