The Kelly criterion is a formula for sizing bets to maximize long-run bankroll growth. It tells you what fraction of your bankroll to risk on each bet given your edge. Bigger edge → bigger bet. No edge → no bet.
The formula
For a simple win/lose bet:
Kelly fraction = (decimal odds × win probability − 1) / (decimal odds − 1)
Where:
- decimal odds — the bet's payout as a decimal (American +150 → 2.50, −110 → 1.91)
- win probability — your honest estimate of the bet's true win chance, as a decimal between 0 and 1 (55% → 0.55)
The output is a fraction. Multiply by your bankroll to get the dollar stake. A Kelly fraction of 0 means no edge — don't bet. A negative Kelly means the bet has negative expected value — definitely don't bet.
Worked example: an even-money bet you think is 55%
You're offered a bet at +100 (decimal 2.00). You think the true win probability is 55% — you have a 5-percentage-point edge over the breakeven 50%.
Kelly fraction = (2.00 × 0.55 − 1) / (2.00 − 1) = (1.10 − 1) / 1 = 0.10
So full Kelly says bet 10% of your bankroll. On a $1,000 bankroll, that's a $100 bet.
Half-Kelly says bet 5% — $50.
Quarter-Kelly says bet 2.5% — $25.
Worked example: a small edge at standard juice
You think a −110 (decimal 1.91) line is actually a 55% true probability — slightly better than the 52.38% breakeven the line implies.
Kelly fraction = (1.91 × 0.55 − 1) / (1.91 − 1) = (1.0505 − 1) / 0.91 = 0.0505 / 0.91 = 0.0555 ≈ 5.55%
Full Kelly: 5.55% of bankroll. Half-Kelly: 2.77%. Quarter-Kelly: 1.39%.
Notice how the same percentage-point edge (3 points above breakeven, both cases) produces a smaller Kelly fraction at −110 than at +100. That's because the worse odds give you less return per unit risked, so the optimal bet size shrinks.
Why most bettors use fractional Kelly
Full Kelly is theoretically optimal — it maximizes the long-run geometric growth rate of your bankroll. In practice, it has two problems:
1. Drawdowns are brutal. Even with a real edge, full-Kelly bettors routinely face 50%+ bankroll drawdowns. Most people can't psychologically handle watching their bankroll get cut in half, even temporarily.
2. Probability estimates are never perfect. The formula assumes you know the true win probability. In reality, you're estimating it. Overestimating your edge causes Kelly to over-bet, which compounds losses fast. Fractional Kelly is a margin-of-safety hedge against your own modeling errors.
Half-Kelly captures about 75% of the long-run growth rate with a fraction of the volatility. Quarter-Kelly captures about 44% with much smoother variance. For most sports bettors, half- or quarter-Kelly is the practical default.
Kelly vs flat staking
Flat staking — betting the same dollar amount on every play — is simpler and works fine if you have only a small edge or no real way to differentiate one bet's edge from another. Kelly's advantage shows up when your edges vary widely. A 10% edge bet "deserves" more capital than a 2% edge bet, and Kelly sizes that automatically.
The flip side: Kelly requires honest probability estimates. If you don't have a real model — just gut feel — flat staking is safer. Kelly amplifies whatever quality is in your estimates, good or bad.
Caveats and edge cases
Simultaneous bets: The single-bet Kelly formula assumes one bet at a time. If you bet on multiple correlated outcomes (different legs of the same game, or two games heavily affected by the same weather), simple Kelly over-bets. Reduce the fraction further when bets aren't independent.
Bookmaker limits: If a sportsbook will only take a limited stake, your Kelly recommendation may be more than you can actually bet. That's not a bug — just the real-world ceiling.
Negative-EV bets: Kelly will return a negative number for any bet where decimal odds × win probability is less than 1. That's the formula telling you "don't bet" — not "bet against."