Are you a betting person? Here’s how to calculate the odds.
Mathematician Aczel (Pendulum, 2003, etc.) surveys probability theory, using no math more complex than algebra. He defines probability, then devotes each short chapter to explaining how it works in some concrete instance, such as the odds of drawing a spade from a deck of cards. Building from simpler to more complex examples, the author offers insights into phenomena that seem counterintuitive to many nonmathematicians, such as the “gambler’s ruin,” a proof that while the so-called law of averages will in the long run produce results that fit the predictions of simplistic mathematics, there is no guarantee that they will do so in the short run. In one long trial of coin flips, the number of heads stayed above the number of tails for nearly three thousand turns; in the very long run, it did even out, but gamblers relying on a 50-50 split would have been bankrupted long before the law of averages came to their rescue. Another counterintuitive result is the likelihood that in a group of 23 people, 2 will share a birthday; Aczel shows how to calculate it. Other startling coincidences, like a chance acquaintance turning out to be your wife’s high-school classmate, depend on an extended web of interests and relationships that give all of us more in common than we realize. The author even manages to tie something as apparently esoteric as Baye’s Theorem to everyday discourse by way of the “Monty Hall Problem,” based on the three doors contestants had to choose among on Let’s Make a Deal. A set of problems at the end lets readers test their understanding, and an appendix applies Aczel’s insights to common gambling games.
An entertaining introduction to one of the most universally relevant and most widely misunderstood branches of mathematics.