The Kelly criterion tells you what share of your bankroll to stake on a bet you think is value. Bigger edge, bigger stake. No edge, no bet. It only works if your estimate of the chance is right, and betting more than Kelly can lose money even when you have an edge.
What the Kelly criterion does
John Kelly, a scientist at Bell Labs, published the formula in 1956. It answers one question: if you have an edge, how much should you bet to grow your money fastest over many bets?
Bet too little and your bankroll grows slowly. Bet too much and the losing runs knock it back further than the wins push it forward. Kelly is the stake in between.
The formula
Stake share = (b × p − q) ÷ b, where b is the decimal odds minus 1, p is your chance of winning and q is 1 minus p.
A horse is 2/1, which is 3.0 in decimal. The price implies a 33.3% chance. You think it's 40%. Then b is 2, and (2 × 0.4 − 0.6) ÷ 2 = 0.1. Kelly says stake 10% of your bankroll.
If your estimate is 33.3% or lower, the answer is zero or negative. Kelly never bets without an edge.
Work out a Kelly stake with your own numbers.Kelly criterion calculator →Overbetting loses money, even with an edge
Here's the catch. Say the true chance is 36%, not the 40% you estimated. You still have an edge, but the right Kelly stake is 4%, not 10%. The table shows what happens to a typical bankroll after 1,000 bets at 2/1 for different stake sizes.
| Stake each bet | Typical change |
|---|---|
| 1.0% | Up 101% |
| 2.5% | Up 290% |
| 4.0% (the right Kelly stake) | Up 385% |
| 8.0% | Up 7% |
| 10.0% (Kelly for a 40% estimate) | Down 83% |
| 15.0% | Down more than 99% |
Staking 10% of the bankroll each time, the full Kelly stake for your overestimate, leaves a typical bankroll down by more than 80%, on bets that win money on average. Staking less than Kelly still grows the bankroll, only more slowly.
Why most people use fractional Kelly
Nobody knows the true chance of a bet. Your estimate will be wrong, and the table shows that being too high costs far more than being too low. Staking half or a quarter of the Kelly amount gives up a little growth in exchange for a big cut in risk.
- Full Kelly: fastest growth if your estimates are perfect, with big swings.
- Half Kelly: about three quarters of the growth with much smaller swings.
- Quarter Kelly: slower growth, and far more room for errors in your estimates.
Kelly needs an edge first
Kelly is a staking plan, not a way to find winners. At bookmaker prices most bets have no edge, and Kelly says stake nothing on them. It's only useful once you can show your estimates beat the market over a large number of bets.
Questions people ask
Is the Kelly criterion good for betting?
It's the right maths for sizing bets when you have an edge. In practice your estimates are uncertain, so most people stake a fraction of the Kelly amount.
What is half Kelly?
Staking half of what the Kelly formula says. It keeps most of the growth and cuts the swings in your bankroll a lot.
Does Kelly work for accumulators?
The formula works for any single bet with known odds and an estimated chance. For an acca you'd need an estimate for the whole acca, and small errors on each leg multiply.