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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.

Win rate (%)Payoff ratio b (win ÷ loss)

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.

Frequently asked questions

Why do most people use half-Kelly?

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 it is a common practical compromise.

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, not take a tiny position.

Why is over-betting so dangerous?

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 estimates, betting full Kelly on an overestimated edge is effectively over-betting.

Does Kelly account for correlated positions?

No. The basic formula assumes one bet at a time with a fixed payoff. Running several correlated trades at their individual Kelly sizes stacks risk far beyond what the formula intends.

Is the Kelly fraction a per-trade risk percentage?

Roughly, it is the fraction of capital to expose, but it is not the same as the stop-based risk-per-trade percentage. Traders often translate Kelly into a much smaller practical risk figure precisely because inputs are uncertain.

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