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taken from Kami no Itte
choreck?: I was thinking on perfect move while watching strong ama/pro games on go servers. Well, toward the endgame move values? tend to be close to several points, say around 6-8 points (komi value) down to 1, then 1/2 and then zero. We start, equally with komi, and all these remind me telescopic series in calculus, (analogy may be wrong!). I think, and feel, that in a perfect game a move value may be at most the komi value. So that at each move, the result of game alternates around zero (like telescopic series), and when the board fills up, alternation amplitude decreases and game finishes with white playig last. Of course sente gote issue changes alternation frequency nature. With komi being an integer, and with its true theoretical value, game results with jigo. Perhaps this alternation is not constant through the endgame. May be, it starts from komi value, say 7, increases a little and then decreases down to zero. May be, this change is due to topology of the board, or say dimension.
I wonder what do you (who knows more) think about this.
HolIgor: Twice that of the komi value. As an example let us consider a sequence of moves with values 4, 3, 2, 1. The first player takes 4, the second 3, the first 2 and the second 1. The score is (4+2) - (3+1) = 2. So, the komi in this game should be 2 , which is equal to the half of the largest move. A general mathematical proof can be found somewhere in the library.
Willemien I doubt this very much.
McFry? Proof: Let Black and White play a game without a komi. With optimal play, Black wins by x points. If Black passes on his first hand and then continues to play optimally, then White wins by x points, because White faces the same situation Black faced before Black passed. So the first hand is worth 2x points, and the optimal komi value is x points, because then optimal play will lead to a draw. Therefore, the first hand is worth twice the optimal komi value.
Also, x is not negative, for if it were, then Black would lose a 0-komi game regardless of play. But if Black passes, then White loses because of the identical situation, so Black has a not-losing strategy, therefore x cannot be negative.
Dalf?: even with perfect play, you cannot tell the real value of a move. One of the intermediate moves, even in the yose (when it is a reply), maybe such that not playing it would lose a big group and the game. You can define "value of a move" the score you lose if you deviate from perfect play, but the example above (getting a group killed), shows that [urgent moves] may be very big. Well, obviously.
blubb: I don't agree here. Knowing perfect play from each situation would rather allow to exactly determine the value of a move. Since passing has a value of zero, a move is worth as much as it gains compared to a pass instead, in terms of the final score after a perfect play continuation.
Bill: As for the first question, sente, ko fights, furikawari, and other battles? may increase the value of the largest play?, at least temporarily. But even if we ignore such hot battles, what few indications we have, such as environmental go games, do not show a linear trajectory in the size of plays.
[@blubb]: That's not true. Passing isn't always equal to a value of zero. Consider a fight where if black goes, whites gets eaten but if white goes, black gets eaten. Passing for black would mean the loss of pieces, as well as the loss of the opportunity to take white's pieces. In this case, passing is not worth zero, but a negative value.
also taken from Kami no Itte
Tomas?: I have two questions about perfect play: Suppose a (hypothetical) computer plays perfect. We can assume that the value of his first move is twice the ideal komi. We can also assume that his last move (a pass) has no value. Can we assume that the value of the moves in between gets smaller every move? And can we maybe even assume that this happens linear? The second question is more like a poll cause nobody can know for certain, but maybe some strong players can give some reasonable estimate: How much handicap would the best pro's today have to give to a perfect playing computer?