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Kelly fraction = (odds x probability - 1) / (odds - 1), using decimal odds. A negative result means no value: do not bet. Most serious bettors stake half or quarter Kelly because probability estimates are imperfect. Please gamble responsibly: GamCare offer free support on 0808 8020 133 or at gamcare.org.uk. 18+.
What The Kelly Criterion Calculator Works Out
- Full Kelly stake: the fraction of bankroll that maximises long-run growth, (odds x probability - 1) / (odds - 1) with decimal odds. A 40% chance at odds of 3.0 gives 10%, so GBP 100 of a GBP 1,000 bankroll. A zero or negative result means the price contains no value and the correct stake is nothing.
- Half and quarter Kelly: the full stake divided by two or four. Full Kelly trusts your probability estimate completely and endures drawdowns that halve the bankroll, so most practitioners run half or quarter Kelly, giving up a little theoretical growth for much smaller swings.
- Your edge: odds x probability - 1. A 40% chance at 3.0 is a 20% edge, since fair odds would be 2.5. Stakes recalculate as the bankroll moves, betting more after wins and less after losses, which is the built-in discipline that flat staking lacks.
- Fraction of full Kelly (advanced): pick any fraction rather than just half or quarter. 25% to 50% is the common professional range.
- Exchange commission (advanced): commission of 2% to 5% on winnings reduces the net odds, which shrinks both the edge and the Kelly stake. Enter 0 for a bookmaker.
- Maximum stake cap and minimum stake (advanced): a cap stops a large edge producing an uncomfortable stake; a bookmaker minimum (often GBP 0.10 to GBP 2) can force you above Kelly on a small bankroll, which the card flags.
- Expected profit on this bet (advanced): stake x edge, the average result over many identical bets rather than what happens on any single one.
- Expected bankroll growth per bet (advanced): the logarithmic growth rate, p x ln(1 + f x b) + (1 - p) x ln(1 - f), with a projection over the number of bets entered. Half Kelly gives about three quarters of the full growth rate with far less volatility.
- Chance of ever halving the bankroll (advanced): at full Kelly there is a 50% chance the bankroll will at some point fall to half; at half Kelly about 12.5%; at quarter Kelly under 1%. This assumes your probabilities are exactly right, and in practice edges are overestimated, so the real risk is higher. Simultaneous or correlated bets need adjusted versions of the formula.
- Please gamble responsibly: Kelly sizes an advantage you actually have, and for most bettors the honest edge is zero or worse. GamCare offer free confidential support on 0808 8020 133. 18+.
