Kelly Criterion Calculator

How the Kelly criterion is calculated

W is winners ÷ (winners + losers). R is the average win ÷ the average loss. If a loss costs a share f of the account and a win adds R times that share, the expected growth per trade is W × ln(1 + f × R) + (1 − W) × ln(1 − f). It is highest where its slope is zero, which gives:

Kelly % = W − (1 − W) ÷ R

John Kelly's 1956 paper, read on 17 October 2026, defines this long-run growth rate and shows that for even-money bets it is highest when the bet is the win probability minus the loss probability, the formula above with R = 1.

Worked example: 40 decisive trades

A hypothetical trader closed 18 winners, 22 losers, and 4 breakeven trades on a 25,000 USD account, with an average win of 300 USD and an average loss of 150 USD. The calculator starts with these winners, losers, averages, and balance, at half Kelly.

1. Win rate: 18 ÷ (18 + 22) = 45%. The 4 breakeven trades count in neither field.
2. Payoff ratio: 300 ÷ 150 = 2. Full Kelly: 0.45 − 0.55 ÷ 2 = 17.5%.
3. Half Kelly: 8.75% of 25,000 USD, so an average loss of 2,187.50 USD. That keeps about 76% of the long-run growth of full Kelly.
4. Standard error of the win rate: √(0.45 × 0.55 ÷ 40) ≈ 7.9 points. At 37.1%, one standard error lower, Kelly is about 5.7%, below the half Kelly of 8.75%.

What the result sizes

Kelly sizes your average loss, not your position value. If your average loss equals the amount you plan to risk to your stop, the share of account corresponds to a risk per trade, which you would convert into shares, contracts, or lots for your instrument. If you often exit before the stop, your average loss is smaller than your planned risk, and the Kelly guide shows how to convert between the two.

What the calculator leaves out

The formula treats every win as the average win and every loss as the average loss. Real trades vary in size, and a spread of outcomes can lower the fraction that grows the account fastest. The standard-error figure covers only the uncertainty in the win rate; the average win and average loss are estimates too, and a few large trades can move them. Above full Kelly, growth falls while drawdowns keep growing: in the example, double Kelly keeps about 6% of the growth of full Kelly. Trading costs count only if they are already in your averages.

In Tradeways, the Kelly criterion widget calculates full Kelly from your closed trades in the dashboard's account scope and global filter, with breakeven trades left out of the win rate. It shows full Kelly only; apply a fraction and check the trade count behind it here.