Betting Math

Kelly Criterion

A formula for optimal bet sizing that maximizes long-term bankroll growth based on your edge and the odds.

Also known as: Kelly bet, Kelly formula, Kelly staking

Definition

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.

Formula

Kelly% = (bp - q) / b
where b = decimal odds - 1, p = true probability of winning, q = 1 - p

Worked Example

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%.

Try It Yourself

Related Terms

Further Reading

← All glossary terms