The Kelly criterion
The bet size that grows fastest, if you knew your edge exactly. · 8 min
Decide first
Risking more per trade makes each win bigger, but losses compound on a smaller account. Somewhere between betting nothing and betting everything is the fraction that makes the account grow fastest in the long run. John Kelly found it in 1956:
For 40% wins at 2R, f* = 0.4 − 0.3 = 10%. The figure shows median growth over 100 trades for every fraction: it rises to a peak at Kelly, falls back to about zero at double Kelly, and turns negative beyond. That right-hand side is the trap: a trader can have a real edge and still shrink the account by betting too much.
How growth depends on what you risk
Median growth over 100 trades for each fraction of equity risked per trade. The peak is the Kelly fraction; past twice Kelly the same edge shrinks the account.
| Risk per trade | Growth per trade | Median over 100 trades | 10 losses in a row cost |
|---|---|---|---|
| 1.0% | 0.19% | 20.8% | 9.6% |
| 2.5% (quarter) | 0.43% | 54.1% | 22.4% |
| 5.0% (half) | 0.74% | 108.5% | 40.1% |
| 10.0% (Kelly) | 0.98% | 164.1% | 65.1% |
| 20.0% (double) | 0.07% | 7.3% | 89.3% |
Then the same edge, 10,000 simulated traders, four sizes. The growth table above is the median; this race shows the spread around it, which is where Kelly's problem lives.
10,000 simulated traders
Simulated data · not real pricesEvery trader takes the same 200 trades of a 40% win rate, 2R edge (expectancy +0.2R, Kelly 10.0%). The wins and losses are identical across the four groups; only the size differs.
Worked example: growth at Kelly
- p = 0.4, W = 2, f = 0.10.
- Growth per trade g = 0.4 × ln(1.2) + 0.6 × ln(0.9) = 0.0729 − 0.0632 = 0.0097.
- Over 100 trades the median account grows by e^(100 × 0.0097) − 1 = 164%.
- At 1% risk the same edge grows 21%: slower, and with a fraction of the swings.
Common mistake: Kelly as the size to use
Kelly is the ceiling, not the target. It assumes the edge is known exactly, the trades are independent, and you can stomach drawdowns of 50% or more along the way. None of these holds for a real trader, which is why the next lesson uses a fraction of it.
Check yourself
- Win rate 40%, average win 3R, losses 1R. Kelly fraction?
- For 40% wins at 2R (Kelly 10%), how does the median growth over 100 trades compare at half Kelly (5%) and double Kelly (20%)?
- Why do professionals almost never risk the full Kelly fraction?
Closing round
Play a round at 1% risk, then replay the same seed at 5%. Same candles, same decisions if you can: compare the equity curves in the two reviews.
Play the round in the simulator →The simulator's markets are generated, not real prices; the round practises the arithmetic, it does not predict anything.
Further reading: Poundstone, Fortune's Formula. The lesson teaches the idea in its own words and exercises.