How it works
The Kelly criterion stakes the share of your bankroll that maximises its long-run growth: your edge divided by the net odds. With a 50% chance at odds of 2.20 the edge is 10%, and Kelly stakes 8.33% of the bankroll. When the edge is zero or negative, Kelly stakes nothing.
Most bettors stake a fraction of Kelly, often a half or a quarter. Full Kelly is only right if your probability is exactly right, and an overestimate makes it stake too much. Half Kelly gives up about a quarter of the growth for half the swings.
The formula
- Kelly share = (probability × decimal odds − 1) ÷ (decimal odds − 1)
- The same as (b × p − q) ÷ b, with b = decimal odds − 1 and q = 1 − p
- Stake = bankroll × Kelly share × your fraction of Kelly
A worked football example
You rate a home win at 50% and the best price is 2.20. The edge is 10%, so full Kelly stakes 8.33% of the bankroll: 83.33 of 1.000.00. Half Kelly stakes 41.67.
What it does not tell you
Kelly is only as good as the probability you give it. It assumes your chance is right, your bets are independent and you can stake any amount. Several bets at once need smaller stakes than Kelly on each alone, and it says nothing about how often you will lose.
Common questions
What does the Kelly criterion tell you?
What share of your bankroll to stake on a bet with an edge so the bankroll grows as fast as possible over many bets. It stakes more when the edge is bigger and nothing when there is no edge.
Why use fractional Kelly?
Because your probability is an estimate. If it is too high, full Kelly overstakes and the bankroll swings hard. Half Kelly keeps about three quarters of the growth with half the volatility, and forgives a wrong estimate far better.
What happens if Kelly gives a negative number?
The price is worse than your chance, so the bet has a negative expected value. Kelly says do not bet, and the calculator shows no stake.
Where do I get the probability from?
From a model or research of your own, not from the odds. The odds’ implied probability includes the bookmaker’s margin, so Kelly on it always says stake nothing. Your probability has to disagree with the price for Kelly to stake anything.
Is Kelly the same as betting in units?
No. Units stake the same fixed amount on every bet. Kelly sizes each bet by its edge and its odds, so stakes rise and fall with the bankroll and with how good each bet is.