Keywords: Ko, Rules, Theory

A quadruple ko is similar to triple ko, except that a quadruple ko involves four kos on the board that are all in play at the same time.

In real games the result of this fight depends on which rules are followed especially the superko rule.

This is therefore also an investigation in superko rules. my idea was to find the longest fight that can happen in this position, not so much to find out who wins or loses.

The fight ends with three passes and when all next moves lead to a position that is illegal under the natural situational superko rule

Motivation for the natural situational superko rule

The motivation for the natural situational superko rule is that this variation of superko rule allows (in theory at least) the longest fight. And therefore other superko rules can be put in the comments.

Motivation for the three passes ends rule

The motivation for ending the game with three instead of two passes is that the first pass of an player can be because it is illegal (under the normal ko rule) to recapture a position and having the game end after only two passes prohibitits this player from retaking the last ko. while this maybe was valid move.

RobertJasiek: What you are looking for is the Spight-Davies-Rickard superko theorem for m n-tuple-kos.

willemien: Can you give a link?

Bill: The defense of the mutual standoff position of a quadruple ko is simple. When the opponent takes a ko, threatening to capture, do not take back in that ko mouth, but respond with a triple ko in the other three. That will be an effective defense under nearly all superko rules in use today.

Black attacks

When Black attacks with , White avoids taking it back.

Continuation

returns to a balanced position. Now is prohibited, because it repeats the position after .

Startposition

This is the startposition and it is Blacks turn to play.

The board outside the part in startposition is unchangable (so no tenuki's or ko threats and the surrounding stones are alive.

### Simple fight 20 moves

Move A B C D Comments
Start
at c
at a
at d
at b
at a
at c
at b
at a d would recreate starting position
pass c would create a natural situational superko(same position as after )
at b
at a positional superko same position as after
at d
at c
at a
at b forced positional superko same position as after
at c
at c
pass b would create an natural situational superko(same position as after )
pass a would recreate position after , c the position after
pass b would recreate position after , d the position after

### longer fight (28 moves)

Move A B C D Comments
Start
at c
at a
pass
at b
at a
at c
at b
at a
at d
at b
at a
at d
at c at a would recreate the starting position
pass at a would recreate same position as after
at d at b would recreate same position as after
at c positional superko same position as after
pass
pass at a would create an natural situational superko(same position as after ), at d would recreate position as after
at b at c would recreate position after
at a
at c
at b
pass at a would recreate position after
at d at c would recreate position after
at c at a would recreate start position. (not natural) situational superko same position as after pass
pass at b would recreate position after
pass at a would recreate position after , at d as after
pass at b would recreate position after , at c as after

### Complex fight (feel free to edit)

Move A B C D Comments
Start
at c
at a
pass
at b
at a
at c
at b
at a
pass at c would create a natural situational superko(same position as after )
at b
at a positional superko same position as after
at d
at c
at a
at b positional superko same position as after
at c
at c
pass at b would create an natural situational superko(same position as after )
pass a would recreate position after , c the one after
pass b would recreate position after d the position after

### old experiments

Move A B C D Comments
Start
at c
at a
at d
at b
at a
at c
at b
at a
pass at c would create a natural situational superko(same position as after )
at b
at a positional superko same position as after
at c
at b positional superko same position as after
at c positional superko same position as after B-
at b
at a at d would recreate starting position [1]
at c

### one to change (make a copy

Move A B C D Comments
Start
at c
at a
at d
at b
at a
at c
at b
at a
pass at c would create a natural situational superko(same position as after )
at b
at a positional superko same position as after
at d
at c
at a
at c
at a at d would recreate starting position [1]
at c

Quadruple ko fight last edited by Dieter on May 10, 2022 - 11:56