Kelly criterion calculator for stake size
Enter the price, the chance you give the bet and your bankroll. The calculator shows the stake the Kelly criterion asks for, in full or as a safer part of it.
The price breaks even at 47.62%. Kelly bets only above that.
Stake and growth at each part of Kelly
| Part of Kelly | Share of bankroll | Stake | Average growth per bet |
|---|---|---|---|
| Quarter Kelly | 2.09% | 20.91 | 0.17% |
| Half Kelly | 4.18% | 41.82 | 0.29% |
| Full Kelly | 8.36% | 83.64 | 0.38% |
| Double Kelly | 16.73% | 167.27 | −0.0036% |
How the Kelly stake is worked out
The criterion picks the share of the bankroll that makes it grow fastest over many bets. It needs two things: the price and your chance of winning. The edge is your chance times the price, minus one. Dividing the edge by the profit per unit, which is the price minus one, gives the share to stake. With no edge the answer is zero.
Worked example
At a price of 2.10 you give the bet a chance of 52.00%. The price breaks even at 47.62%, so the edge is 9.20% per unit. Full Kelly is 8.36% of the bankroll: 83.64 from 1,000. Half Kelly stakes 41.82.
A price in fractional or American form goes through the odds format converter first. How long a bankroll lasts when the edge is against you is shown by the bankroll survival calculator. And the break-even point moves with the margin, which the margin and fair odds calculator takes out of a market.
What Kelly cannot do for you
- It trusts your chance completely. Overrate the bet a little and full Kelly stakes far too much.
- It has nothing to offer on casino games. Their edge is negative on every bet, so the stake Kelly gives is zero.
- It maximises growth in the long run and ignores how rough the ride is. Half Kelly gives up some growth for much smaller swings.
Questions about the Kelly criterion
What does Kelly say for a coin that wins 55.00% at even money?
Stake 10.00% of the bankroll. The edge is the chance times 2.00 minus one, and at even money the Kelly share equals the edge.
Why do many bettors use half Kelly?
Because their chance is an estimate. In the example half Kelly keeps 75.01% of the growth of full Kelly, 0.29% against 0.38% per bet, with half the stake at risk.
What happens if my chance is wrong?
The stake is wrong too. If the real chance in the example is 50.00% instead of 52.00%, full Kelly is 4.55%, far below the 8.36% you staked.
Does Kelly work on crash, dice or slots?
No. Every bet on a game with a house edge has a negative expected profit, and the formula then returns zero or less. No staking plan turns a negative edge into a positive one.