Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street

by William Poundstone

Quick Summary

A narrative history connecting information theory, gambling, and Wall Street through the lives of Claude Shannon, Edward Thorp, and John Kelly Jr. Poundstone traces how the Kelly Criterion -- a formula for optimal bet sizing derived from Shannon's information theory at Bell Labs -- was applied first to beat casino games and horse racing, then adapted by Thorp and others to generate extraordinary returns in the stock market, while sparking a fierce intellectual debate with Paul Samuelson and the efficient market theorists.

Detailed Summary

William Poundstone's "Fortune's Formula" weaves together three seemingly disparate threads -- information theory, gambling, and financial markets -- into a compelling narrative about the Kelly Criterion and its controversial application to investing. The book was named Amazon's #1 Nonfiction Book of 2005.

Part One ("Entropy") introduces Claude Shannon, the father of information theory, whose work at Bell Labs on the mathematical theory of communication revolutionized telecommunications and laid the intellectual groundwork for the digital age. Shannon's insight that information could be quantified using the concept of entropy connected abstract mathematics to practical engineering problems. The book then introduces John Kelly Jr., a Bell Labs physicist who in 1956 published a paper showing how Shannon's information theory could be applied to gambling: given an information advantage (an "edge"), there is a mathematically optimal fraction of one's bankroll to wager on each bet that maximizes the long-term geometric growth rate of wealth while minimizing the risk of ruin. This became known as the Kelly Criterion.

The narrative also introduces Emmanuel Kimmel, a gambler who exploited information advantages in horse racing through a private wire service that received results before the bookmakers, and the mathematical work that formalized the relationship between information, probability, and optimal betting.

Part Two ("Blackjack") follows Edward Thorp, a mathematics professor who developed the first mathematically proven card-counting system for blackjack and field-tested it in Las Vegas casinos. Thorp's "Beat the Dealer" (1962) demonstrated that the Kelly Criterion could be practically applied: by sizing bets proportionally to the card-counting edge, a player could maximize long-term returns. The book details Thorp's casino exploits, including encounters with cheating dealers and the eventual casino industry response of multi-deck shoes and countermeasures.

Part Three ("Arbitrage") traces Thorp's transition from casino gambling to Wall Street, where he founded Princeton-Newport Partners, one of the first quantitative hedge funds, and developed warrant and convertible bond arbitrage strategies that generated consistent returns with minimal risk. This section also covers the broader transformation of Wall Street through quantitative methods, including the rise of Michael Milken's junk bond empire, the development of the Black-Scholes options pricing model by Robert C. Merton and others, and the ongoing debate about market efficiency.

Part Four ("St. Petersburg Wager") addresses the intellectual controversy between the Kelly Criterion advocates (led by Thorp and Henry Latane) and the mainstream finance establishment (led by Paul Samuelson). Samuelson argued that the Kelly Criterion was inappropriate for real-world investing because it assumes an infinitely long time horizon and ignores the utility preferences of individual investors. The Kelly camp countered that maximizing geometric mean returns is the only strategy that guarantees eventual superiority over any other strategy given enough time. This debate connects to foundational questions in economics about risk, utility, and rational decision-making that trace back to Daniel Bernoulli's 1738 St. Petersburg paradox.

The book also covers Shannon's own investing exploits (his "Shannon's Demon" thought experiment about extracting returns from random fluctuations through rebalancing) and the evolution of these ideas through Long-Term Capital Management's spectacular collapse in 1998, which demonstrated the real-world risks of leverage even when the underlying mathematical models are correct.