Luck, Logic, and White Lies: The Mathematics of Games, by Jörg Bewersdorff, translated by David Kramer, 2004. 504 pp., $49.00 paper. ISBN 1- 56881-210-8. A K Peters; (781) 416-2888; www.akpeters.com.
Classifying this book, a translation of a German text, is difficult. It is definitely not a textbook, since there are no exercises. It is not an encyclopedia, although it does treat a large variety of games. It is not a history of the subject, although there is a strong historical flavor. The best description is that the book shows, in a very inviting way, that mathematical tools can be applied to a wide variety of games, from the familiar (dice games, nim, fair division) to the surprising (Chutes and Ladders, Monopoly). The games are divided into three major categories: games of chance, combinatorial games, and strategic games. The presentation is engaging. Each chapter begins with an interesting question about one or more games and then attempts to answer the question. In the course of finding answers, significant mathematics is used and/or discussed, including combinatorics, Markov chains, Monte Carlo methods, and Godel's incompleteness theorem. The author also indicates the historical context of many of the questions, so the reader encounters both successes and failures in attempts at solutions.
As might be expected given the scope of the book, the mathematical level varies greatly. Some of the mathematical material is accessible to high school students, while other parts demand much more effort. There is considerable use of mathematical symbolism. The general flow of many of the chapters can be followed without understanding every mathematical detail, however. Readers are directed to many additional resources (often, German publications) for exploring topics or problems more deeply. There are a few typographical errors, and some (not serious) inconsistencies. A table of 100 numbers between 1 and 99,? for example, includes 100 (p. 98). I would recommend this book to high school and college teachers for their own enrichment, as a resource book for good students, and as a source for classroom activities.
Sonora, CA 95370
Mathematics Teacher, 99/5 (Dec. 2005/ Jan. 2006), p. 382