The Kelly Criterion: Optimal Bet Sizing for Maximum Growth
The mathematical formula that tells you exactly how much to bet. Used by professional gamblers, hedge funds, and anyone who takes edge seriously.
What is the Kelly Criterion?
The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. It calculates the optimal percentage of your bankroll to wager on a bet with a positive expected value, maximizing long-term growth rate.
The Formula
f = (bp - q) / b**
Where:
- f* = fraction of bankroll to wager
- b = net odds received (decimal odds - 1)
- p = probability of winning
- q = probability of losing (1 - p)*
Worked Examples
Example 1: Even Money Bet
- Odds: +100 (even money), b = 1
- Your edge: 55% win rate, p = 0.55, q = 0.45
- Kelly = (1 × 0.55 - 0.45) / 1 = 10%
- Bet 10% of your bankroll
Example 2: Underdog
- Odds: +200, b = 2
- Your edge: 40% win rate, p = 0.40, q = 0.60
- Kelly = (2 × 0.40 - 0.60) / 2 = 10%
- Bet 10% of your bankroll
Example 3: Favorite
- Odds: -150, b = 0.667
- Your edge: 65% win rate, p = 0.65, q = 0.35
- Kelly = (0.667 × 0.65 - 0.35) / 0.667 = 12.5%
- Bet 12.5% of your bankroll
Why Full Kelly is Dangerous
Full Kelly maximizes long-term growth but creates enormous volatility:
- 50% drawdowns are common
- Requires perfect probability estimates (impossible in practice)
- Emotionally brutal during losing streaks
Fractional Kelly
Most professionals use fractional Kelly — betting a fraction of the full Kelly recommendation:
| Fraction | Growth Rate | Drawdown Risk | Recommended For |
|---|---|---|---|
| Full Kelly | Maximum | Extreme | Nobody in practice |
| 75% Kelly | 94% of max | High | Aggressive pros |
| 50% Kelly | 75% of max | Moderate | Most professionals |
| 25% Kelly | 44% of max | Low | Conservative/new |
Half Kelly is the sweet spot — you sacrifice only 25% of the growth rate while dramatically reducing drawdown risk.
Kelly for Multiple Simultaneous Bets
When you have multiple bets at the same time, the total Kelly allocation should not exceed your comfort level. A simple approach: calculate Kelly for each bet independently, then scale all bets down proportionally if the total exceeds your risk tolerance.
The Bottom Line
The Kelly Criterion is the mathematically optimal bet sizing strategy. But it requires accurate probability estimates and emotional discipline. For most bettors, flat betting at 1-2% of bankroll is a safer and simpler approach that still captures most of the benefit.