Kelly Criterion Calculator
Calculate optimal bet sizing to maximize long-term bankroll growth
Recommended Bet Size
$83.33
8.3% of bankroll
Full Kelly would be
8.3% ($83.33)
Use Fractional Kelly
Most pros use 25-50% Kelly to reduce variance. Full Kelly is mathematically optimal but very aggressive.
Understanding the Kelly Criterion
The Kelly Criterion is a mathematical formula for optimal bet sizing that maximizes long-term bankroll growth. Developed by John Kelly at Bell Labs in 1956, it's used by professional bettors, poker players, and investors worldwide.
The Kelly Formula
f* = (bp - q) / b
Where:
- f* = Fraction of bankroll to bet
- b = Decimal odds - 1 (profit per unit)
- p = Probability of winning
- q = Probability of losing (1 - p)
Example Calculation
You find a bet at +150 odds (2.50 decimal) and estimate a 45% win probability:
- b = 2.50 - 1 = 1.50
- p = 0.45
- q = 0.55
- f* = (1.50 × 0.45 - 0.55) / 1.50 = 0.0833 = 8.33%
With a $1,000 bankroll, full Kelly suggests betting $83.30.
Why Use Fractional Kelly?
While full Kelly maximizes long-term growth, it comes with significant variance. Most professionals use fractional Kelly (typically 25-50%) because:
- Reduced variance: Smoother bankroll growth
- Error margin: Accounts for probability estimation errors
- Psychological comfort: Easier to stick with during downswings
- Still optimal: Half Kelly has 75% of full Kelly's growth rate
When Kelly Says Don't Bet
If the Kelly formula returns zero or negative, it means you don't have an edge at the given odds. The mathematically correct play is to pass on the bet entirely.
