# The Kelly Criterion The Kelly formula is widely used in gambling. It is a variable staking approach where stakes depend on the profitability of a bet. The more profitable a bet, the higher the stake. Kelly has demonstrated that it is the staking approach that maximizes the geometric growth rate of a gambler’s portfolio.

## The formula

Kelly = (P * odds – 1)/(odds – 1)

Assuming you start with a bank of 100, Kelly states that to maximize your returns you should bet a proportion of your bank equal to (P * odds – 1)/(odds – 1), where odds are decimal and P is the winning probability of a runner. The bank value should be updated at each bet.

## The intuition

The numerator is equal to the expected return of the bet. So, the more profitable the bet, the higher the fraction invested. The denominator is a function of the odds. Risky bets tend to come at higher odds so, intuitively, the Kelly criterion establishes a trade-off between expected return and risk.

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