Kelly Criterion Calculator
Calculate the mathematically optimal bet size to maximize bankroll growth while managing risk.
Quick Kelly Fractions
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 bet to maximize long-term growth rate while avoiding bankruptcy.
The key insight: bet in proportion to your edge. More edge = larger bet. No edge = no bet. This balances growth against the risk of ruin.
p = win probability | q = loss probability (1 - p)
Or more intuitively:
Your edge divided by the odds you're getting
Example Calculation
Example: +150 odds, 45% win probability
You estimate 45% chance of winning at +150 (2.50 decimal).
p = 0.45, q = 0.55
Kelly = (1.50 × 0.45 - 0.55) / 1.50
Kelly = (0.675 - 0.55) / 1.50
Kelly = 0.125 / 1.50
Kelly = 8.33% of bankroll
On $1,000 bankroll: bet $83.30
Half Kelly: bet $41.65
Example: -110 odds, 55% win probability
Standard -110 line, you estimate 55% (5% edge over implied 52.4%).
p = 0.55, q = 0.45
Kelly = (0.909 × 0.55 - 0.45) / 0.909
Kelly = (0.50 - 0.45) / 0.909
Kelly = 5.5% of bankroll
Half Kelly: 2.75% of bankroll
Why Use Fractional Kelly?
Full Kelly maximizes expected bankroll growth, but comes with extreme variance. In practice, most professional bettors use fractional Kelly (typically 25-50%) for several reasons:
- Probability estimation error: You're never 100% certain of true probabilities. Overestimating your edge leads to overbetting.
- Variance reduction: Half Kelly achieves ~75% of full Kelly's growth rate but with dramatically lower variance.
- Psychological comfort: Smaller bet sizes are easier to stick with through losing streaks.
- Simultaneous bets: If betting multiple games, full Kelly on each overexposes your bankroll.
Quarter Kelly (25%): Very conservative, recommended for uncertain edges
Frequently Asked Questions
What if Kelly recommends a negative percentage?
A negative Kelly means you have negative expected value — don't bet. The odds don't offer enough value for your estimated probability. Either your probability estimate is wrong, or it's simply a bad bet.
Kelly says 20%+ of my bankroll — isn't that too aggressive?
Probably yes. Large Kelly percentages usually indicate either a huge edge (rare) or overestimated probability (common). Use fractional Kelly — if full Kelly says 20%, half Kelly would be 10%, quarter Kelly would be 5%.
How do I handle multiple bets at the same time?
Calculate Kelly for each bet independently, then use a fraction of each. Some bettors divide their Kelly fraction by the number of simultaneous bets. For correlated bets, the math gets more complex — reduce sizing further.
What's the difference between Kelly and flat betting?
Flat betting (same amount every bet) ignores edge size. Kelly bets more on better edges and less on marginal ones. Kelly is mathematically superior for long-term growth but requires accurate probability estimates.