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Kelly Criterion Calculator
Calculate a Kelly stake fraction from an entered win probability, American odds, bankroll and fractional Kelly multiplier.
Kelly Stake Calculator
Convert your probability estimate into bankroll-aware stake size. Compare full / half / quarter Kelly side-by-side.
Kelly sizing assumes your probability estimate is accurate. Use fractional Kelly when uncertainty is real.
The math
Given a true win probability p and decimal odds d (so net payoff per unit staked is b = d − 1), the Kelly fraction is:
f* = (b·p − (1−p)) / b
When f* ≤ 0, calculated EV is zero or negative and the displayed stake is zero. When f* > 0 it's the fraction of bankroll that maximizes the expected logarithm of bankroll over repeat plays.
Why fractional Kelly
Full Kelly is optimal only under perfect knowledge of p. In reality, your probability estimate has error — your model might say 55% when the true rate is 51% or 58%. Over-betting compounds estimation error: if you bet 5% of bankroll thinking edge is 3% but it's only 1%, you size for an edge you do not have. Betting above the true Kelly fraction lowers expected log growth and raises drawdown risk; expected money can still be positive even when expected log growth is negative. Fractional Kelly (multiplier between 0.10 and 0.50) shrinks the stake toward zero and can reduce drawdown risk at the cost of growth.
Quarter Kelly (0.25) stakes one quarter of the full-Kelly calculation. Compare the displayed scenarios under different probability estimates; no fraction removes estimation risk.
Common pitfalls
- Stale-bankroll Kelly. Recompute Kelly with your current bankroll after every meaningful bet. The whole point of the formula is to compound; holding a stale "bet size" defeats it.
- Implied probability from the same book as edge estimate. If you back into p by devigging the same book you're betting at, the result is a margin-free estimate. It can still be below the offered price's break-even probability. For -110 / -110, the no-vig estimate is 50%, while the offered price needs 52.38%. Your p needs to come from a separate model — your own, a market consensus across sharper books, a closing-line proxy.
- Cross-correlated bets. Kelly assumes independent wagers. If you Kelly six correlated NFL spread bets on the same Sunday, you're effectively making one big bet six times — your real bankroll variance is much higher than the formula suggests.
FAQ
What is the Kelly criterion?
The Kelly criterion is a bet-sizing formula that maximizes long-run logarithmic growth of bankroll. Given a true probability of winning p, decimal odds offered b+1, the optimal fraction of bankroll to bet is f* = (b·p − (1−p)) / b. If f* is zero or negative, the displayed stake is zero. Calculated EV is zero at break-even and negative below it. Above zero, the formula gives the formula-derived stake assuming repeated bets with the same entered probability and price.
Full Kelly vs fractional Kelly — which is safer?
Full Kelly uses the full calculated fraction; quarter Kelly uses 0.25 times that fraction. Smaller fractions reduce the stake and can reduce drawdown exposure under the same assumptions. They do not guarantee a particular drawdown, and an inaccurate probability estimate can still produce an unsuitable stake.
How accurate does my probability estimate need to be?
Kelly stake fractions are sensitive to the entered probability. If an entered 3% probability gap is actually 1% or −1%, the calculated full-Kelly stake is based on the wrong input. Fractional Kelly multiplies the formula's result by a smaller factor.
Why does the calculator say "do not bet" sometimes?
If the entered probability equals the offered-price break-even probability, calculated EV is zero. Below it, calculated EV is negative. Kelly returns a zero stake in either case. The break-even probability is shown next to the inputs so you can see how much edge you'd need at the current odds to make any bet rational.
Does the bankroll input matter for the math?
Not for the percentage. Kelly's optimal fraction is independent of bankroll size — it's purely a function of edge and odds. The bankroll input only translates the percentage into a dollar stake for convenience. Re-Kelly your bankroll after every bet (or batch of bets) if you want to stay precisely optimal.
See how bankroll varies across 200 simulated paths, with the median and lower (p10) and upper (p90) percentiles, plus methodology and FAQ.
Devig the book to get fair probability — use as input to Kelly here.
Compare the calculated expected value for the entered legs and prices.