

Because 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), it is a scientific gambling method. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956.

It assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. 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. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula for sizing a bet. Example of the optimal Kelly betting fraction, versus expected return of other fractional bets.
