# The Mathematics of Games and Gambling (2nd edition).

The Mathematics of Games and Gambling (2nd edition) Edward W. Packel Published by The Mathematical Association of America (2006) 192 pp., hard cover, ISBN 0-88385-646-8 RRP US\$44.00

This book begins with the history of many gambling-related games and activities and then brings out the elementary probability theory behind each of these games and activities. It can be divided into two parts: Chapter 1 to Chapter 3 and Chapter 4 to Chapter 7. The first part is suitable for readers who are interested in games for leisure and gambling purposes but do not have a strong mathematics background. The second part involves more mathematics and probability, such as counting methods and probability distributions. High school students will find this book a good preparation for doing an elementary statistics and probability course at university level. This book is also a good resource for first year university students, in particular in mathematics and statistics, to understand the theories behind the games.

The author explains the notions and axioms of probability without technical language. Fair dice and cards are used to demonstrate probability calculations and the odds of one event against another one. The mathematical expectation or the expected pay-off of a game is extremely important to readers as the players or the gamblers can use this value to judge whether the game is fair, or is biased in favour of themselves or their opponents.

Counting methods are essential in probability calculations. The author distinguishes between permutations and combinations. He also demonstrates the selection of outcomes with and without replacement using poker, bridge, and Keno type games. Personally, I think the binomial distribution and the normal approximation to binomial probabilities are probably the most difficult mathematics for most readers of this book. But I would say the gambler's ruin problem is the most interesting topic to readers, as it presents the cases when the player will be ruined in a repeated game with different winning probabilities.

This second edition provides a number of websites and online resources for games and is updated with popular games such as online poker. It is a good reference for the mathematics of games and gambling.
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