Amir D. Aczel’s Chance: A Guide to Gambling, Love, The Stock Market, & Just About Everything Else, is an entertaining little book, as the title implies. Since the book assumes no prior knowledge of probability theory, it lends itself nicely as supplemental reading for students in introductory courses in probability as well as statistics.
The first half of the book gives a very elementary, non-mathematical introduction to the basic rules for probability theory involving unions and independence of events. The second half contains some well-written, interesting uses of these rules, starting with a treatment of random walks and the gambler’s ruin. But there is no excuse for the sloppy ways the formulas are written for the probability of reaching a fortune of size m + n, starting with a fortune of size m. Non-mathematical readers do not need that kind of confusions in a book intended for exactly that audience.
The question of what is randomness is answered in a chapter five pages long. Then follows short chapters on Pascal’s triangle, the inspection paradox, and the birthday problem. The book really comes into its own in the last third where the author takes up additional uses of probability theory. It is good to see a book like this giving a discussion of coincidences we experience every day but do not discuss much in our classes. A student audience may find good guidance in the chapter on how to succeed in love and other activities as well as how to make decisions under uncertainties. Bayes' theorem gets its own well-written chapter. I do not understand why the chapter on the normal distribution is included, it does not seem to add much to the presentation. Also, I do not understand why there is an appendix written by Brad Johnson on various card games and why that material is not integrated into the earlier parts of the book.
Gudmund Iversen is Professor Emeritus of Statistics at Swarthmore College.