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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114) - Hardcover
Synopsis
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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About the Author
József Beck is a Professor in the Mathematics Department of Rutgers University. He has received the Fulkerson Prize for Research in Discrete Mathematics and has written around 100 research publications. He is the co-author, with W. L. Chen, of the pioneering monograph Irregularities of Distribution.
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
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ISBN 10: 0521461006
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Encyclopedia of Mathematics and Its Applications: Combinatorial Games: Tic-Tac-Toe Theory (Volume 114)
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ISBN 10: 0521461006
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
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Combinatorial Games : Tic-tac-toe Theory
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
Published by
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ISBN 10: 0521461006
ISBN 13: 9780521461009
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
Published by
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ISBN 10: 0521461006
ISBN 13: 9780521461009
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Combinatorial Games: Tic-Tac-Toe Theory (Hardcover)
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ISBN 10: 0521461006
ISBN 13: 9780521461009
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Hardcover. Condition: new. Hardcover. 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, Jozsef 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. 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. This is the subject of combinatorial game theory. Most board games are a challenge for mathematics: to analyze a position one has to examine the available options, and then the further options available after selecting any option, and so on. This leads to combinatorial chaos, where brute force study is impractical. In this comprehensive volume, Jozsef 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 exact results about infinite classes of many games, leading to the discovery of some striking new duality principles. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521461009
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Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications, Series Number 114)
Published by
Cambridge University Press, 2008
ISBN 10: 0521461006
ISBN 13: 9780521461009
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Combinatorial Games : Tic-tac-toe Theory
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