Fortune's Formula

William Poundstone

4 ideas

1. Kelly Criterion: Bet Your Edge Over Odds

   To maximize long-run wealth growth, stake a fixed fraction of your current bankroll equal to your edge divided by the odds (f = edge/odds), which is the same as maximizing the expected logarithm of wealth. Because you always bet a fraction of what remains, you shrink your bets as you lose and in principle never hit zero. John Kelly derived it at Bell Labs in 1956 from Claude Shannon's information theory, showing that the maximum growth rate of a gambler's capital equals the information rate of his private tip channel.

2. Overbetting Is Worse Than Underbetting

   Growth rate is an asymmetric hill around the Kelly fraction. Betting twice Kelly drives long-run growth to roughly zero, and betting more produces near-certain ruin despite a genuine edge, while betting half Kelly keeps about three-quarters of the growth with far less volatility. The book uses leveraged blowups such as Long-Term Capital Management to argue that ruin usually comes from sizing, not from a lack of edge.

3. Edward Thorp: Blackjack Tables to Hedge Fund

   MIT math instructor Edward Thorp used computer analysis to prove that card counting beats blackjack, then tested it in Nevada casinos with Kelly-sized bets and published the method in 'Beat the Dealer' (1962). He also built a wearable roulette-predicting computer with Claude Shannon. He then moved the same approach to warrants and convertible arbitrage at Princeton-Newport Partners, which returned about 20% a year for roughly two decades with almost no losing quarters, an existence proof that a measured edge plus disciplined sizing can compound reliably.

4. Maximizing Growth Versus Maximizing Utility

   Paul Samuelson attacked Kelly by arguing that maximizing the geometric mean (log wealth) is optimal only for an investor whose utility happens to be logarithmic, so it is not a universal rule even over long horizons. He made the point in a 1979 paper written entirely in one-syllable words. The dispute shows the difference between the expected outcome averaged across many hypothetical investors (the arithmetic mean) and the compounded outcome one investor actually lives through over time (the geometric mean), which decides whether 'maximize expected value' is the right goal at all.

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