Kelly calculator
Enter your bankroll, the price you can bet and how often it should win. See the full, half and quarter Kelly stake, and how much growth and risk each one carries.
Money set aside for betting only
The price at the book you would bet with
A win chance of 42.02%
- EV as a share of the stake
- +2.94%A 42.02% chance at +145 is worth more than it costs.
- Full Kelly share of bankroll
- 2.03%(b × p − q) ÷ b, with b = 1.45 (decimal odds minus 1), p = 42.02% and q = 57.98%.
Stake on a $5,000 bankroll
Full Kelly
- Stake
- $101.42
- 2.03% of the bankroll. Fastest growth if the win chance is exactly right, and the biggest swings.
- Growth kept
- 100%
- Chance the bankroll halves at some point
- 1 in 2
Half Kelly
- Stake
- $50.71
- 1.01% of the bankroll. Most of the growth for far less risk.
- Growth kept
- 75%
- Chance the bankroll halves at some point
- 1 in 8
Quarter Kelly
- Stake
- $25.35
- 0.51% of the bankroll. What ArbWins's +EV board stakes, because a fair price is only an estimate.
- Growth kept
- 44%
- Chance the bankroll halves at some point
- 1 in 128
Growth kept is the share of full Kelly's long-run growth rate. The chance of halving is the standard long-run approximation and assumes the win chance is right.
What the Kelly criterion does
The Kelly criterion picks the share of your bankroll that grows it fastest over many bets, given the price and your chance of winning: f = (b × p − q) ÷ b, where b is the decimal odds minus 1, p the win chance and q = 1 − p. When the bet has no edge, f comes out at zero or below and the answer is not to bet.
A worked example
Take a $5,000 bankroll and an underdog at +145 (b = 1.45) whose fair price is +138, a 42.02% chance of winning. Then f = (1.45 × 0.42017 − 0.57983) ÷ 1.45 = 2.03% of the bankroll. Full Kelly stakes $101.42, half Kelly $50.71 and quarter Kelly $25.35. These are the calculator's starting numbers.
Growth against risk
Full Kelly grows the bankroll fastest only if the win chance is exact, and it swings hard. Under the standard long-run approximation, a full-Kelly bettor has a 1 in 2 chance of seeing the bankroll fall to half its size at some point.
Staking less gives up surprisingly little growth. Half Kelly keeps about 75% of full Kelly's growth rate, and the chance of halving drops to 1 in 8. Quarter Kelly keeps about 44%, and the chance drops to 1 in 128. Going the other way is costly: at twice Kelly the expected growth is about zero, and above that the bankroll shrinks even with a real edge.
Why ArbWins stakes a quarter
The win chance is an estimate, and Kelly is very sensitive to it. In the example, if the true chance is 41.02% rather than 42.02%, the right stake is 0.34% of the bankroll. Full Kelly at 2.03% is about six times that, and the bankroll is expected to shrink. Quarter Kelly, at 0.51%, is about 1.5 times the right stake and still grows.
ArbWins's +EV board shows a quarter-Kelly stake beside every bet for that reason, sized from your bankroll and rounded to the dollar.
Work out the edge first with the EV calculator. A bet with negative EV has no Kelly stake at any fraction.