The Kelly Criterion is a formula from probability theory that answers one of the most important questions in trading and betting: what fraction of your capital should you risk on each trade to maximize long-term growth? Developed by John L. Kelly Jr. at Bell Labs in 1956, it has been used by professional gamblers, quantitative hedge funds, and investors like Edward Thorp, who applied it to both blackjack and the stock market.
Risk too little and your account grows slower than it could. Risk too much and volatility destroys you — even a strategy with a genuine edge will eventually hit a losing streak that a heavily over-leveraged account cannot survive. The Kelly fraction is the mathematical sweet spot between those two failure modes.
Where f* is the optimal fraction of capital to risk, W is your win rate (as a decimal), and b is your payoff ratio — average win divided by average loss.
Worked example: suppose you win 55% of your trades, your average winner is $160 and your average loser is $100. Then W = 0.55, b = 1.6, and f* = 0.55 − 0.45 / 1.6 = 0.269. Full Kelly says risk 26.9% of your account per trade — which brings us to the most important caveat.
Full Kelly maximizes the growth rate, but the ride is brutal: drawdowns of 50% or more are expected, and any error in your estimated win rate makes over-betting likely — and over-betting beyond Kelly actively destroys capital. That is why practitioners use fractional Kelly:
If the calculator shows a negative Kelly fraction, your strategy has no positive expectancy at these numbers — no position size fixes that. Improve the win rate or the payoff ratio first; you can explore that trade-off with our win rate calculator.
Fixed fractional sizing ("always risk 1%") is simple and robust but ignores your edge. Kelly scales risk to the quality of the opportunity: a bigger edge justifies a bigger position. In practice, many traders combine the two — compute half Kelly, then cap it at their fixed maximum. To see how your risk per trade translates into the probability of blowing up an account, try the risk of ruin calculator, and use the position size calculator to convert a risk percentage into an exact number of shares. You can also stress-test any win rate and payoff combination over hundreds of simulated trades with the Monte Carlo probability simulator.
The formula is f* = W − (1 − W) / b, where W is your win rate as a decimal and b is your payoff ratio (average win ÷ average loss). The result is the fraction of your capital that maximizes long-term compound growth. For example, a 55% win rate with a 1.6 payoff ratio gives f* = 0.55 − 0.45/1.6 ≈ 26.9%.
Full Kelly assumes you know your true win rate exactly and tolerates enormous drawdowns — routinely 50% or worse. Half Kelly retains roughly three-quarters of the growth rate with about half the volatility, and it protects against the common case where your real edge is smaller than your backtest suggests. Betting beyond true Kelly actually reduces long-term growth, so erring low is the safer side.
A negative result means the strategy has negative expected value — the combination of win rate and payoff ratio loses money over time. No position sizing scheme can make a losing strategy profitable; the correct Kelly bet on a negative-edge game is zero.
Yes, as a guide rather than a literal instruction. Day traders typically compute half or quarter Kelly from their trade history and then cap the result at 1–2% of the account per trade. The formula is most reliable when your statistics come from at least 100 real trades, since small samples over- or under-estimate the true win rate.
Yes — Edward Thorp famously applied it to portfolio management, and it underlies many position-sizing frameworks in quantitative finance. For long-only investing, the inputs become expected return and variance rather than win rate and payoff ratio, but the principle is identical: size positions in proportion to edge over risk.