Kelly criterion calculator: stake size from odds and your probability

The Kelly criterion calculator turns a price and your own probability estimate into a stake. Enter American or decimal odds, the chance you give the bet, your bankroll and a Kelly fraction. It prints your edge, the full Kelly percentage, the fractional stake and the amount in dollars. The stake is zero when the edge is zero or negative.

Edge, per $1 staked

5.00%

Full Kelly, % of bankroll

5.50%

Stake at your fraction, % of bankroll

5.50%

Stake in dollars

$55.00

Break-even probability at this price

52.38%

At -110 with your estimate of 55%, the edge is 5.00% and the Full Kelly stake is 5.50% of the bankroll, or $55.00.

The stake is only as good as the probability you type in. Kelly assumes that number is right, and if it is too high the stake is too big. This page is arithmetic on your estimate: it does not say whether the estimate is right and it does not predict any result.

The Kelly formula

f* = (b × p − q) ÷ b

f* is the share of your bankroll to stake. b is the decimal odds minus 1 (the profit on a $1 stake), p is your probability estimate as a number from 0 to 1, and q is 1 − p. When b × p − q is zero or negative, f* is taken as 0. Fractional Kelly multiplies f* by 1/2 or 1/4.

Worked example

Odds of -110 are 1.909 in decimal, so b = 0.909. Your estimate is 55%, so p = 0.55 and q = 0.45. Then f* = (0.909 × 0.55 − 0.45) ÷ 0.909 = 0.05 ÷ 0.909 = 5.5% of bankroll. On a $1,000 bankroll that is $55.00 at full Kelly, $27.50 at half Kelly and $13.75 at quarter Kelly. The edge is 0.55 × 1.909 − 1 = 5.0% per $1 staked. At an estimate of 50% the edge is -4.5% and the stake is $0.

Questions

What is the Kelly criterion?

The Kelly criterion is a formula for the share of a bankroll to stake on one bet, given the odds and your own estimate of the probability. It returns f* = (b × p − q) ÷ b. It depends entirely on the estimate: the formula cannot tell you whether the estimate is right.

Why do people use half or quarter Kelly?

Full Kelly assumes the probability is exact, and any error in it is magnified in the stake. Half or quarter Kelly stakes a fixed share of the full figure, which cuts the stake and the swings in the bankroll. It is a sizing choice, and the page prints all three so you can compare the dollar amounts.

What does a negative edge mean in a Kelly calculation?

A negative edge means the price pays less than your own estimate says the bet is worth: the probability you entered is below the break-even probability of the odds. The formula then gives a negative number, and this page shows a stake of $0 and says there is no bet at this price by your estimate.

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