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Game theory
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Difficulty: Beginner
Keywords: Problem, Theory
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
RafaelCaetano: This is a bit confusing. These links point to "classical" game theory, which is quite general but more related to economy than to games like go. I've read the history of this page and it seems that it started with the assumption that classical game theory has much to say about go, but this page doesn't say exactly what. Perhaps the author confused it with combinatorial game theory? OK, it can be said that CGT is a branch of a general game theory, but so what? Now, this page has been edited quite a bit, and frankly I can't see what it's about.
See game theory interface for comments on how to approach combinatorial game theory as a go player. Go belongs to the class of games of partisan combinatorial games, whose general mathematical treatment did not come until John Conway saw go being played. For more information see the books: On Numbers and Games[1] by John Conway. Also Mathematical Go: Chilling Gets the Last Point by Elwyn Berlekamp and David Wolfe. BillSpight: Go is a 2-person zero-sum game with perfect information. In the end game it tends to decompose into more or less independent regions, each of which is a game. Combinatorial games add and subtract. Games with kos do not add and subtract, and are not, strictly speaking, combinatorial games. For instance, a zero game may be a ko threat. Adding a zero game to a combinatorial game does not change it, just as adding zero to a score does not change it. But adding a ko threat to a ko may change it, even if the threat is a zero game. However, much of combinatorial game theory can be applied to go, particularly thermography, a method that determines the count and size of plays in a position. Thermography has been extended to cover kos by Professor Berlekamp and myself. A related concept, temperature, is useful in thinking about go. Go is a zero-sum game. One person loses and one person wins. But are individual local battles zero-sum? This is a question to pose; but the standard answer by means of the exchange concept leaves no mystery. If one player gains locally, that says just the same as the other player losing. Characteristic of go is the trade-off for'assets' of different kinds: typically territory against influence. There will be, in all cases, a number based on a 'best play' continuation after that, which tells one how many points were gained or lost in a local sequence. In most cases outside the endgame we aren't likely to be able to give that number exactly. (Sebastian:) Let's look at it this way: With a simple mathematical operation we can, instead of looking at the scores for B and W individually, look at B+W and B-W. Go as a game only regards B-W. What would be the use of tallying up B+W at every instant if you disregard it in the end? RafaelCaetano: Just make up a few examples yourself and see what it turns out. Tip: use area rules. [1] No go content. Page edit 4 July 2003 by Charles Matthews Path: CGTPath · Prev: DominatedOptions · Next: MinimaxDiscussion Path: PleaseReviewMe · Prev: SowDiscordInTheEnemySCamp · Next: KanazawaSolution43 This is a copy of the living page "Game theory" at Sensei's Library. ![]() |