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Game Theory
Keywords: Problem
Game Theory is a system for describing "games" and practical problems that can sometimes lead to the best (most "rational") solution for a player.
(This is very simplified. Go As game theory applies to go, I think there are some very valuable concepts that can be used to analyze a position. Go is a zero-sum game. One person loses and one person wins. It is not possible for both to win, because the 1/2 point komi does not allow ties. But are individual battles zero-sum? At first glance, they do not appear to be. Both players can come out better off (such as in a joseki). In zero-sum situations, all outcomes are matched, ie if black gains 10 points, white gains 10 loses. But everywhere on this site, I read remarks like "this piece trades off territory for influence" or vice versa. This, to me, shows that battles are zero-sum. I think this needs a bit more explanation. In games like economics, the aim is to maximize your profits. It does not matter how well other players do because no matter how much money they make, you can still make as much as possible. However, in Go, the "real" score (IMO) is the difference between scores. Since both players are competing for the same resources and there is a finite amount of it, every point white takes is a point black cannot take. Since the difference of the score is important, that is what a player should try to maximize. (Eg maximize the lead) So if we look at it this way, battles can be seen as zero-sum. If black takes 15 points of territory, black is 15 points ahead of white (and conversely white is 15 points behind black, so the sum is 0). If white take 8 points of territory and black gains 8 points of influence, white is 0 points ahead, black is 0 points behind, so the sum is 0. More later.
-- SifuEric
TakeNGive (10k): Game theory is interesting to me, but i know little about it. Q: (for Sifu, or whoever knows) How would zero-sum theory quantify the value of a reducing attack -- that is, a play by Black that turns some of what should have been White's territory into dame? This is a copy of the living page "Game Theory" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |