Kelly criterion: how much of your bankroll to stake
The Kelly criterion tells you what share of your bankroll to stake when a bet has positive expected value. The bigger the edge, the bigger the recommended stake, but the formula also knows exactly when not to bet at all. This guide explains the formula, two worked examples, and why in practice it pays to stake only a fraction of what Kelly recommends.
The idea
A stake shouldn't be a fixed number — it should grow with the edge and shrink when the edge is small or absent. The Kelly criterion is a formula that turns the odds and your probability estimate into the share of your bankroll to stake so that long-run bankroll growth is maximised while the risk of going broke stays minimal.
For comparison, if you always staked the same fixed amount regardless of the size of the edge, the bankroll would grow linearly but would swing just as hard even when there's barely any edge at all. Kelly's logic lets the bankroll compound instead — every stake is recalculated from the current bankroll, so it automatically grows after a win and shrinks after a loss.
The formula
The formula: f* = (b × p − q) / b, where p is your estimated probability of winning, q = 1 − p is the probability of losing, and b is the net odds, meaning the odds minus 1 (what you win per euro staked, not counting the stake itself). The result f* is the bankroll share recommended for the stake; if the formula returns a negative number, the recommended stake is zero — that bet isn't worth taking.
The same formula can also be written as f* = EV / (odds − 1), because the numerator b × p − q is really the same as EV divided by one unit of probability — both forms give the same answer.
A useful sanity check: if your probability estimate exactly matches the implied probability with the margin removed, EV is zero, and the f* formula also returns exactly zero — which is correct, since that bet has no edge at all. The Kelly formula never recommends a positive stake for a bet with zero or negative EV.
Worked example
Odds of 2.10, p = 50%, b = 1.10, q = 0.50: f* = (1.10 × 0.50 − 0.50) / 1.10 ≈ 0.045, or 4.5% of the bankroll. With a €1,000 bankroll that's ≈ €45 at full Kelly, or ≈ €15 (1.5% of the bankroll) at fractional, ⅓ Kelly.
The negative case: odds of 1.90, p still 50%: f* = (0.90 × 0.50 − 0.50) / 0.90 ≈ −0.056 — a negative number means the EV on this price is negative, so the recommended stake is €0, meaning simply don't bet.
Why fractional Kelly
Full Kelly assumes your probability estimate is exact, but in reality it's always only approximate, so full Kelly can swing a bankroll hard just from estimation error alone. On top of that, several dozen bets can be open at once in practice — kefas recommends 30–50 value bets a day, after all — and their risks partly overlap. Fractional Kelly, most often ⅓ Kelly, cuts the stake size but only slightly slows bankroll growth while cutting the swings a lot.
Practical bankroll rules
Recompute the stake from your current bankroll, not the starting one — as the bankroll grows the stake grows with it, and as it shrinks the stake shrinks too. Never stake on a bet when Kelly's EV is negative: the formula simply returns zero or a negative number in that case, and that means don't bet, not bet small.
Kelly with several bets open at once
The formula is really built for a single, isolated bet, but in practice you often have several different matches open at once. If those matches are unrelated to each other, each can be calculated separately. But if several bets depend on something in common — say, several markets on the same team in the same match — their risks partly overlap, and calculating each one separately at full Kelly can leave the bankroll more exposed than the formula actually intends.
The practical rule is to treat such related bets as one combined position and apply a more modest, fractional Kelly share to the group as a whole, rather than the full share to each one individually. That's another reason fractional Kelly is the safer choice in real life, when several dozen bets can be open at once, rather than taking the formula's number with no adjustment at all.