Kelly criterion calculator
Work out the Kelly stake for a price and a probability, as a share of a bankroll, with full, half or quarter Kelly.
Read as decimal odds: 2.10
Kelly stake: 11.36, 1.1% of the bankroll.
Kelly gives a share of a bankroll in theory, and only when the probability is right. Never stake more than you can afford to lose.
How it works
The Kelly criterion is a formula from information theory. Given a price and a probability, it gives the share of a bankroll that grows the bankroll fastest over many repeats, if the probability is right.
Full Kelly is (probability × price − 1) / (price − 1) with decimal odds. With no edge it is 0, and the calculator never shows a negative stake.
Probabilities are estimates, and full Kelly on an estimate that is too high loses money fast, so many people use a fraction such as half or quarter Kelly. The result is a theory of sizing, not a reason to stake.
Worked example
A price of 2.10 (+110), a probability of 50% and a bankroll of 1,000.
- The edge is probability × price − 1 = 0.5 × 2.10 − 1 = 0.05.
- Full Kelly divides the edge by the profit per unit: 0.05 / (2.10 − 1) = 4.55% of the bankroll.
- Quarter Kelly takes a quarter of that: 1.14%, or 11.36 of 1,000.
- At 2.00 and 50% there is no edge, so Kelly says 0. It never gives a negative stake.