Let's suppose that you have a position where you can move to a local count of G with gote or S with sente That condition requires R to be gote, and in the counterexample it is sente. I suspect that in practice a lot of people would check cases 1 and 2 and skip case 3.Įdit: The condition, A > 2D, was what allowed me to come up with the counterexample. A fair amount of the time none of the cases will be satisfied, for either choice of plays, which means that the comparison has to be read out, which is what people tend to do anyway. is a gote with a relatively small follow-up. I think that it is necessary to make the comparisons tractable, but the resulting simplifications are not always intuitive. The logical simplification of the tree is not always straightforward. However, it can be pruned pretty drastically. Well, even with only four small games the game tree is fairly large.
I also need to understand where your class of counter-examples fits into the picture of your implied new proposition.Īlthough the cases are interesting in theory, we might say that they are already slightly more complicated than players would want to apply in practice. I suppose you have done it in your mind and maybe I could do it in writing now that I see the proof structure but I suppose I lack time during the few days before the European Go Congress and during it.ĭoes the completeness of the cases pop out naturally during working out the proof? Anyway, interesting, thank you! The sketch of your proof needs to be worked out. So the structure of a proof starts with playing the difference game, whose advantage is that the environment is part of the input but drops out quickly so case study is restricted to the two local endgames.
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