Get Rich: Here's The Math


The Untold Story of the

Scientific Betting System

That Beat the Casinos

and Wall Street

By William Poundstone

Hill and Wang; 386pp; $27

( below)

Editor's Review

Four Stars
Star Rating

The Good A colorful, sprawling account of a scientific wagering system, the Kelly method.

The Bad Some mathematical details can be heavy going for casual readers.

The Bottom Line An amazing story that gives a big idea the needed star treatment.

In July, 1956, the august Bell System Technical Journal published one of the oddest articles in the history of communications research -- an equation-filled treatise on how to make money at the racetrack if you have inside information on which horse is likely to win. Betraying no sense of incongruity, the article, by a young Texan physicist named John L. Kelly Jr., prescribed how much of your bankroll to bet based on two things: how certain you are of betting right (your "edge") and your winnings if you are right (the odds).

Fortune's Formula, by William Poundstone, is the sometimes-deep, sometimes-Runyonesque tale of the Kelly system's origins in research at Bell Laboratories and how people have used it to make money since. Although Kelly wrote about the horses, his approach is at least as useful on Wall Street. Legg Mason Capital Management CEO Bill Miller, among the most consistently successful investors of recent decades, wrote two years ago that "the Kelly criterion is integral to the way we manage money."

Parts of this amazing story have been told before. Edward O. Thorp, a gambling mathematician who co-founded the successful hedge firm Princeton Newport Partners, popularized the Kelly criterion in the 1960s with two books, Beat the Dealer and Beat the Market. Today, gamblers talk of using "Kelly" or "half-Kelly" when placing their bets.

But no one has ever told the whole colorful, sprawling tale until Poundstone. Fortune's Formula stretches from 18th century St. Petersburg, Russia, to the present-day U.S. and features characters ranging from such lowlifes as mobsters Al Capone and Longy Zwillman to intellectual giants like Paul Samuelson. The economist was so irritated by the Kelly approach that in 1979 he wrote a scholarly article against it, mocking his opponents' intelligence by using only one-syllable words.

Fortune's Formula will appeal to readers of such books as Peter L. Bernstein's Against the Gods, Nassim Nicholas Taleb's Fooled by Randomness, and Roger Lowenstein's When Genius Failed. All try to explain why smart people take stupid risks. Poundstone goes them one better by showing how hedge fund Long-Term Capital Management, for one, could have avoided disaster by following the Kelly method.

What is the Kelly criterion? It's a system that tells you how much of your money to bet to maximize the growth rate of your wealth -- while controlling risk. Technically speaking, it says the fraction of your payroll that you bet should equal your edge divided by the odds. Although Poundstone is a good explainer, the details can be heavy going for casual readers. Here's an example from the book that, for the purpose of simplicity, omits the track's take: The tote-board odds for Secretariat are 5 to 1, so a winning $100 bet pays $600. But you have a tip that Secretariat actually has a 1 in 3 chance of winning, so you have a one-third chance (instead of one-fifth) of winning $600. Dividing $600 by 3 gives you a weighted average payout of $200. Subtracting your bet leaves you with a profit of $100. The edge is defined as the profit divided by the wager, namely $100 divided by $100, or 1. The odds are defined as 5 to 1, or simply 5. So edge/odds equals 1/5, meaning you should bet one-fifth of your bankroll on Secretariat. That's it.

In his 1956 paper, Kelly demonstrated that a gambler with an edge who reinvested all profits would earn more money in the long run with his strategy than any other and could never go broke (because no bet is ever as big as the bankroll except for sure winners). This grew out of the work of the genius Claude Shannon, a Bell Labs colleague who pioneered information theory. Shannon showed that the more certainty there is about the accuracy of information received, the higher a communication circuit's capacity ("R"). For Kelly, the more certain the tips, the higher the growth rate of the gambler's stake ("G"). Kelly connected his work and Shannon's succinctly: Gmax=R. Poundstone says this equation "is as beautifully daring as E=mc2."

Kelly died of a brain hemorrhage on a Manhattan sidewalk at age 41, in 1965, apparently never having used his own criterion to make money. Economists are still divided over his legacy. Critics say the Kelly criterion's returns are too volatile for many people, and it doesn't work unless you reinvest all profits.

But Kelly's invention remains both useful and fascinating. It's possible to "tame" the system's swings by making bets half the recommended size ("half Kelly"). Anyway, the Kelly criterion is just kind of cool. Poundstone says that to a limited extent, it "has entered the company of pi and the golden section as one of those rare mathematical ideas that captures the imagination of nonmathematicians." That's a bit much. Still, Poundstone deserves credit for giving this big idea the star treatment it deserves.

By Peter Coy

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