Luck, Logic, and White Lies: The Mathematics of Games, by Jörg Bewersdorff, translated by David Kramer. Wellesley, MA, A. K. Peters. 2005. 486p, bibliog., index. ISBN 1-56881-210-8. $49.00. LC Call no.: QA269.B39413 2005.

Subjects: Game Theory.

Reviewer: Holly Flynn, Mathematics Librarian, Michigan State University Vernon G. Grove Research Library, flynnhol@msu.edu

1. Games of Chance 1
2. Dice and Probability 3
3. Waiting for a Double 6 8
4. Tips on Playing the Lottery 12
5. A Fair Division 23
6. The Red and the Black 27
7. Asymmetric Dice 33
8. Probability and Geometry 37
9. Chance and Mathematical Certainty 41
10. Winning the Game 57
11. Which Die is Best 67
12. A Die is Tested 70
13. The Normal Distribution 77
14. And Not Only at Roulette 90
15. When Formulas Become too Complex 94
16. Markov Chains and the Game Monopoly 106
17. Blackjack 121
18. Which Move is Best 137
19. Chances of Winning and Symmetry 1149
20. A Game for Three 162
21. Nim 168
22. Lasker Nim 174
23. Black-and-White Nim 184
24. A Game with Dominoes 201
25. Go 218
26. Misere Games 250
27. The Computer as Game Partner 262
28. Can Winning Prospects always be Determined 286
29. Games and Complexity 301
30. A Good Memory and Luck 318
31. Backgammon 326
32. Mastermind 344
33. Rock-Paper-Scissors 355
34. Minimax Versus Psychology 365
35. Bluffing in Poker 374
36. Symmetric Games 380
37. Minimax and Linear Optimization 397
38. Play It Again, Sam 406
39. Le Her 412
40. Deciding at Random 419
41. Optimal Play 429
42. Baccarat 446
43. Three-Person Poker 450
44. QUAAK 465
45. Mastermind 474

Index 481

Ever since Beat the Dealer by mathematician Edward O. Thorp was published in 1962, people have been fascinated by the idea of using mathematics to win games. While Dr. Thorp’s book only looked at card counting in blackjack, Luck, Logic, & White Lies looks at winning strategies for all kinds of games, from "rock-paper-scissors" to Monopoly to roulette.

Luck, Logic, & White Lies was originally written in German in 2001. It has since been translated into English by David Kramer and is now in its third edition. This latest edition explains some new developments in the field of game theory and corrects some errors that were in previous editions.

Jorg Bewersdorff, the author of the book, knows a great deal about the gaming industry. He is the general manager of a German game design company and is the director of research and development for a company that designs money-changing machines.

The book under review is arranged in three parts. The first part deals with games of chance. These are games such as roulette in which the influence of chance dominates the decisions of the players. Games of this sort can be analyzed with probability theory. Probability, the author explains, is a measure of the certainty with which a random event occurs.

In the second section of the book, the author writes about combinatorial games, or games whose uncertainty rests on the number of possible moves. Chess and checkers are examples of this kind of game. Combinatorial games can be analyzed with a variety of mathematical methods such as Zermelo’s Theorem.

Finally, the third section of the book deals with strategic games, in which all of the players do not have all of the same information about the current state of the game. "Rock-paper-scissors" is a strategic game. A branch of mathematics known game theory is used to analyze games of this sort. Game theory has been studied since the early 1940’s and is used to solve real-world problems, not just games.

Bewersdorff points out that most games combine elements of strategy, chance, and combinatorics, so a variety of methods may be needed to win a single game. The author also assumes very little mathematical knowledge, so the reader need not be skilled at high-level math to make sense of this book. For those who are interested in advanced mathematics, a bibliography of "specialist literature" is included in each section. Each chapter can be read individually, too, so the reader who is interested in one specific game does not need to read the entire book. Each chapter begins with a question, such as "in the game of Monopoly, one wishes to evaluate the various properties according to the expected income from rent. How should one proceed? (p. 106)." The author then explains what the problem is and the mathematical methods that can be used to solve it.

This book is a must for anyone interested in gaming. Since it is not particularly scholarly, it would be most suitable for a public library or even an undergraduate academic library. Students with an interest in mathematics will find this book to be of interest.