Mazur, What’s Luck Got to Do with It?

Joseph Mazur’s new book What’s Luck Got to Do with It? The History, Mathematics, and Psychology of the Gambler’s Illusion (Princeton University Press, 2010) engagingly summarizes a broad spectrum of literature on gambling—and, yes, he considers investing a form of gambling. A former math professor, Mazur grew up in an environment where betting on horses and playing the numbers were family pastimes. He has fond memories, but he puts his money on probability theory.

Mazur first takes us on a journey from the Neanderthals to the world markets in 2008. He interweaves the histories of gambling and probability theory. For instance, he notes that under Henry VII gambling was forbidden save during the twelve days of Christmas when the public “was not only permitted to gamble but encouraged to do so in church.” (p. 17) And, in addition to writing about the best known early work in probability theory such as Bernoulli’s Ars Conjectandi, he illustrates how the trigram system from the I-Ching can be viewed as an early stab at combinatorial mathematics.

The second part of Mazur’s book introduces some of the basics of probability theory and uses them to show how gamblers so often delude themselves, sometimes with a little help from the house. In a primitive example, if a blinking neon sign over a slot machine reads “This bank pays 99 percent,” the naïve (and wishful) interprets it to mean that he is almost certain to win. In fact, of course, “all it means is that over an infinite number of plays of the slot machine the player will receive 99 percent of all the money he or she already spent.” (p. 149)

Mazur then looks at compulsive gambling and why we have such a hard time psychomanaging risk. He shares insights from behavioral economics and psychology. In the final analysis, however, he argues that “some—if not most—gambling behavior is primarily connected to an intrinsic desire to manipulate luck in order to validate life, to test the forces of uncertainty under a fantasy of knowing something unknowable or to experiment with the new. Making choices based on scant knowledge is an essential function of consciousness.” (p. 216)

We can improve our odds by understanding principles that underlie the “choices based on scant knowledge” that we make, at least when these choices can be analyzed statistically. For instance, gamblers are inclined to embrace the Monte Carlo fallacy as a guiding principle. This fallacy presumes that an event remembers its history; the roulette player therefore mistakenly believes that he should bet on black after a long run of red. (A roulette wheel clearly has no memory; traders do. So is the Monte Carlo fallacy really a fallacy in the financial world?)

We can also try to tilt the odds in our favor by engaging in activities that require both skill and luck, not just luck (as in lotteries or slot machines). For instance, there are blackjack strategies that give the player a 3 percent advantage over the house. A good poker player, keenly aware of the basic odds of various hands, will be able to make an intuitive probability calculation that will at least in part inform his decision to drop, call, or raise.

Mazur’s book is a quick read and thoroughly enjoyable. Even though he’s not particularly knowledgeable about the markets and in his eagerness to bring investing and trading under the mantle of gambling succumbs to reductionist thinking (“investments should be viewed as simply poker games based on a risk-reward evaluation” [p. 59]), he’s shed light on the enduring appeal of luck. Just think of the comment that Jim Simons of Renaissance Technologies, renowned for its phenomenally successful quant trading, made to a gathering of potential investors: “Luck is largely responsible for my reputation for genius. I don’t walk into the office in the morning and say, ‘Am I smart today?’ I walk in and wonder, ‘Am I lucky today?’” (Institutional Investor, November 2000)