Kelly Criterion The Bet Sizing Formula Behind Blackjack and Wall Street

The Kelly criterion is a bet sizing formula that sets what fraction of a bankroll to stake, and getting that fraction wrong destroys an otherwise sound edge.

John Larry Kelly Jr. published it at Bell Labs in 1956 in A New Interpretation of Information Rate, deriving it from Claude Shannon's work on noisy communication channels rather than from any theory of finance.

The rule is to maximize the expected logarithm of wealth, which on an even money bet at probability p collapses to staking 2p minus 1 of the account, or 20 percent on a coin that lands heads 60 percent of the time.

Edward Thorp carried it out of the seminar room into casinos with Beat the Dealer in 1962 and then into markets, reporting a thirty year total of 80 billion dollars worth of bets.

Its promise is asymptotic: across enough identical trials no other constant fraction compounds faster, and a Kelly bettor never goes broke.

The formula only knows the edge it is fed, so an overstated probability becomes an overbet, and doubling the Kelly fraction surrenders the entire growth advantage.

Thorp and most working practitioners therefore stake a fraction of Kelly, a half or a quarter, buying drawdowns they can live through at the cost of some growth.

The formula has hard evidence behind it, drawn from how badly trained people do without it. Victor Haghani and Richard Dewey gave 61 economics students and finance professionals $25 and a coin they were told landed heads 60 percent of the time; 28 percent went bust and only 21 percent reached the $250 cap, against the 95 percent a disciplined stake would have hit, and just five had ever heard of Kelly (Elm Wealth). The sums are larger now than a seminar. NBC News counted $197 million riding on 1,408 midterm markets at Kalshi and Polymarket in July. How much to bet gets settled on November 3.