Pair ko rule: How does it compare to superko?

[john.tromp]

@antonTobi

I think that if white connects a ko, black will be able to escape.

If after Black J10, White fills the ko at G10, then Black can fill at K8.

After M8 J6 J9 H5 K5 (defending against the double-atari at L6) G4,

Black can make 2 eyes.

[LuisB]

You’re right. This is a good example of a situation that would play out differently under the pair ko rule.

[LuisB]

Is it an alternative in the sense of also preventing infinite games?

Yes, it is. In fact, the longest 19x19 Go game played under pair ko rules cannot be longer than 19^4 moves.

[LuisB]

@Feijoa

You cannot play at point B immediately after an incursion by your opponent at point A if, on any earlier turn, you played at point B immediately after an incursion by your opponent at point A. Passing is always allowed. Suicide is not allowed.

Am I understanding correctly that in the normal case, when White makes the capture at A (the first incursion),

then Black can immediately recapture (“played at point B immediately after an incursion”), and White can recapture again, but then a second move at B is blocked?

Yes. That’s why I recommend using the pair ko rule along with the ko rule.

@Feijoa

An incursion is a play by one player in a territory owned by the other player. A territory is a maximal set of connected empty points. You own a territory if all stones connected to it are of your color.

Also is this an example of White playing at B immediately after an incursion at A?

No, A is not an incursion because the empty board is surrounded by 0 colors, not 1.

[john.tromp]

White at B is an incursion though, so if Black next plays at C, then if much later, White plays at B again after Black has captured it, then Black would not be allowed to play at C next.

At that later time, the players may not remember the earlier “incursion” though, and would be making illegal moves without realizing it. That seems less of an issue with superko.

[john.tromp]

the longest 19x19 Go game played under pair ko rules cannot be longer than 19^4 moves.

It can go on longer since an incursion can be followed by a pass.

[john.tromp]

@LuisB

An incursion is a play in an empty area only connected to enemy stones.

It would make more sense to me of an incursion was simply a play on a point all of whose adjacent points are occupied by enemy stones. By necessity, an incursion must capture some of these stones in order to gain a liberty (single stone suicides are not allowed in any ruleset I know of; one can pass to get the same result).

What’s the point of considering any move in strict enemy territory to be an incursion? Doesn’t having many more moves be incursions make the rule harder to apply?

[LuisB]

@john.tromp

the longest 19x19 Go game played under pair ko rules cannot be longer than 19^4 moves.

It can go on longer since an incursion can be followed by a pass.

Good catch! You could in fact create a cooperative cycle like that. The rules should forbid instead the repetition of pairs of plays with any number of passes in between, where the first play in the pair is an incursion and the two plays can be made by the same player of by different players.

I just fixed this in the Sensei’s Library entry:

You cannot play at point B immediately after an incursion by your opponent at point A if, on any earlier turn, you played at point B immediately after an incursion by your opponent at point A. Similarly, you cannot play at point B after an incursion by you at point A, with no other plays in between, if, on any earlier turn, you played at point B after an incursion by you at point A, with no other plays in between. In this case, A and B are separated by an opponent’s pass. Suicide is not allowed. Passing is always allowed.

[LuisB]

@john.tromp

@LuisB

An incursion is a play in an empty area only connected to enemy stones.

It would make more sense to me of an incursion was simply a play on a point all of whose adjacent points are occupied by enemy stones. By necessity, an incursion must capture some of these stones in order to gain a liberty (single stone suicides are not allowed in any ruleset I know of; one can pass to get the same result).

What’s the point of considering any move in strict enemy territory to be an incursion? Doesn’t having many more moves be incursions make the rule harder to apply?

The point is that all cycles include at least one play in an empty area connected only to enemy stones, so defining incursions like that guarantees a finite game. Your suggestion would allow many cooperative cycles and some forced cycles like eternal life.

[john.tromp]

Good point; you can play forever without making any captures with the capturing stone temporariy having no liberties.