The Kelly criterion is a formula that tells you what fraction of your bankroll to bet to grow it as fast as possible over the long run, given your edge and the odds. It is elegant, mathematically optimal under its assumptions, and frequently misused. Here is how it works and how to use it safely.
The formula
- b = net decimal odds (decimal price − 1)
- p = true probability of winning
- q = 1 − p
An equivalent form that is easy to remember:
where edge = p × decimal − 1.
Worked examples
Example 1: even money with a 3% edge Price +100 (b = 1), p = 51.5%. Kelly = (1 × 0.515 − 0.485) ÷ 1 = 3.0% of bankroll.
Example 2: favorite Price −150 (decimal 1.667, b = 0.667), p = 62%. Edge = 0.62 × 1.667 − 1 = 3.3%. Kelly = 0.033 ÷ 0.667 = 5.0%.
Example 3: underdog Price +300 (b = 3), p = 27%. Edge = 0.27 × 4 − 1 = 8%. Kelly = 0.08 ÷ 3 = 2.7%.
Notice the underdog with a bigger edge gets a smaller bet. Kelly automatically scales down volatile bets.
Why full Kelly is dangerous
Kelly assumes you know your true edge exactly. You do not. Your edge is an estimate from a fair line that might be off by a percentage point or two.
- If you overestimate your edge, full Kelly overbets, and overbetting is far worse than underbetting. Betting twice the Kelly fraction gives zero expected growth; more than that and you expect to shrink.
- Even with the right edge, full Kelly produces stomach-churning swings: drawdowns of 50% or more are normal over long periods.
Fractional Kelly
That is why almost everyone uses a fraction:
| Fraction | Growth vs full Kelly | Volatility |
|---|---|---|
| Full | 100% | Very high |
| Half | ~75% | About half |
| Quarter | ~44% | About a quarter |
Half Kelly keeps about three-quarters of the growth with half the swings, and protects you if your edge is overstated. Quarter Kelly is the common default for +EV bettors. (Fractional Kelly.)
Practical Kelly rules
- Use a conservative edge: the worst case across devig methods, not the best case. (How to devig odds.)
- Use quarter Kelly (or less for props and live bets).
- Cap any single bet, for example at 2% of bankroll.
- Account for simultaneous bets. Ten Kelly bets at once on the same night are riskier than ten bets in sequence; scale down when exposure stacks up.
- Recalculate bankroll regularly, not after every bet.
OddsHype suggests quarter-Kelly stakes with a hard cap by default. Try your own numbers in the Kelly calculator.
Kelly vs flat betting
Flat betting is simpler and more forgiving of bad edge estimates. Kelly grows faster when edges are accurately measured. A popular compromise: flat units, but scale to 0.5 or 1.5 units based on confidence. (Flat vs percentage betting.)
Frequently asked questions
What is the Kelly criterion in betting?
A formula that sets bet size as a fraction of bankroll based on your edge and the odds, maximizing long-term growth if your edge estimate is accurate.
Should I use full Kelly?
Almost never. Edge estimates are uncertain, and full Kelly overbets when you overestimate. Quarter to half Kelly is standard.
What if Kelly says to bet zero?
Then the bet has no edge (or a negative one) at that price, and you should not bet it.