I have come up with a new way to prevent cycles. I call it the pair ko rule. It goes like this:
Quote: There is an off-board location called memo. Whenever you make a play immediately after an enemy play in your territory, add to the memo an entry with your opponent's last move, your current move and your color. Do not include information about captured stones. Some examples of valid entries are "B6 M15 Black" and "O10 D4 White". Your territory is all empty regions touching your stones only.
You cannot make a play that requires you to repeat an existing entry on the memo. Passing is always allowed. Suicide is not allowed.
For convenience, this rule can be complemented with the basic ko rule. Otherwise, every ko can be taken three times in succession before the first ko threat is needed. This makes the game longer but does not change the result.
Since highly skilled players can replay their games from memory, I think they would have no trouble complying with the pair ko rule even without the memo. Note that this only requires players to keep track of 17 new bits of information for every play in enemy territory, while superko requires keeping track of 573 new bits for every move.
Pair ko produces almost the same game as superko, but it affects long cycles differently. It also turns double-ko seki into a complex ko fight, which seems good news to me. Does it change the result of any other non-cyclical positions? Do you think it would be a good replacement for superko?
(As an aside, since all forced cycles include at least one sequence of two consecutive plays in enemy territory, the rule could even be simplified to: "Do not repeat a sequence of two consecutive plays in enemy territory, one by each player. A play is defined by its color and its coordinates, regardless of any captures it makes." This would still allow cooperative cycles, but those are not a concern.)
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