A formula for optimal bet sizing that maximizes long-term bankroll growth based on your edge and the odds.
The Kelly Criterion calculates the optimal fraction of your bankroll to bet given your edge and the available odds. It maximizes the expected logarithmic growth of your bankroll — the fastest possible growth rate without risking ruin.
Full Kelly is mathematically optimal but produces volatile swings. Most professional bettors use fractional Kelly (typically 25-50% of the full Kelly amount) to reduce variance at the cost of slightly slower growth.
Kelly requires accurate probability estimates. If your probabilities are wrong, Kelly can be worse than flat betting.
Kelly% = (bp - q) / b where b = decimal odds - 1, p = true probability of winning, q = 1 - p
True probability 55%, decimal odds 2.10 (b = 1.10). Kelly = (1.10 × 0.55 - 0.45) / 1.10 = (0.605 - 0.45) / 1.10 = 0.141 = 14.1% of bankroll. Half Kelly = 7.05%.
The average profit or loss per bet if you made the same wager thousands of times. Positive EV means long-term profit.
BankrollThe total amount of money set aside exclusively for betting or trading. Never money you can't afford to lose.
VarianceThe natural fluctuation in results around your expected value. High variance means bigger swings even with an edge.