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 The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. Members include teachers at the college and high school level; graduate and undergraduate students; and mathematicians and scientists. (2006) 192 pp., hard cover, ISBN ISBN
International Standard Book Number
ISBN International Standard Book Number
ISBN n abbr (= International Standard Book Number) → ISBN m 0-88385-646-8 RRP RRP n abbr (= recommended retail price) → PVP m US$44.00
This book begins with the history of many gambling-related games and activities and then brings out the elementary probability theory probability theory
Branch of mathematics that deals with analysis of random events. Probability is the numerical assessment of likelihood on a scale from 0 (impossibility) to 1 (absolute certainty). 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 Many probability distributions are so important in theory or applications that they have been given specific names. Discrete distributions
With finite support
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 permutations and combinations: see probability.
permutations and combinations
Number of ways a subset of objects can be selected from a given set of objects. In a permutation, order is important; in a combination, it is not. . He also demonstrates the selection of outcomes with and without replacement using poker, bridge, and Keno type games. Personally, I think the binomial distribution binomial distribution
The frequency distribution of the probability of a specified number of successes in an arbitrary number of repeated independent Bernoulli trials. Also called Bernoulli 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.