Kelly criterion

In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. Assuming that the expected returns are known, the Kelly criterion leads to higher wealth than any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity). J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956.

The practical use of the formula has been demonstrated for gambling, and the same idea was used to explain diversification in investment management. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors including Warren Buffett and Bill Gross use Kelly methods. Also see Intertemporal portfolio choice. It is also the standard replacement of statistical power in anytime-valid statistical tests and confidence intervals, based on e-values and e-processes.