What Is the Kelly Criterion?

The formula that beat blackjack in Las Vegas and the formula that built the first quantitative hedge fund are the same formula. It was written to keep phone calls from dropping.

In 1956, a physicist named John Kelly worked at Bell Labs, down the hall from Claude Shannon — the man who had just invented information theory, the mathematics of how much signal a noisy channel can carry before it turns to garbage. Kelly asked his neighbor's theory a gambler's question: if a bettor keeps receiving the same noisy tips over a private wire, what fraction of his bankroll should ride on each one?

His answer fits on one line:

Bet the fraction of your bankroll equal to your edge over the odds. p is your probability of winning. q is the probability of losing. b is the payout. When you hold no edge, f* is zero — the formula orders you to sit. When the odds tip your way, it tells you exactly how far to lean.

Run your own numbers — the calculator on this site computes f* live. Open the calculator.

Six years later, a young mathematician named Edward Thorp pointed that phone-line equation at a blackjack table. Thorp had already proven that counting cards shifts the odds as a deck runs down. What he lacked was the other half of the answer — not whether to bet, but how much. Kelly was the missing half. Thorp published Beat the Dealer in 1962, and the casinos of Nevada rewrote their rules over one book. Shannon himself joined the project on the side, helping Thorp build a wearable computer the size of a cigarette pack to beat roulette.

Then Thorp made the obvious move: a market is a casino with longer hours. He opened Princeton Newport Partners in 1969, sized every position by Kelly, and ran one of the first quantitative funds ever built — famous for nearly two decades without a losing year. Today, some fraction of Kelly sits inside the sizing discipline of quantitative desks everywhere.

And here is why it was all one equation from the start. Kelly's rule falls out of maximizing the logarithm of your wealth:

That expected log growth is the exact quantity Shannon maximized as the rate of a communication channel. Growing money at the optimal speed and moving information at the optimal speed are the same mathematical problem. Bits and dollars obey one law.

Kelly was studying a telephone line. He never knew he was also telling every card counter and every quant on earth precisely how much to put on the table.