Kelly Criterion Calculator
Calculate full, half, quarter or custom Kelly sizing from your estimated win probability, payoff odds and bankroll. Compare the model probability with the break-even probability before considering any stake.
Kelly calculation results
| Scenario | Modeled bankroll after outcome | Change |
|---|---|---|
| Win | — | — |
| Loss | — | — |
Kelly criterion formula
Full Kelly fraction: f* = (b × p − q) ÷ b, where b is net profit per unit risked, p is win probability and q = 1 − p.
For decimal odds, b equals decimal odds minus 1. Positive American odds convert to decimal odds as 1 + odds ÷ 100; negative odds convert as 1 + 100 ÷ |odds|. A profit-to-loss ratio can be entered directly as b. The applied percentage equals the positive full-Kelly fraction multiplied by the selected Kelly fraction.
Important: Kelly sizing is extremely sensitive to probability and payoff estimates. A positive result is not a recommendation, guarantee or risk limit. If the calculated full Kelly value is zero or negative, the model has no positive allocation.
Verified examples
| Inputs | Full Kelly | Applied result |
|---|---|---|
| $1,000 bankroll; 55% probability; decimal odds 2.00; half Kelly | 10.0000% | 5.0000% or $50.00 |
| $2,500 bankroll; 45% probability; American odds +150; quarter Kelly | 8.3333% | 2.0833% or $52.08 |
| $1,000 bankroll; 40% probability; decimal odds 1.80; full Kelly | −35.0000% | 0% or $0.00 because the model edge is negative |
How to use the calculator
- Enter the bankroll or capital reserved for this decision.
- Enter your independently estimated win probability.
- Select the odds format and enter the payoff.
- Select full, half, quarter or custom Kelly.
- Review the break-even probability, model advantage and outcome amounts—not only the stake.
Limits and assumptions
- The model assumes two mutually exclusive outcomes: a full win at the entered payoff or a full loss of the stake. Pushes, partial losses, fees, taxes, slippage and correlated positions are excluded.
- Bankroll must be greater than zero and no more than 1 trillion. Probability ranges from 0% through 100%. Numeric inputs accept up to six decimal places.
- Decimal odds range from 1.01 through 10,000. American odds must be at least +100 or at most −100, with absolute value no greater than 100,000. A direct net profit ratio ranges from 0.01 through 10,000.
- A custom Kelly fraction ranges from 0% through 100%. The calculator never allocates a negative amount: a nonpositive full-Kelly result produces a modeled stake of zero.
- Repeated opportunities must be independent and use a stable, well-calibrated probability for the classic long-run interpretation. Real markets and wagers may violate those assumptions.
Frequently asked questions
What is half Kelly?
Half Kelly multiplies the positive full-Kelly fraction by 50%. It reduces model exposure, but it cannot correct inaccurate odds, probabilities or assumptions.
Why can the Kelly percentage be negative?
A negative result means the entered probability is below the break-even level implied by the payoff. The calculator shows a zero applied allocation rather than a negative stake.
Are American and decimal odds equivalent?
Yes, after conversion. For example, +150 equals decimal odds 2.50 and −200 equals decimal odds 1.50.
Can I use Kelly criterion for investing?
The equation can model a binary payoff when you supply a defensible probability and net payoff ratio. It does not model continuous returns, drawdowns, portfolio correlation or changing opportunities.
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