| Combinatorial Games: Tic-Tac-Toe Theory Contributor(s): Beck, József (Author) |
|
 |
ISBN: 0521461006 ISBN-13: 9780521461009 Publisher: Cambridge University Press OUR PRICE: $209.00 Product Type: Hardcover - Other Formats Published: March 2008 Annotation: 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, J??zsef 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Game Theory - Mathematics | Discrete Mathematics |
| Dewey: 519.3 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 1.75" H x 6.47" W x 9.35" (2.67 lbs) 748 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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, J zsef 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. |
Contributor Bio(s): Beck, Jozsef: - Jozsef 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. |