Short answer: the Kelly criterion is a formula for the fraction of your bankroll to risk on a bet or trade that has positive expected value. It needs two inputs: your probability of winning and the odds, meaning how much you gain per unit risked. The stake it returns maximises the long-run logarithmic growth of your capital. For traders it is a ceiling, not a target. Most people who use it risk a quarter or a half of the full stake, because the inputs are estimates and full Kelly makes equity swing violently.
What the Kelly criterion measures
John L. Kelly Jr. published the idea in 1956 while working at Bell Labs on information theory. His question was plainly stated: if you know your edge, how much should you stake each time so that capital grows fastest without ever hitting zero? Stake less than the answer and growth is slower than it could be. Stake more and growth also slows, because losses along the way become needlessly large. Stake well beyond it and expected growth turns negative, even though every single bet still has an edge.
That is why people call it optimal betting. It is optimal only if your probability estimate is honest and the payoff is stable, and in trading both are wobbly. So treat the formula as the upper limit of sensible bet sizing, with the rest of your risk management sitting underneath it.
The formula and a worked example
For a bet that either wins or loses:
f = p minus (1 minus p) divided by b
- f is the fraction of your bankroll to risk.
- p is your probability of winning.
- b is the odds, the amount you win per unit risked. A trade that gains 1.5R against a 1R loss has b of 1.5.
Round numbers make the arithmetic plain. Start with a 10,000 account. The journal shows 55 winners per 100 trades, and the average winner is 1.5 times the average loser. So p is 0.55, b is 1.5, and the loss probability is 0.45. Divide 0.45 by 1.5 to get 0.30. Subtract that from 0.55 and the Kelly fraction is 0.25.
Full Kelly says risk 25 percent of equity, or 2,500, on the next trade. With a 50-pip stop on a major pair, that is 50 per pip, roughly five standard lots. Two losses in a row and the account sits near 5,600. The maths is correct and the result is still unusable for a human being.
How to estimate your edge before you use Kelly
Both inputs come from your records, not from hope. A common approach:
- Take the last 100 closed trades from one strategy in one market, recorded in R-multiples.
- p is winners divided by total trades. Count breakeven trades as losses so the estimate stays humble.
- b is the average winner divided by the average loser on actual exits, the realised version of your risk-reward ratio.
- Subtract spread, commission and slippage first, because that cost quietly shrinks b on every short-term strategy.
- Confirm the result has positive expected value with the trading expectancy formula. If expectancy is zero or negative, the Kelly fraction is zero.
With 30 trades, the estimate of p can easily be off by ten points, and Kelly amplifies that error. A patchy journal that mixes setups produces a lopsided p and a stake the edge cannot support.
Where the Kelly criterion is used, and how it compares
Kelly began in gambling and still lives there. In sports betting, a punter compares their own fair probability with the odds on offer. Decimal odds of 2.5 mean b is 1.5. If the punter believes the true probability of winning is 0.45, the stake is 0.45 minus 0.55 divided by 1.5, about 8 percent of the bankroll. Poker players use the same logic for bankroll management, treating each buy-in as a fraction of the total roll. Traders apply it to position size, almost always in a fractional form, because market inputs are fickle.
| Sizing method | How the stake is set | Behaviour in a losing run | Who it suits |
|---|---|---|---|
| Fixed fraction, such as 1 percent | Fixed share of current equity | Stake shrinks with equity, ruin is rare | Most retail CFD traders |
| Full Kelly | Fraction derived from p and b | Deep, lumpy drawdowns, fastest growth on paper | Bettors with stable, verified edges |
| Fractional Kelly | Quarter to half of full Kelly | Far smoother, keeps most of the growth | Traders with 200 or more logged trades |
| Martingale | Double after each loss | Blows up on an ordinary streak | Nobody with a finite account |
Limitations of full Kelly in real markets
- Estimation error. In markets, p and b come from a small, stale sample and they drift. Overestimate p by five points and full Kelly turns from optimal into over-betting.
- Drawdown depth. At full Kelly, a 50 percent drawdown is an ordinary feature of the equity curve, even when the edge is genuine.
- Fat tails. The formula assumes the loss is exactly 1R. Slippage through a stop on a news release makes the real loss bigger and the sizing brittle.
- Correlated positions. Three open trades on USD pairs are one bet in three costumes. Sizing each one separately overstates what you can risk in total.
This is where the risk of ruin becomes the more useful number. It tells you how likely a given fraction is to breach the level where you can no longer trade.
Fractional Kelly and a checklist for choosing your fraction
Fractional Kelly means risking a set share of the full Kelly stake. Half Kelly keeps roughly three quarters of the theoretical growth rate while cutting the volatility of the equity curve by about half. Quarter Kelly keeps just under half the growth for a quarter of the volatility. That trade is generous: most of the growth for a fraction of the pain. On the 10,000 account above, quarter Kelly is 625 per trade, a stake most CFD traders would still find precarious.
Run this checklist before trusting any fraction:
- Are p and b based on at least 100 closed trades from one strategy, net of costs?
- Does the edge survive if you remove the single best trade?
- Does the stake stay below any daily or total loss limit you trade under?
- Would a five-loss streak at this size leave you calm enough to take the sixth signal?
- Have you cut the fraction further for correlated open positions?
- Will you recalculate after every 50 trades rather than when a loss stings?
If any answer is no, halve the fraction and keep collecting data. The tedious part, logging trades, is what makes the tidy formula worth anything.
Kelly inside a prop-firm evaluation
Evaluation accounts add hard limits that Kelly never modelled: a daily loss limit and a total drawdown. Those limits define ruin far above zero. At Pivex the daily loss limit resets each day and the total drawdown is static, so the ruin line does not creep upward as you profit. Suppose an evaluation allows a total drawdown of 6 percent. A quarter-Kelly stake of 6.25 percent breaches it in a single loss.
So flip the order. Start from the limits, not from the edge. Take the daily loss limit, decide how many losing trades you want to survive inside it, and derive the risk per trade. Then use the smaller of that number and your fractional Kelly, which is mostly the limit-derived one. A trader with a 4 percent daily limit who wants room for four losses risks 1 percent per trade. The one-step evaluation has no clock on the attempt and no minimum day count, so no deadline pushes you to size up. The built-in assistant on Pivex shows how close you sit to each limit. Kelly then answers a different question: whether your edge is big enough that a small stake still grows the account at a useful pace.
Next step: pull your last 100 trades into a spreadsheet and compute p and b after costs. Write full, half and quarter Kelly beside the risk you actually take. If you trade a Pivex evaluation, compare each of those against the daily loss limit and the static drawdown before changing anything. Results vary, but the comparison alone usually shows whether your sizing is stingy, sensible or reckless.
Related guides: risk of ruin in trading and the trading expectancy formula.
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