Ing-Spight Ko Rule
Board play: A play that places a stone on the board.
A board play is considered the same as another board play if and only if:
1) the same player makes the play;
2) the stone is placed on the same point;
3) if the stone is connected to other stones, they are on the same points;
4) if any stones are removed, they are removed from the same points.
Comment: Just playing on the same point does not make a play the same as another play. Snapback is not ko.
Cycle: A sequence of board plays that may repeat.
Odd cycle: A cycle consisting of an odd number of plays.
Comment: An odd cycle cannot repeat immediately, since the same player cannot play twice in a row.
Even cycle: A cycle consisting of an even number of plays.
Ko: An even cycle that does not contain an odd cycle, even if the odd cycle occurs with intervening plays.
Comment: If the sequence, abc, is an odd cycle, the sequence, adebfgch contains it, with intervening plays. This definition prevents the players from colluding to make a ko out of two odd cycles. That may not matter in casual games, but such collusion may be undesirable in tournaments.
Ko play: A play in a ko.
Hot stone: A stone that has been played in the current sequence of ko plays.
A hot stone may not be captured unless that capture is not a ko play.
Comment: If a player claims that her opponent has captured a hot stone, she must show that the hot stone was played as part of a ko, that all plays since it was played have been ko plays, and that the capture of that stone is part of a ko. Then the capture is undone and the opponent may make another play.
An odd cycle may be played once only, even with intervening plays.
All of - are hot stones. White may not continue the ko without playing elsewhere or passing. Ing classifies this as a Fighting ko (ko type).
is hot. White may not play at a.
Suppose that and are ko threat and reply.
All of - are hot. Black may not now continue the ko. By contrast, under a superko rule White is prohibited from continuing the superko first (next diagram.)
returns to the same position, but in an odd number of plays. This is not a ko but an odd cycle, and is allowed only once. No stones are hot.
Ing classifies this as a disturbing ko. Disturbing kos may be played only once.
- are all hot. White cannot now continue the ko.
It is apparent that White cannot win this ko, because only White needs to find ko threats. White is dead.
Ing classifies this as a disturbing ko, but as a disturbing ko mutual life, not a disturbing ko death.
In 5 moves White can return to the original position. So this is a ko by our definition. Ing apparently classifies this as a disturbing ko, even though it plays as a fighting ko under these rules.
The main way that this ko rule differs in its effect from Ing rules is that a double ko death can never be used as a ko threat. Ing allows it to be used once. Also, at least one of Ing's official examples has a different status.
Bill: This page arose from my reexamination of Ing's distinction between fighting kos and disturbing kos. Ing's ko definitions are circular, because he claims that questions of life and death are decided only by capture, but whether ko stones may be captured depends upon whether a ko is fighting or disturbing, and that depends upon whether the question of life and death is settled for that ko. There are examples of disturbing kos that would be fighting kos if their life/death status were defined differently.
What struck me in my reading this time was a distinction that Ing makes between fighting and disturbing kos. In a fighting ko the players capture and recapture the same stone or stones, while in a disturbing ko they capture different stones. In that case, prohibiting the recapture of ko stones would affect fighting and disturbing kos differently, and virtual play with that prohibition could distinguish between them. (See Fighting Ko and Disturbing Ko /Logical definition.)
I then realized that I could make a ko rule for actual play that would not require making the fighting/disturbing ko distinction, but would have the same effect as making that distinction by virtual play. That, of course, is much simpler and far preferable. To do so, the prohibition against recapture could not be lifted by just any play, but had to remain in effect during ko plays. Only non-ko plays (including passes) can lift the prohibition.
I could not completely eliminate the fighting/disturbing ko distinction in this way. Ing classifies odd cycles as disturbing kos, with no restriction on capture except for allowing them to be played only once. That is the reason for the odd cycle rule.
(More thoughts): The classification of fighting/disturbing ko by hypothetical play depends upon ko bans that are not removed. To translate that to actual play, ko bans have to remain even when other moves in the ko are made, while non-ko plays remove the ban. The question is, what is a ko play? When you are given a ko to classify, there is no problem with that, but how do you determine whether a play is a ko play before the ko cycle is completed? (BTW, Ing actually does identify ko plays before they are made to determine which stones are hot.) The problem with that is that there may be hidden kos that depend upon the mutual sacrifice of a number of stones. A quite ordinary play might turn out to be a ko play, and banned because of that. The fact that Ing allows suicide makes this possibility more likely.