How to Optimize Your Bankroll Sizing with the Kelly Criterion
Learn the exact mathematical formula used by Warren Buffett and sharp sports bettors to grow bankrolls exponentially while controlling variance.
Table of Contents
1. What Is the Kelly Criterion?
Developed in 1956 by Bell Labs scientist John L. Kelly Jr., the Kelly Criterion is a mathematical formula that calculates the optimal size of a series of bets. Originally designed to assist with noise signals in long-distance telephone calls, it was quickly adopted by legendary investors like Warren Buffett and Edward Thorp to maximize compound growth of capital.
2. The Mathematical Kelly Formula
f* = (b * p - q) / b
- f* = Fraction of bankroll to bet
- b = Decimal odds - 1 (net payout odds)
- p = Probability of winning (true estimated probability)
- q = Probability of losing (1 - p)
3. Full Kelly vs. Fractional Kelly (Half & Quarter)
While Full Kelly theoretically provides the fastest exponential growth rate, it carries severe drawdown volatility. Professional quantitative sports investors utilize Half Kelly (50%) or Quarter Kelly (25%).
4. Combining Kelly with Monte Carlo Simulations
To ensure your Kelly fraction never leads to bankroll depletion, test your strategy in DCODDS's Monte Carlo Risk of Ruin Engine.
5. Frequently Asked Questions (FAQ)
What if Kelly recommends a negative fraction?
If f* < 0, it means the bet has negative expected value (-EV). You should pass and place zero stake on that bet.