THE PERFECT BET

A lucid yet sophisticated look at the mathematics of probability as it’s played out on gaming tables, arenas, and fields.

Scissors cut paper, rock smashes scissors, paper covers rock: we all know the game, and some of us have a sense of when to play which of the three choices. Game theory, writes Kucharski (London School of Hygiene and Tropical Medicine), would hold that the optimal strategy is simply to choose randomly, by which you would come out even in the long term. However, most of us are more predictable than that: if we win with rock over scissors, then we’ll choose rock next time. We may shift our strategies, but we’re not playing randomly—and in any event, Kucharski observes, “the irony is that even truly random sequences can contain seemingly nonrandom patterns.” Sure, card counting works to some extent, but most mathematical behavior is a kind of learned guesswork and a lot of hunch playing. The author doesn’t reveal secrets of winning so much as he looks at the myriad ways the math is working against us. “Finding a biased roulette wheel,” he notes by way of example, “isn’t the same as finding a profitable one,” but even so, finding a roulette wheel that “churns out numbers that are uniformly distributed” generally requires collecting a vast body of information about that wheel, something that computers are better at doing than people. The same is true at the parimutuel racetrack, the boxing ring, and every other venue for wagering: having sufficient information is key to making any sort of bet that isn’t a mere stab in the dark. Even the most seasoned of bettors is thus usually to be found somewhere along what mathematicians call Poincaré’s third level of ignorance.

Kucharski’s book, which necessarily oversimplifies an extremely complex subject, is no cure for that ignorance, but gamblers and math buffs alike will enjoy it for its smart approach to real-world problems.