risk
Kelly Criterion
The mathematically optimal bet size that maximizes long-term growth rate. In practice, traders use "half Kelly" or less for safety.
Formula
f* = (p · b - q) / b where q = 1 - p
Variables
- f*
- Optimal fraction of capital to risk
- p
- Probability of winning (e.g., POP)
- q
- Probability of losing (1 - p)
- b
- Win/loss ratio (avg win / avg loss)
Worked Example
Inputs
- POP
- 70%
- Avg Win
- $150
- Avg Loss
- $350
Calculation Steps
- 1
p = 0.70, q = 0.30, b = 150/350 = 0.4286 - 2
f* = (0.70 × 0.4286 - 0.30) / 0.4286 - 3
f* = (0.30 - 0.30) / 0.4286 = 0.00 - 4
Full Kelly = 0% → trade has no edge at fair pricing
Result: Kelly = 0% — no edge to exploit (need better entry or management)
Intuition
Kelly often suggests surprisingly large bet sizes. In practice, use "quarter Kelly" (f*/4) because the formula assumes you know exact probabilities — you don't. Overbetting is far more dangerous than underbetting.