J. Bewersdorf: Luck, Logic and White Lies: The Mathematics of Games, A.K. Peters, Wellesley, 2004, 486 pp., USD 49, ISBN 1-56881-210-8

The book is divided into three parts roughly corresponding to topics indicated in the title of the book. Games of chance are investigated in the first part. The influence of randomness is typical for roulette and various dice and card games. In the middle part, the second type of games is analyzed (combinatorial games, e.g., chess and go). The book ends up with strategic games. Rock-paper-scissors is the most simple and well-known game considered in this part. The author reviews mathematical methods that have been developed for different types of games according to their character. For games of chance an important mathematical tool is provided by probability theory, which can help to answer question what is a probability to win for a particular player as well as more complicated questions. Combinatorial games are investigated by mean of combinatorial gametheory. Due to a large number of combinations involved, it is necessary to look for algorithms and computational procedures in order to solve specific problems. Mathematical game theory is applied to analysis of strategic games. Many other examples of more or less known games are used to explain mathematical methods considered (e.g., backgammon, Monopoly, blackjack, nim, domino, memory, mastermind, poker, checkers, Hex, Le Her, baccarat, nine menís morris, go-moku). The book is well-written and can be recommended to all readers with interest in game theory. Although a lot of mathematics is used in the text, it doesnít require a deep mathematical background. There are many references (mostly in German) helping to find more detailed information about considered topics. (zpw)

Newsletter of the European Mathematical Society, 56 (June 2005), p. 45