Quick answer
Kelly criterion: The Kelly criterion is a formula for the fraction of a bankroll to stake that maximises long-run growth, given your probability estimate and the odds; it comes from J. L. Kelly's 1956 paper.
Also called: Kelly stake, Kelly fraction
Explained, with an example
For decimal odds d, let b = d − 1, p = your probability and q = 1 − p; then f* = (b·p − q) / b [1]. Example: p = 0.55 at 2.00 → f* = (0.55 − 0.45) / 1 = 10%. If f* ≤ 0 there is no edge. Full Kelly is very sensitive to errors in p, so many people use a fraction (e.g. half Kelly). See Expected value.
Formula
f* = (b · p − q) / b
b = decimal odds − 1, p = your probability, q = 1 − p
f* ≤ 0 → no position; fractional Kelly = k × f*Try it: tools and tutorials
Frequently asked questions
What is the Kelly criterion?
The Kelly criterion is a formula for the fraction of a bankroll to stake that maximises long-run growth, given your probability estimate and the odds; it comes from J. L. Kelly's 1956 paper.
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Sources
- J. L. Kelly Jr., "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 1956 — Bell Labs (PDF copy hosted by Princeton), accessed 2 Nov 2026