Compute the mathematically optimal bet size for compounding bankroll growth based on your edge and odds. The Kelly Criterion balances aggressive growth against bankruptcy risk — bet too small and you give up compounding; bet too large and variance can wipe out the bankroll before edge materializes.
The Kelly formula
Kelly Criterion: f* = (bp − q) / b, where:
- f* = optimal fraction of bankroll to wager
- b = decimal odds minus 1 (the profit per unit staked if win)
- p = your probability of winning
- q = your probability of losing (1 − p)
Example: Bet at +150 (decimal 2.50, b = 1.5). You estimate 50% probability of winning. Kelly = (1.5 × 0.5 − 0.5) / 1.5 = 0.25 / 1.5 = 16.67%. Stake 16.67% of bankroll on this bet.
If Kelly suggests a negative number, the bet is -EV — don't take it. The calculator above clamps negative Kelly to zero.
Why fractional Kelly is usually correct
Full Kelly maximizes long-run geometric bankroll growth, but at substantial short-term variance. A 50% bankroll drawdown is mathematically possible — and emotionally devastating — even when betting at full Kelly with positive edge.
Fractional Kelly (typically 0.25 to 0.5 of full Kelly) sacrifices some long-run growth for substantially reduced variance. Half-Kelly captures roughly 75% of full-Kelly growth with 50% of full-Kelly variance.
Practical recommendation: most retail bettors should use 0.25-0.5 Kelly. Full Kelly is mathematically optimal but emotionally unsustainable for most. Conservative bettors benefit from fractional Kelly's smoother bankroll trajectory.
Worked Kelly example
You estimate the Bills are 56% to cover -3 against the Patriots. The market is at -110 (decimal 1.909, b = 0.909). Your bankroll is $5,000.
Full Kelly: f* = (0.909 × 0.56 − 0.44) / 0.909 = (0.509 − 0.44) / 0.909 = 7.6%.
Full Kelly stake: $5,000 × 7.6% = $380.
Half Kelly stake: $190.
Quarter Kelly stake: $95.
If your edge estimate (56% true probability) is correct, full Kelly produces fastest long-term bankroll growth. If you're overconfident — say true probability is 53% not 56% — full Kelly massively over-bets. Quarter Kelly compensates for probability estimation error.
Common Kelly mistakes
- Using full Kelly without testing edge accuracy. Full Kelly assumes perfect probability estimation. Most retail bettors overestimate edge. Quarter Kelly is far safer.
- Ignoring correlation across bets. Kelly assumes independent bets. If you have multiple correlated +EV bets (e.g., multiple legs on the same NFL game), summing individual Kelly stakes overstates total exposure.
- Not adjusting for parlays. Parlay Kelly is a separate calculation: treat the parlay as a single bet with combined probability and combined odds.
- Forgetting to recompute after wins/losses. Kelly is bankroll-relative. After a 20% bankroll drawdown, your stake size should drop 20% even if Kelly fraction stays the same.
Frequently asked questions
What is the Kelly Criterion?
A formula for computing optimal bet sizing: f* = (bp - q) / b. It balances expected growth against variance, producing the bankroll fraction that maximizes long-term compounding given your estimated edge.
Should I use full Kelly?
Most bettors should use fractional Kelly (0.25-0.5x full). Full Kelly maximizes long-term growth but at painful short-term variance. Half-Kelly captures ~75% of full-Kelly growth with 50% of variance.
What if Kelly suggests negative?
Don't take the bet. Negative Kelly means -EV — the offered odds price you against your probability estimate. Negative results clamp to zero in our calculator.
How accurate must my probability estimate be?
Reasonably accurate, especially with full Kelly. If your edge estimate is off by 30%+, full Kelly massively over-bets and risks bankroll destruction. Fractional Kelly is more forgiving of estimation error.
How does Kelly relate to EV?
EV tells you whether to bet (positive = yes). Kelly tells you how much. Use both together: filter for +EV opportunities, size with Kelly.
What's the difference between Kelly and unit sizing?
Unit sizing uses fixed dollar amounts regardless of edge. Kelly scales stake with edge size — bigger edge = bigger stake. Kelly is more efficient mathematically but requires accurate probability estimation.
Can I use Kelly for parlays?
Yes, but treat the parlay as a single bet. Compute combined probability (multiply leg probabilities, assuming independence) and combined odds. Apply Kelly to the parlay's combined edge and odds.
How does drawdown work under Kelly?
Full Kelly produces 50%+ drawdowns regularly even with positive edge. Half-Kelly drawdowns max at ~30%. Quarter-Kelly drawdowns max at ~15%. The trade-off is long-term growth speed.