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Combinatorial Games: Tic-Tac-Toe Theory [Hardcover]

József Beck

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Book Description

April 21 2008 0521461006 978-0521461009 1
Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solitaire and hex. The main challenge of combinatorial game theory is to handle combinatorial chaos, where brute force study is impractical. In this comprehensive volume, József Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine the exact results about infinite classes of many games, leading to the discovery of some striking new duality principles. Available for the first time in paperback, it includes a new appendix to address the results that have appeared since the book's original publication.

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Review

"This is an excellent, extensive, and readable review of combinatorial game theory... The book, which is very hard to put down, ends with an extremely helpful dictionary and list of open problems."
M. Bona, University of Florida for CHOICE

"A most thorough and useful treatment of the subject (so far insufficiently presented in the literature), with an enormous store of results, links with other theories, and interesting open problems."
A. Pultr, Mathematical Reviews

"József Beck has done a tremendous amount of work in this area. Many results appear in this book for the first time. This is a great book that brings many (all?) of the results in this field under one roof."
William Gasarch for SIGACT News

Book Description

In this comprehensive volume, József Beck shows readers how to escape from the combinatorial chaos arising in the analysis of many games by using the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Striking results are obtained and new duality principles discovered.

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