santo wrote:
I've been thinking some more about this "resumptions are important for Japanese rules analysis", which I was not aware of before (mannen ko is now the only position that I know with this property
A simpler one is
1EyeFlaw. But I think the option to resume playing is a natural part of the game, regardless of rules used (and passes lift bans).
Quote:
But arbitrary resumptions could lead to a similar effect: players could resume again and again and make a capture-exchange in the double ko. Even more, depending on how carefully the opponent of the repeating player plays, two different "final positions" might appear, so not all the resumptions are ending with exactly the same board. These are equivalent as the difference would just be which "side" of the double ko is open, but nevertheless it is confusing to have an inter-resumption-cycle with more than one final-position occurring. How is it decided when to definitely stop, and which of those two to use for scoring? Maybe in some more complex case the different positions among the long inter-resumption cycle might lead to different results in the game. Is there a procedure for this?
Good questions. Some of these also came up in the examples section of sensei's RR page. First, I think an important (unwritten) assumption is that although several resumptions are possible, one can not resume the game an infinite times (in practice).
But even with finite resumptions, cycles spanning stops remain a question. In particular, it seems very hard to get the correct ruling for ALL three of examples
1+
2+
6 of RR. (Most current rulesets have problems in
example 6, and superko in 1 as well.)
What is a true final position? Two approaches seem possible for answering this.
With superko, since repetition is forbidden, you just need positions that are stable under superko. So double ko seki is a stable seki and stoppable not because of passes but because of this stability (with the two stable positions score-wise equivalent - luckily).
With normal ko, I think the first idea could be that two successive passes, if happen periodically and infinitely, should be enough to claim an end position and reject an infinite cycle. This works for things like mannenko or example 1, but example 6 shows this condition is not sufficient. OC in that case, the stop positions are not equivalent score-wise, which hints at a possible refinement. (But example 9, which I yet to finish analysis of, remains particularly challenging here.)
I doubt actual rulesets thought a lot about these questions theoretically. CJK rules are often incomplete, even for more practical things. Superko breaks any cycle, without worrying whether that is correct or not (1EyeFlaw and others). With RR you have minimal superko as a possible answer.