Kelly Criterion

The Kelly Criterion is a mathematical formula used to determine the optimal fraction of a bankroll to wager on a bet or investment, based on the perceived edge (probability of winning minus probability of losing) and the odds offered. Developed by John L. Kelly Jr. in 1956, it maximizes the long‑term growth rate of wealth by balancing risk and reward, assuming known probabilities and payoffs.

For example, if a trader estimates a 60 % chance of a trade succeeding with a 2‑to‑1 payoff, the Kelly fraction is (0.60 × 2 − 0.40) / 2 = 0.20, suggesting a 20 % stake of the bankroll. Applying the criterion helps traders size positions to exploit an edge while avoiding over‑betting that could lead to ruin, making it a cornerstone of advanced risk‑management and position‑sizing strategies.