Kelly criterion calculator

What the Kelly criterion is

The Kelly criterion was published by John L. Kelly Jr. in 1956. It gives the fraction of your capital to commit to a bet with a positive edge, in order to maximise the long-run growth rate of your wealth. For a bet with two outcomes the formula is f = p − q ÷ b.

At decimal odds, this calculator uses b = odds − 1. If the formula returns zero or a negative number, there is no positive edge to size at that price, and it returns nothing to stake.

A worked example

Take evens (2.0, so b = 1) and an estimated 55% chance of winning. Then f = 0.55 − 0.45 ÷ 1 = 10% of the bankroll at full Kelly. At half Kelly the result is 5%. On a £200 bankroll, that is £10.00. The calculator opens on these numbers.

Why the estimate matters

The biggest weakness of the Kelly criterion is that it depends entirely on knowing the true win probability, and in betting that is only an estimate. Overstating your edge leads the formula to return dangerously large sizes.

Full Kelly is notoriously aggressive and very sensitive to errors in your inputs. Many people use a fraction of it, such as half Kelly, to reduce volatility. If full Kelly gives 10% of the bankroll, half Kelly gives 5%.

A win percentage taken from your own record on bets at similar odds is one way to estimate the probability, rather than guessing it.

How this calculator works

• Odds can be typed as decimals (3.5), fractions (5/2) or evens.
• The win probability is a percentage above 0 and below 100.
• The bankroll is optional. Leave it blank to see only the fraction.
• Percentages and amounts are rounded to two decimal places.

Questions

What is the Kelly criterion?

The Kelly criterion, published by John L. Kelly Jr. in 1956, gives the fraction of your capital to commit to a bet with a positive edge, in order to maximise the long-run growth rate of your wealth.

What is the Kelly formula?

For a bet with two outcomes it is f = p − q ÷ b. Here p is the probability of winning, q is the probability of losing (1 − p), and b is the payoff ratio, the size of a win relative to a loss. At decimal odds, this calculator uses b = odds − 1.

What does a zero or negative result mean?

It means there is no positive edge to size at that price, so the formula returns nothing to stake.

What are half Kelly and quarter Kelly?

Full Kelly is notoriously aggressive and very sensitive to errors in your inputs, so many people use a fraction of it, such as half Kelly, to reduce volatility. A multiplier scales the result: if full Kelly gives 10% of the bankroll, half Kelly gives 5%.

Where does my win probability come from?

It is your own estimate, and the Kelly result depends on it entirely. Overstating your edge makes the formula return dangerously large sizes. A win percentage taken from your own record on bets at similar odds is one way to estimate it.

Is this calculator advice?

No. It evaluates the formula from the numbers you enter. It is a calculation, not advice on how much to risk, and any decision about a stake is yours.