The formula for a trader
Betting sites write Kelly with odds. For a trader who risks a fixed amount on each trade it is simpler: f* = W − (1 − W) ÷ R, where W is the win rate (0 to 1) and R is the average win divided by the average loss. The result f* is the share of the account to lose on a trade that hits its stop. If f* is zero or negative, the strategy has no edge in this sample and Kelly says to risk nothing.
The same inputs give the expectancy, W × R − (1 − W), in units of the amount risked. Kelly is positive exactly when expectancy is positive.
Worked table
Illustrative inputs (E). Each row applies the formula above.
| Win rate | Average win : average loss | Expectancy per trade | Full Kelly (fraction to risk) | Half Kelly |
|---|---|---|---|---|
| 50% | 2 : 1 | +0.50 R | 25.0% | 12.5% |
| 40% | 2 : 1 | +0.20 R | 10.0% | 5.0% |
| 40% | 1 : 1 | -0.20 R | 0% (no edge) | 0% |
| 60% | 1 : 1 | +0.20 R | 20.0% | 10.0% |
| 35% | 3 : 1 | +0.40 R | 13.3% | 6.7% |
| 30% | 2 : 1 | -0.10 R | 0% (no edge) | 0% |
Read the second row: a 40% win rate with winners twice the size of losers has an expectancy of +0.20 R and a full Kelly of 10%. Risking 10% of the account per trade on a strategy that loses 60% of the time is a lot, which is the first sign that full Kelly is a theoretical ceiling and not a plan. The third row shows the opposite: a 40% win rate with equal wins and losses has no edge.
Why traders use a fraction of Kelly
- The inputs are estimates. Your win rate and payoff come from a limited sample. Over a few dozen trades they can be far from the true values, and overestimating the edge pushes you above the real Kelly fraction, where growth falls and losses grow.
- Drawdowns are deep. In a standard continuous-time approximation (Thorp, 2006, "The Kelly Criterion in Blackjack, Sports Betting and the Stock Market"), betting a fraction c of full Kelly gives a chance of ever falling to a fraction x of the starting level of about x^(2/c − 1). That is an approximation (E), not a forecast for your account.
| Fall from the starting level | Full Kelly: chance of ever reaching it | Half Kelly | Quarter Kelly (c = 0.25) |
|---|---|---|---|
| 20% | 80% | 51.2% | 20.97% |
| 50% | 50% | 12.5% | 0.78% |
| 75% | 25% | 1.6% | 0.01% |
At full Kelly the approximation gives a one-in-two chance of the account halving at some point. At half Kelly it is 12.5%. That gap is why half or quarter Kelly is the usual choice.
Limits when you apply it to trades
- Trades are not independent bets with fixed odds: stops slip, gaps happen, and results cluster in regimes.
- Open positions that move together add up. Five correlated trades at 1% behave like one at 5%.
- Prop-firm accounts have hard drawdown and daily limits. Those limits, not Kelly, cap your risk. See how much to risk in a challenge.
Using it in practice
- Pull win rate and average win and loss from a log (see how to keep a trading log).
- Enter them in the Kelly criterion calculator.
- Treat the answer as an upper bound, take a fraction of it, and compare with your fixed rule in how much to risk per trade.
- Check the downside with the risk of ruin calculator.
Trading can lose money. This page is education, not advice.
Try it with your own numbers
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Pre-set for the market you trade
Pip, point and tick values differ by instrument. These calculators start from each one's contract, with worked examples:
Quick questions
What is the Kelly criterion in trading?
A formula for the share of your account to risk per trade that maximises long-run growth: f* = W − (1 − W) ÷ R, with W the win rate and R the average win divided by the average loss.
Is full Kelly safe?
No. It needs exact inputs and still produces deep drawdowns. In the usual approximation there is about a 50% chance of the account halving at some point.
What is half Kelly?
Risking half of the Kelly fraction. It gives up some growth for much smaller drawdowns, and it leaves room for errors in the win rate and payoff.
What if Kelly comes out negative?
Then expectancy is negative in your sample. Kelly says to risk nothing until the strategy changes or more data shows an edge.
A defined edge starts at a defined level.
These indicators help you mark the levels a stop and a target sit at.
Premium indicators come with a 7-day free trial on request: how the trial works.
Keep reading
Last updated November 2026. For education only. Not financial advice.