The Kelly Criterion is the mathematically optimal formula for sizing bets to maximize long-term bankroll growth. Developed by physicist John Kelly in 1956, it's used by professional gamblers, investors, and sports bettors who want to grow their bankroll as fast as possible without going broke.
The Kelly Formula
Kelly % = (bp - q) / b
Where:
- b = net odds on the bet (profit per $1 wagered)
- p = your estimated probability of winning
- q = probability of losing (1 - p)
Example: You estimate a 55% chance of winning a bet priced at -110 (b = 100/110 ≈ 0.909): Kelly % = (0.909 × 0.55 - 0.45) / 0.909 = (0.5 - 0.45) / 0.909 = 0.055 = 5.5%
This means betting 5.5% of your current bankroll on this bet maximizes long-term growth.
Why Full Kelly Is Dangerous
Kelly maximizes the geometric growth rate — but it also maximizes variance. A string of losses can devastate your bankroll even when you have a genuine edge.
The solution most professionals use: Fractional Kelly, typically 25-50% of the full Kelly amount. Half Kelly gives you most of the growth benefit at much lower variance. Quarter Kelly is conservative but much safer for bettors with uncertain edge estimates.
The Problem: Edge Estimation
The Kelly formula is only as good as your edge estimate. If you think you have 55% probability on a bet but actually have 51%, full Kelly will significantly over-bet. This is called Kelly overestimation and leads to bankroll degradation despite supposedly having an edge.
For sports bettors, this means:
- Use fractional Kelly (25-50%)
- Calibrate your edge estimates over time — do your 55% confidence bets win at 55%?
- Track results by confidence level to know if your estimates are accurate
The Practical Version
If you don't want to calculate Kelly precisely for every bet, use these proxies:
- High-confidence bet with clear edge: 2-3% of bankroll
- Moderate confidence: 1-1.5% of bankroll
- Low confidence or small edge: 0.5-1% of bankroll
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