Quadruple ko fight

    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.

This page is about the fight that can follow in such a situation.

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

Feel free to add variations only if they are longer than the longest found allready. And do add comments about moves that are illegal. But do start with the same 2 first moves.

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.


Please add comments on the above here.

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

willemien: Can you give a link?

RobertJasiek: [ext] Yes.


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.

[Diagram]
Black attacks  

When Black attacks with B1, White avoids taking it back.

[Diagram]
Continuation  

W6 returns to a balanced position. Now B7 is prohibited, because it repeats the position after B1.


[Diagram]
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 treat?s and the surrounding stones are alive.

Table of contents


Simple fight 20 moves

Quadruple Ko fight
Move A B C D Comments
Start B B W W
B1 at c B B B1 W
W2 at a W2 B B W
B3 at d W B B B3
W4 at b W W4 B B
B5 at a B5 W B B
W6 at c B W W6 B
B7 at b B B7 W B
W8 at a W8 B W B d would recreate starting position
B9 pass W B W B c would create a natural situational superko(same position as after B3)
W10 at b W W10 W B
B11 at a B11 W W B positional superko same position as after W6
W12 at d B W W W12
B13 at c B W B13 W
W14 at a W14 W B W
B15 at b W B15 B W forced positional superko same position as after W2
W16 at c W B W16 W
B17 at c W B W B17
W18 pass W B W B b would create an natural situational superko(same position as after W10)
B19 pass W B W B a would recreate position after B7, c the position after B3
W20 pass W B W B b would recreate position after W10, d the position after W16


longer fight (28 moves)

Quadruple Ko fight
Move A B C D Comments
Start B B W W
B1 at c B B B1 W
W2 at a W2 B B W
B3 pass W B B W
W4 at b W W4 B W
B5 at a B5 W B W
W6 at c B W W6 W
B7 at b B B7 W W
W8 at a W8 B W W
B9 at d W B W B9
W10 at b W W10 W B
B11 at a B11 W W B
W12 at d B W W W12
B13 at c B W B13 W B13 at a would recreate the starting position
W14 pass B W B W W14 at a would recreate same position as after W4
B15 at d B W B B15 B15 at b would recreate same position as after B1
W16 at c B W W16 B positional superko same position as after B11
B17 pass B W W B
W18 pass B W W B W18 at a would create an natural situational superko(same position as after W10), W18 at d would recreate position as after W12
B19 at b B B19 W B B19 at c would recreate position after B15
W20 at a W20 B W B
B21 at c W B B21 B
W22 at b W W22 B B
B23 pass W W B B B23 at a would recreate position after B15
W24 at d W B W W24 W24 at c would recreate position after W10
B25 at c W B B25 W B25 at a would recreate start position. (not natural) situational superko same position as after pass B3
W26 pass W B B W W26 at b would recreate position after W4
B27 pass W B B W B27 at a would recreate position after B1 , at d as after B21
W28 pass W B B W W26 at b would recreate position after W4, at c as after W8


Complex fight (feel free to edit)

Quadruple Ko fight
Move A B C D Comments
Start B B W W
B1 at c B B B1 W
W2 at a W2 B B W
B3 pass W B B W
W4 at b W W4 B W
B5 at a B5 W B W
W6 at c B W W6 W
B7 at b B B7 W W
W8 at a W8 B W W
B9 pass W B W B B9 at c would create a natural situational superko(same position as after B3)
W10 at b W W10 W B
B11 at a B11 W W B positional superko same position as after W6
W12 at d B W W W12
B13 at c B W B13 W
W14 at a W14 W B W
B15 at b W B15 B W positional superko same position as after W2
W16 at c W B W16 W
B17 at c W B W B17
W18 pass W B W B W18 at b would create an natural situational superko(same position as after W10)
B19 pass W B W B a would recreate position after B7, c the one after B3
W20 pass W B W B b would recreate position after W10 d the position after W16


old experiments

Quadruple Ko fight
Move A B C D Comments
Start B B W W
B1 at c B B B1 W
W2 at a W2 B B W
B3 at d W B B B3
W4 at b W W4 B B
B5 at a B5 W B B
W6 at c B W W6 B
B7 at b B B7 W B
W8 at a W8 B W B
B9 pass W B W B B9 at c would create a natural situational superko(same position as after B3)
W10 at b W W10 W B
B11 at a B11 W W B positional superko same position as after W6
W12 at c B W W W12
B13 at b B B13 W B positional superko same position as after W6
W12 at c B W W W12 positional superko same position as after B-
B13 at b B B13 W B
W14 at a W14 B W B W14 at d would recreate starting position [1]
B15 at c W B B15 B


one to change (make a copy

Quadruple Ko fight
Move A B C D Comments
Start B B W W
B1 at c B B B1 W
W2 at a W2 B B W
B3 at d W B B B3
W4 at b W W4 B B
B5 at a B5 W B B
W6 at c B W W6 B
B7 at b B B7 W B
W8 at a W8 B W B
B9 pass W B W B B9 at c would create a natural situational superko(same position as after B3)
W10 at b W W10 W B
B11 at a B11 W W B positional superko same position as after W6
W12 at d B W W W12
B13 at c B W B13 W
W14 at a W14 W B W
B15 at c W B B15 W
W14 at a W14 B W B W14 at d would recreate starting position [1]
B15 at c W B B15 B

Quadruple ko fight last edited by 68.122.10.31 on June 4, 2015 - 01:00
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