Chance by Amir Aczel

Aczel, Amir D. Chance: A Guide to Love, the Stock Market, and Just About Everything Else. New York: MJF Books, 2004.
ISBN-13: 978-1-56731-735-0
ISBN-10: 1-56731-735-9

Chance is an introduction to the basic principles of probability and how they can be applied to understanding real-life activities. The math is not difficult. Someone with a good foundation in arithmetic and algebra should be able to follow it. Where more advanced math might be needed, Aczel presents the gist and moves on.

One of the interesting issues brought up in the book is how probability can give rise to counterintuitive situations. What we sense may be the likelihood of something may be very different than the probability worked out mathematically—the math better fits reality. One of these examples is how random events can, and often do, result in unexpected aggregations. For example, a fair coin has equal chances of coming up heads or tails, but if you flip it enough times, you’ll find times when heads (or tails) may be repeated in hundreds or thousands of sequential flips. Unlike events can be surprisingly likely if given enough trials.

This may be why unlikely things sometimes happen in gambling, because it is so common. Aczel acknowledges the early history of probability as a way to understand gambling problems. He draws several examples from casino games, poker and horseracing. The mathematician’s admonition concerning casino gambling is don’t do it. Most betting games are good examples of probability because the potential risks and payoffs are known. Poker provides and example of dealing with uncertainty. For those who follow the ponies, an appendix by Brad Johnson provides an understandable description of how pari-mutuel betting works.


Not all the examples are drawn from gambling. Aczel also describes how probability relates to polling and polling errors, coincidences, and making choices in life and in games.

A drawback of the edition I read was typographical errors in some of the mathematical formulas and equations. Those familiar with the notation will quickly sort out what was intended, and others can follow the text. In one instance, the formula is made wrong by the typo, but the text describes it correctly.