> The growth-optimal stake from your win rate and payoff, the half and quarter fractions — and the range your sample size supports, with the working shown.

- Canonical: https://hadalinstruments.com/tools/kelly-criterion-calculator/

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Tool

# Kelly criterion calculator

The Kelly criterion computes the fraction of a bankroll that maximises long-run growth for a bet with a known win rate and payoff. The operative word is **known**. A trading win rate is an estimate from a finite sample, Kelly is violently sensitive to it, and the cost of the two errors is not symmetric — so this calculator asks how many trades your win rate came from, and answers with the range that sample supports rather than a single number pretending to certainty.

Full Kelly —

Full Kelly at your stated win rate —

Across your sample's range —

Half Kelly / quarter Kelly —

Expectancy per trade at your numbers —

At your bankroll, full Kelly stakes —

## What Kelly actually optimises

The criterion maximises the expected growth *rate* of a bankroll under repeated bets — not the expected value of any single bet, and not comfort. Growth compounds geometrically, and so does its destruction: stake above the full Kelly fraction and growth falls; at roughly twice the full stake, expected growth crosses back through zero with the edge still intact. Overbetting a genuine edge loses money. That asymmetry — underbetting costs some growth, overbetting can cost everything — is the entire case for the fractional stakes below the headline figure.

## Why the sample size is not optional

The formula treats your win rate as the truth. Your win rate is a measurement with error bars, and Kelly amplifies that error into the stake. The range row re-runs the formula at the ends of a Wilson 95% interval for your win rate given the trades it came from: a rate of 52% from sixty trades is consistent with a true rate anywhere from the high thirties to the mid sixties, and the stakes at those two ends are not neighbours. When the pessimistic end gives zero, your sample has not ruled out that the correct stake is nothing — that is a finding, and the panel says it rather than hiding it behind the point estimate.

Fractional Kelly is estimation-error insurance with a known price: at half the full stake you keep about three-quarters of the growth rate at about a quarter of the variance. Given that the win rate is estimated rather than known, the half figure is where most of the argument actually lands.

## What this does not do

Kelly's assumptions are a laboratory: bets independent, identically distributed, with a two-outcome payoff, repeated indefinitely. Trades are none of those things — win rates drift, payoffs vary trade to trade, returns arrive fat-tailed and correlated — and every violation argues for staking *less* than the formula says, never more. There is also no compounding projection here, deliberately: a growth curve drawn from these inputs would be an invention wearing arithmetic.

And the win rate you typed is taken as given. A win rate selected from many tried variants is not a measurement of anything — whether yours survives that test is what the [Overfit Auditor](https://hadalinstruments.com/instruments/overfit-auditor/) bounds, and no staking formula repairs a number that was never real.

A Kelly fraction is a share of bankroll; turning it into lots at a stop distance is the [position size calculator](https://hadalinstruments.com/tools/position-size-calculator/). The downside question — how likely a given sizing is to run the account into a floor it cannot come back from — is the [risk of ruin calculator](https://hadalinstruments.com/tools/risk-of-ruin-calculator/), built on the same Wilson machinery. The term is defined at [risk of ruin](https://hadalinstruments.com/glossary/risk-of-ruin/). The payoff ratio a Kelly fraction takes as its input is the [risk reward ratio calculator](https://hadalinstruments.com/tools/risk-reward-calculator/), and what a fraction compounds to over a run of trades — before survival is accounted for — is the [forex compounding calculator](https://hadalinstruments.com/tools/forex-compounding-calculator/). The full list is under [calculators](https://hadalinstruments.com/tools/). And when the inputs cannot support an answer, the panel above refuses and says why rather than rendering a zero — [why an instrument refuses to answer](https://hadalinstruments.com/docs/insufficient-n/) is that design, written down.