Kelly Criterion

The Kelly criterion is a formula that tells you the bankroll fraction to bet on any +EV opportunity to maximize long-run growth. Developed by John Kelly Jr at Bell Labs in 1956, it’s the foundational sizing model for sharp bettors, hedge fund managers, and anyone who has to size repeated bets where they have an edge.

The formula

f* = (b × p − q) / b

Where:

• b = the multiple of your stake you’d win (decimal odds − 1)
• p = your true probability of winning
• q = 1 − p (probability of losing)

Example: a coin-flip bet at +120 odds (decimal 2.20, b = 1.20) where you actually believe the win probability is 0.55:

f* = (1.20 × 0.55 − 0.45) / 1.20 = 0.21 / 1.20 = 17.5% of bankroll

On a $1,000 bankroll, full Kelly would say bet $175. That’s enormous compared to typical 1u-2u sizing — and that’s the point. Kelly maximizes growth, but the variance is brutal.

Why most bettors use fractional Kelly

Full Kelly is mathematically optimal if your probability estimate is exact. It’s not. Most bettors overestimate their edge, which means they over-bet via Kelly. Even when your estimate is accurate, full Kelly produces 50%+ drawdowns regularly.

Common practice:

• Half Kelly — half the recommended size; about half the variance, only slightly slower growth
• Quarter Kelly — even more conservative; preferred when probability estimates are uncertain or the bettor can’t tolerate large drawdowns
• Tenth Kelly — sometimes used as a hard ceiling for retail bettors who haven’t proven their model out yet

The Kelly criterion calculator on this site shows full, half, and quarter Kelly side-by-side so you can pick what fits your appetite.

When Kelly is negative

If f* comes out negative, the bet is -EV — your probability is below the implied probability priced by the book. Don’t bet. Kelly is silent on direction; if you genuinely think the opposite side will hit, take that side at the matching odds (which may not be available).

Limitations

• Kelly assumes you know your true probability. You usually don’t.
• Single-bet Kelly. Real bettors face many bets at once. Multi-bet Kelly is more complex; correlated bets need joint optimization.
• Variance is high even at fractional sizing. Have the bankroll for it.

In practice

• Track your CLV (closing line value) for hundreds of bets before trusting your probability estimates.
• Default to half or quarter Kelly until your model is well-validated.
• Cap any single bet at 5% of bankroll regardless of what Kelly says — protects against model error.