Kelly Criterion

Kelly Criterion

Mathematics

Definition

A formula used to determine optimal bet sizing as a fraction of bankroll, in order to maximize long-term growth of wealth. It uses the edge (probability advantage) and the odds to calculate the ideal stake.

Formula

For a given bet: $f^* = p - \frac{q}{b}$, where $p$ is probability of winning, $q = 1-p$ is probability of losing, and $b$ is the net odds multiplier (e.g. $b = 2$ for even money). The result $f^*$ is the fraction of bankroll to wager.

Example

If you estimate Crawford has a 60% chance to win (p = 0.6) and his odds are +100 (even money, $b = 1$), the **Kelly criterion** says to bet $0.6 - 0.4/1 = 0.2$ → **20%** of your bankroll. In practice, many bettors use a fraction of Kelly for safety.