Bewersdorff, Jörg. Luck, Logic and White Lies: The Mathematics of Games, tr. by David Kramer. AK Peters, 2004. 464 p. ISBN 1-56881-210-8, pbk $49.00
The character, not just the content, of college mathematics differs markedly from what comes before. Likewise, advancing to research mathematics requires of the student yet further adjustment. Students who have secured all the fundamentals and wish to learn how mathematicians really think accordingly prize self-contained books on attractive, active topics. For such students, E. Berlekamp, J. H. Conway, and R. Guy's magisterial Winning Ways for Your Mathematical Plays (CH, Sep'82), the most important mathematical treatment of combinatorial games, holds a distinct attraction. Unfortunately, a student, once drawn in, may find Winning Ways technically self-contained but nevertheless a tad too sophisticated; the authors make a beeline right to their own novelties and leave little space for building context. Game designer Bewersdorff not only offers a gentle stepping-stone to Winning Ways but also treats combinatorial games side by side with games of chance (probability theory) and games of imperfect information (Von Neumann's game theory), all the better for students to glean common themes and see the differences. Fortunately, Bewersdorff has in no way sacrificed to the altar of accessibility all the delicate examples that demonstrate the idiosyncratic phenomena that charge this subject. This is a meticulous book that fills a real need. Combinatorial games of a special sort--connection games--feature objectives with a topological character. For example, in Hex, the best-known of them, each player seeks to make the first chain linking his or her two opposite sides of a rhomboidal hexagonal grid. Software engineer Browne's book, an obvious labor of love, catalogs hundreds of variations on this theme. For each game, the author sets forth the rules, describes the history, accesses the challenges, rates the interest, reviews the practical playability, and generally offers some strategy tips. Students of computer science will find each game here a potential project, namely, the creation of a strong, automated opponent. Students of mathematics should turn to the 25 pages of appendixes that discuss graph theory, the Shannon game, strategy stealing, point-pairing strategies, Sperner's lemma, tessellations, and more, offering ample possibilities for entertaining enrichment of any discrete mathematics course.
Summing Up: Bewersdorff: Highly recommended; Browne: Recommended. Both books: Upper-division undergraduates through faculty. D. V. Feldman, University of New Hampshire
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