Guide
The Kelly criterion
The Kelly criterion sizes a bet in proportion to its edge: f* = (bp − q) / b, where b is decimal odds minus one, p is your estimated win probability and q is 1 − p. It maximises the long-run growth rate of a bankroll — under the assumption that p is correct.
Published 2026-09-01 · Last reviewed 2026-09-01 · BetBuddy editorial
The textbook formula
Kelly returns the fraction of the current bankroll to stake. A negative result means no bet: the price is shorter than your estimate justifies.
b = odds − 1 · q = 1 − p · f* = (b × p − q) / b
Worked example
Odds 2.50, estimated probability 45%. Then b = 1.50, p = 0.45, q = 0.55.
f* = (1.50 × 0.45 − 0.55) ÷ 1.50 = (0.675 − 0.55) ÷ 1.50 = 0.0833, i.e. 8.33% of bankroll. On a €1,000 bankroll that is a €83.33 stake.
Now change the estimate to 42%: f* = (0.63 − 0.58) ÷ 1.50 = 0.0333, a €33.33 stake. A three-point change in the estimate cut the stake by 60% — Kelly is extremely sensitive to the accuracy of p.
An equivalent form worth knowing
Kelly can be rewritten as edge divided by the net odds, which makes the relationship to expected value explicit: the stake fraction is the expected value per unit staked divided by b.
f* = (p × odds − 1) / (odds − 1) = EV per €1 / b
Why nobody sensible bets full Kelly
Full Kelly maximises growth only if the probability is exactly right. In betting it never is: p is an estimate from a model or a market signal, and Kelly's stake sizes rise sharply as the estimate becomes optimistic.
The practical consequences of full Kelly are severe drawdowns — falls of 50% or more from a peak are routine — and heavy over-staking whenever the estimate is biased upward.
The standard remedy is fractional Kelly: stake a fixed fraction of f*, commonly a quarter or a half. Half-Kelly retains roughly three-quarters of the theoretical growth rate for materially less variance, and it degrades far more gracefully when p is wrong.
Practical caveats
Kelly assumes conditions that rarely hold exactly in football betting.
- It assumes a known probability. You have an estimate with error bars.
- It assumes bets are sequential and independent, not several correlated selections on one match day.
- It assumes the full bankroll is available for every bet and that stakes can be sized freely.
- It ignores bookmaker limits, minimum stakes and rounding.
Kelly here vs Kelly in production
This page explains the general mathematics. BetBuddy's Fractional Kelly strategy is a specific production implementation with its own fraction, caps, rounding and minimum executable stake, applied to the robot's own selections in strictly sequential order.
Read the strategy page for the exact implementation and its tracked record; the two are deliberately not the same document.