Kelly Criterion Calculator
Calculate the classic two-outcome Kelly fraction from an entered win probability and payoff ratio, compare a chosen full, half or quarter fraction, and optionally translate it into account-currency units. The page evaluates assumptions; it does not recommend a position size.
What does the Kelly Criterion calculator calculate?
It applies the classic binary formula f* = p − (1 − p) ÷ b, where p is the entered win probability and b is average gain divided by average loss magnitude. A positive result is the model fraction associated with maximum expected log growth under those exact assumptions—not a verified trading edge or recommended risk percentage.
- The breakeven win probability is 1 ÷ (1 + payoff ratio).
- Full, half and quarter Kelly are displayed as mathematical scale choices, not safety labels.
- An optional reference balance converts the selected fraction into account-currency units without creating a trade size.
Enter the binary-model assumptions
Use win and loss observations measured on one consistent gross-or-net basis.
Binary Kelly result
Kelly Binary Fraction model 1.1.0.
Fraction comparison
Bars use a zero-to-100% display scale. A negative raw fraction is preserved in its text label and shown with no positive fill.
How to use the calculator
- Estimate the win probability from a clearly defined set of comparable outcomes. The calculator does not judge the sample or whether the estimate remains stable.
- Divide the average gain by the average loss magnitude on the same gross-or-net basis, then enter that payoff ratio.
- Optionally enter a reference balance and choose a full, half, quarter or zero scale view. These labels are multipliers, not recommendations.
- Compare the entered win probability with the formula breakeven and inspect how estimation error could change the result before using a separate position-size workflow.
What the binary Kelly equation says
The classic formula uses a probability of winning, the complementary probability of losing and net payoff odds. It selects the fraction that maximizes expected logarithmic capital growth inside that simplified model.
A payoff ratio of b has a formula breakeven win probability of 1 ÷ (1 + b). The difference between the entered probability and that threshold makes assumption sensitivity visible.
When the raw fraction is zero or below, the entered assumptions do not produce a positive Kelly fraction. The calculator displays zero for the positive and scaled views but preserves the signed raw result.
Worked examples
| Entered scenario | Derived output | Meaning |
|---|---|---|
| 55% win; 1.5 payoff; half Kelly; 10,000 balance | 25.00% raw; 12.50% displayed; 1,250.00 balance units | Breakeven is 40.00%; the selected fraction models +18.75% on a win and −12.50% on a loss. |
| 50% win; 1.0 payoff | 0.00% raw Kelly | The entered assumptions equal the 50.00% formula breakeven before costs. |
| 40% win; 1.0 payoff | −20.00% raw; 0.00% displayed | No positive Kelly fraction exists under the entered assumptions. |
Model and execution limitations
- The model has exactly two outcomes and assumes the entered probability and payoff remain stable.
- It does not verify data quality, sample size, independence, stationarity, tail losses, costs, slippage or broker loss limits.
- Estimation error can materially change a Kelly fraction, especially when the assumed edge is small.
- The optional balance amount is only the selected model fraction multiplied by the entered balance. It is not a forex lot size and does not use stop distance, pip value, contract size or leverage.
- The displayed fraction is not a position size, leverage instruction, suitability assessment or recommendation.
The CFTC cautions that hypothetical results have inherent limitations and that actual results can differ because of factors including spreads, commissions, liquidity and execution. The result on this page should be read within the narrower boundaries stated above.
Frequently asked questions
- For this two-outcome model, f* = p − (1 − p) ÷ b, where p is the assumed win probability and b is average gain divided by average loss magnitude.
- Only that the entered two-outcome assumptions do not produce a positive mathematical Kelly fraction.
- No. This page evaluates a formula and explicitly does not recommend a position size or risk level.
- Use average gain divided by average loss magnitude on one consistent gross-or-net basis. The page cannot verify that estimate.
- It lets you inspect a chosen percentage of a positive mathematical Kelly result without labeling that fraction as safe, conservative or recommended.
- For payoff ratio b, the binary model reaches zero arithmetic edge when win probability equals 1 divided by 1 plus b.
- No. It is only the selected fraction multiplied by the optional reference balance. Forex position size also requires instrument, stop distance, pip value, contract and broker constraints.
- No. Its mathematical result depends on the model assumptions. Real probabilities, payoffs, costs and sequences can differ.
Method sources and provenance
- J. L. Kelly Jr., 1956 — Primary publication for the logarithmic-capital-growth criterion.
- Stanford risk-constrained Kelly paper — Academic treatment of the Kelly growth objective and the need to distinguish it from explicit drawdown-risk constraints.
- CFTC trading-system advisory — Official limitations for hypothetical and past-performance claims.
Local calculation: Inputs are processed in the browser by the named versioned model. The page does not send entered balances, rates, probabilities or notes to a calculation API.
Continue the performance workflow
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