Table of Contents: - Games of Chance 1
- Dice and Probability 3
- Waiting for a Double 6 8
- Tips on Playing the Lottery 12
- A Fair Division 23
- The Red and the Black 27
- Asymmetric Dice 33
- Probability and Geometry 37
- Chance and Mathematical Certainty 41
- Winning the Game 57
- Which Die is Best 67
- A Die is Tested 70
- The Normal Distribution 77
- And Not Only at Roulette 90
- When Formulas Become too Complex 94
- Markov Chains and the Game Monopoly 106
- Blackjack 121
- Which Move is Best 137
- Chances of Winning and Symmetry 1149
- A Game for Three 162
- Nim 168
- Lasker Nim 174
- Black-and-White Nim 184
- A Game with Dominoes 201
- Go 218
- Misere Games 250
- The Computer as Game Partner 262
- Can Winning Prospects always be Determined 286
- Games and Complexity 301
- A Good Memory and Luck 318
- Backgammon 326
- Mastermind 344
- Rock-Paper-Scissors 355
- Minimax Versus Psychology 365
- Bluffing in Poker 374
- Symmetric Games 380
- Minimax and Linear Optimization 397
- Play It Again, Sam 406
- Le Her 412
- Deciding at Random 419
- Optimal Play 429
- Baccarat 446
- Three-Person Poker 450
- QUAAK 465
- Mastermind 474
Index 481 Ever since
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. |

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