Combinatorial Games: Tic-Tac-Toe Theory

Encyclopedia of Mathematics and its Applications #114

by Jozsef Beck

Traditional game theory has been successful at developing strategy in games of incomplete 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.

Genres: Mathematics

748 pages, Hardcover

First published March 20, 2008

Reviews

[Nathan Rose · Rating 4 out of 5]

Cool book. Didn't have time to finish before it was due (ILL is not very forgiving on renewals or overdues.) Discussed some of the theory involved in strategy (combinatorial) games, like tic-tac-toe, tetris, solitare etc. Not all moves are statistically equal, but modeling all available moves and the combinations of future moves generates a massive matrix that's just too large/complex to be useful. This book offered some ideas on ways around the plug-and-chug method of analysis, but I just didn't have the time to finish. Definitely a summer reading list book.