Kelly Criterion Calculator
Betting Too Much on a Good Edge Can Still Ruin You
The Kelly Criterion, developed by Bell Labs scientist John Kelly Jr. in 1956, answers a specific question: given a wager with a known edge, what fraction of a bankroll maximizes long-run growth without risking ruin from a losing streak. Betting more than the Kelly fraction actually reduces long-run growth despite feeling more aggressive, because variance compounds against an oversized stake faster than the edge can recover it.
The Formula
where b = net decimal odds − 1, p = win probability, q = 1 − p
f* is the fraction of bankroll to wager. A result of zero or negative means the bet has no positive expected edge at the given odds and probability, and the mathematically correct stake is nothing at all.
How Edge Size Changes the Recommended Fraction
| Win probability | Kelly fraction of bankroll |
|---|---|
| 40% | −20.00% (no bet) |
| 45% | −10.00% (no bet) |
| 50% | 0.00% (no edge) |
| 55% | 10.00% |
| 60% | 20.00% |
At even-money odds, the Kelly fraction happens to equal twice the edge over 50% — a 55% true win probability against 50% break-even implied odds produces a 10% Kelly stake. Below true 50%, the formula correctly returns a negative number, meaning no bet.
Where This Gets Used
- Sizing bets with a genuine, known edge — primarily relevant in contexts like poker tournaments, sports betting with a proven model edge, or investment position sizing, where the bettor's estimated win probability can differ from the market's implied probability.
- Illustrating why casino games rarely qualify — standard casino games carry a built-in house edge on every bet, meaning the true win probability is always below the break-even threshold, so Kelly correctly returns zero or negative for essentially all of them.
- Comparing full Kelly to fractional Kelly — many practitioners bet a fraction of the full Kelly stake (commonly half) specifically to reduce the swings that come with the full formula.
How to Use This Calculator
- Enter Decimal Odds for the wager (e.g. 2.50).
- Enter your estimated Win Probability as a percentage.
- Select Calculate to see the recommended Kelly fraction of bankroll to stake.
Related Calculations
Convert odds formats before entering them here with the Betting Odds Converter, or use a simpler fixed-percentage approach with the Bankroll Management Calculator.