Kelly Criterion Calculator
Find the Kelly and half-Kelly fraction of capital to stake from a win probability and payoff ratio.
Quick answer: The Kelly criterion gives the fraction of capital that maximises the long-run growth rate of a repeated bet with a known edge. It equals the win probability minus the losing probability divided by the payoff ratio. The tool also reports half-Kelly, the fraction most practitioners actually use, because full Kelly is extremely volatile and unforgiving of estimation error.
How to use it
Enter your win probability and the payoff ratio b, which is the average win divided by the average loss. The output is the full Kelly fraction and half-Kelly. A negative Kelly means the edge is against you and the growth-optimal stake is zero. Kelly assumes the win rate and payoff are known exactly, which they never are in trading, so treat it as an upper bound.
Formula
Kelly f* = W − ( 1 − W ) ÷ b ; Half-Kelly = f* ÷ 2
W is the win probability as a decimal; b is the payoff ratio (average win divided by average loss). A negative f* means no positive-growth stake exists.
Limitations — what this calculator does not model
- Assumes the win probability and payoff are known exactly; real estimates are noisy, and overstating the edge means over-betting.
- Models one bet at a time with a fixed payoff — it ignores correlation across a multi-strategy book.
- Full Kelly is extremely volatile; most systems use half-Kelly or less, which the tool also reports.
- It is a growth-optimal exposure, not a stop-based risk-per-trade limit; translate it conservatively before use.
Frequently asked questions
Why do most systems use half-Kelly or less?
Full Kelly produces violent equity swings and assumes your edge is known perfectly. Half-Kelly keeps most of the long-run growth while roughly quartering the variance, which is why a live sizing module almost always caps at a fraction of Kelly.
What does a negative Kelly fraction mean?
It means the bet has negative expectancy at the inputs given, so the growth-maximising stake is zero. In plain terms, you should not take the trade at all — a useful automatic filter against sizing into a strategy that only looked profitable in-sample.
Why is over-betting so dangerous in a live system?
Growth rate rises to a peak at full Kelly then falls sharply beyond it, and staking above Kelly can drive long-run growth negative even with a real edge. Because live win rates are noisy estimates, feeding an overstated edge into a Kelly sizer is effectively over-betting, so systems shade the inputs conservatively.
Does Kelly account for correlated positions across a live book?
No. The basic formula assumes one bet at a time with a fixed payoff. Running several correlated strategies at their individual Kelly sizes stacks risk far beyond what the formula intends, so a live book needs a joint fraction that reflects correlation, enforced by the risk engine.
How should a live system feed W and b into Kelly?
From an out-of-sample or rolling live trade record, never the data used to build the strategy, and shaded conservatively because the estimates are noisy. Recomputing the fraction as fresh trades arrive lets the sizer adapt while conservative inputs guard against the formula's asymmetric penalty for overestimation.
Is the Kelly fraction the same as my stop-based risk per trade?
No. Kelly is the growth-optimal fraction of capital to expose; the stop-based risk-per-trade percentage is a separate, usually much smaller operational limit. Systems translate Kelly into a conservative practical risk figure precisely because the inputs are uncertain.
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