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 of the Kelly Criterion Calculator
The Kelly Criterion Calculator is a teaching aid, not a live risk system. It does not model the following:
- Estimation error in the win rate and payoff — Kelly is highly sensitive to its inputs, and full Kelly on optimistic estimates risks ruin
- Non-stationary edges; the true probabilities change, which is why practitioners use a fraction of full Kelly
- Correlated simultaneous bets, for which single-bet Kelly overstates the safe size
- Trading costs, gaps and the discrete whole-lot sizes that real F&O positions must use
Frequently asked questions
How do I estimate W and b for Kelly from a backtest?
Estimate the win probability and the ratio of average win to average loss from an out-of-sample trade record, not the data you used to build the strategy. Because these estimates are noisy, shade them conservatively before computing the fraction, or the in-sample optimism inflates the recommended size.
Why do backtesters not size at full Kelly?
Full Kelly is optimal only if the edge is known exactly and never changes, which a backtest can never promise. Since the growth curve falls steeply past the peak, a small overestimate of the backtested edge pushes you into lower growth and severe drawdowns, so fractional Kelly is the norm.
What drawdowns does full Kelly imply in a backtest?
Full Kelly routinely produces backtested drawdowns on the order of the win probability, which most traders could never sit through. This severity, visible when you re-run a backtest at full Kelly sizing, is a key practical reason fractional Kelly is preferred.
Can Kelly tell me a backtested strategy is not worth trading?
Yes. If the computed f* is zero or negative, the formula is telling you the backtested bet has no positive edge and should not be sized at all. It is a useful discipline against deploying strategies that only looked profitable in-sample.
Why is a Kelly fraction from a backtest fragile?
Because it depends on precise, stationary estimates of edge that markets do not provide, and its penalty for overestimating edge is asymmetric and severe. A backtested Kelly should be treated as an upper bound, with fractional Kelly and conservative inputs as the standard defence.
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