Kelly Criterion Calculator
Calculate the optimal bet size using the Kelly Criterion.
Maximize long-term growth while managing risk with full and half-Kelly recommendations.
The Kelly Criterion is a mathematical formula for calculating the optimal fraction of your capital to risk on each trade or bet, maximizing the long-term geometric growth rate of your account. It was developed by John L. Kelly Jr. at Bell Labs in 1956, originally for telephone signal transmission, and later applied to gambling and investing.
The full Kelly formula:
Kelly % = W − (L / R)
Simplified equivalent:
Kelly % = (Win Rate × Average Win − Loss Rate × Average Loss) / Average Win
Variable definitions:
- W = Win probability (as a decimal, e.g., 0.55 for 55% win rate)
- L = Loss probability = 1 − W
- R = Win/Loss ratio = Average winning trade size / Average losing trade size
Worked example: A strategy wins 55% of trades (W = 0.55). Average win = $150. Average loss = $100. R = $150 / $100 = 1.5
Kelly % = 0.55 − (0.45 / 1.5) = 0.55 − 0.30 = 0.25 (25% of account per trade)
This means risking 25% of your account on each trade maximizes long-term geometric growth.
Full Kelly vs. Fractional Kelly in practice:
| Approach | % of Kelly | Growth | Volatility |
|---|---|---|---|
| Full Kelly | 100% | Maximum | Extreme — 50%+ drawdowns common |
| Half Kelly | 50% | ~75% of max | Roughly 50% less volatility |
| Quarter Kelly | 25% | ~50% of max | Much smoother equity curve |
| Fixed 1–2% risk | Conservative | Lower | Very stable |
Why most professionals use fractional Kelly: Full Kelly is theoretically optimal only if your probability estimates are perfectly accurate. In real trading, win rates and payoff ratios fluctuate — any estimation error pushes full Kelly into over-betting territory. Half Kelly sacrifices roughly 25% of long-term growth but cuts volatility dramatically.
When Kelly is negative or zero: A Kelly percentage of 0% or negative means the strategy has no positive edge — the expected value is zero or negative. Do not take this trade at all. Fix the strategy before risking capital.
Important caveats:
- Kelly assumes you can bet fractional amounts (not always possible with whole shares)
- It assumes returns are independent (real markets have serial correlation)
- Kelly is a long-run formula — over short periods, even a high-Kelly strategy can show losses
- Never bet more than Kelly recommends, even if you feel confident — this is mathematically provable