Kelly Criterion
A mathematical formula that determines the optimal bet size to maximize long-term bankroll growth.
The Kelly Criterion is a formula developed by John Kelly Jr. in 1956 that calculates the mathematically optimal fraction of your bankroll to bet on a positive EV opportunity.
The Kelly Formula
Kelly % = (bp – q) / b
Where:
- b = net odds received (e.g., +200 means b = 2)
- p = probability of winning
- q = probability of losing (1 – p)
Fractional Kelly
Many bettors use "half Kelly" or "quarter Kelly" (betting a fraction of what full Kelly recommends) to cut the swings while keeping the sizing logic. Full Kelly can produce large swings.
Kelly Assumptions
Kelly assumes you can accurately estimate true probability. Overconfidence (overestimating p) leads to overbetting and potential ruin.
Key Takeaways
- Kelly Criterion determines optimal bet sizing for positive EV opportunities.
- Full Kelly maximizes long-term growth but creates high variance.
- Fractional Kelly (half, quarter) is more practical for most bettors.
- Kelly requires accurate probability estimation. Garbage in, garbage out.
Examples
- At +100 (b = 1) with a 55% win estimate: (1 × 0.55 − 0.45) / 1 = 0.10. Full Kelly says bet 10% of your bankroll. Half Kelly says 5%.
- At +200 (b = 2) with a 30% win estimate: (2 × 0.30 − 0.70) / 2 = −0.05. A negative result means don't bet.
Related Terms
Test Your Knowledge
1 / 3Do you know what Expected Value (EV) means?
The average outcome of a bet over time. Positive EV bets profit in the long run.
Frequently Asked Questions
What does a negative Kelly number mean?
It means the bet has no edge at those odds. Kelly says don't bet.
Is full Kelly too aggressive?
For most bettors, yes. Probability estimates are never perfect, and full Kelly punishes overestimates hard. Half or quarter Kelly gives up a little growth for much smaller swings.