How the Kelly criterion calculator works
The Kelly criterion calculator turns an edge into a stake. Type your betting bank, the odds in any format (5/2, 3.5 or +250), and your chance of winning as a percentage. Then pick a Kelly fraction: full, half, quarter or tenth.
You get the stake in pounds, the share of your bank it represents, your edge (the expected profit per £1 staked) and the expected profit on the bet. The note underneath shows what full Kelly would stake and the chance the odds imply, so you can see how far your view differs from the market's.
The chance you type is your own estimate, not the bookmaker's. Everything the calculator shows depends on that one number.
The Kelly formula
The formula was published in 1956 by John L. Kelly Jr., a researcher at Bell Labs. For a simple bet it reads:
f* = (bp - q) / b
- f* is the share of your bank to stake.
- b is the decimal odds minus 1 (the profit per £1 staked).
- p is your chance of winning, and q is 1 - p, your chance of losing.
A 60% chance at evens: b = 1, so f* = (0.6 - 0.4) / 1 = 20% of the bank. A 40% chance at 2/1 (3.0): b = 2, so f* = (0.8 - 0.6) / 2 = 10%. The odds imply 33.3%, you rate it 40%, and the edge is +20%. On a £1,000 bank:
| Kelly fraction | Share of bank | Stake | Expected profit |
|---|---|---|---|
| Full Kelly | 10% | £100.00 | £20.00 |
| Half Kelly | 5% | £50.00 | £10.00 |
| Quarter Kelly | 2.5% | £25.00 | £5.00 |
| Tenth Kelly | 1% | £10.00 | £2.00 |
Why fractional Kelly is so common
Kelly maximises the long-run growth of a bank only if your probability is right. Overrate a horse and the formula over-stakes it. Say the true chance of that 2/1 shot is 35%, not 40%: full Kelly at 35% is 2.5% of the bank, so staking 10% puts four times the right amount at risk.
Nobody knows the true chance of a horse race, so many bettors stake a fraction of Kelly to cover the error in their own numbers and to smooth out the swings. Full Kelly can mean deep falls in the bank even when the edge is real. A fixed bank and a staking plan are covered in our guide to betting on horses to win over time.
When Kelly says no bet
If the chance the odds imply is as high as yours or higher, there is no edge and Kelly stakes nothing. A 30% chance at 2/1 is a no bet: the price implies 33.3%, so the formula comes out negative and the calculator shows £0.00. Check what a price implies with the implied probability calculator.
Kelly is a way to size a bet, not a reason to make one. Only bet what you can afford to lose, and if betting stops being fun, our responsible gambling page lists free, confidential help.