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Kelly criterion calculator
Last reviewed August 2026
The calculator
Full Kelly would stake 51.34. It maximises long-run growth in theory and is far too aggressive in practice, because it assumes your probability is exactly right — and yours is an estimate off a bookmaker's line. At 0.25× Kelly you give up about 56% of the theoretical growth rate and cut the volatility to roughly 0.25× — a trade worth making precisely because the growth figure assumes an estimate you do not actually have.
The formula
Kelly asks a specific question: what fraction of your bankroll maximises its long-run growth rate? For a simple win-or-lose bet at decimal odds it has a closed form.
f = (p × offered − 1) / (offered − 1) = edge / b
// worked: fair 2.1561 (p = 46.3796%), offered 2.30, bankroll 1000
edge = 0.463796 × 2.30 − 1 = 0.066730
f = 0.066730 / 1.30 = 5.13% → stake 51.33 at full Kelly
Two properties fall out of it that are worth internalising. The stake scales with the edge, not with confidence or with how much you like the bet. And it stakes nothing at all when the edge is zero or negative — there is no Kelly stake for a bad price, only for a good one.
Why fractional Kelly
Full Kelly is optimal given a correct probability. That condition never holds. Your p comes from de-vigging a bookmaker's line, which is an estimate with its own error — and Kelly is asymmetric about that error: overestimating your edge makes you overbet, and overbetting compounds against you far faster than underbetting costs you.
It is worth being precise about the trade, because it is routinely oversold. Staking a fraction k of full Kelly keeps k(2 − k) of the maximum growth rate — so quarter Kelly keeps about 44%of it, not "most". What it buys is a quartering of volatility, and, much more importantly, survivability when your estimate is wrong.
That second part is the whole argument. The growth rate full Kelly maximises is the growth rate given a correct probability. If yours is optimistic by even a little, full Kelly is not maximising anything — it is overbetting, and the true growth rate can go negative while the formula still reports a confident stake. Fractional Kelly gives up a knowable amount of theoretical upside to avoid an unknowable amount of real downside.
| Fraction | Stake | Growth kept | Character |
|---|---|---|---|
| Full Kelly | 51.33 | 100% | Theoretically optimal, practically reckless. Assumes p is exact. |
| Half Kelly | 25.67 | 75% | Aggressive but defensible if your estimates are well calibrated. |
| Quarter Kelly | 12.83 | 44% | The common choice. Half the growth for a quarter of the volatility. |
| Tenth Kelly | 5.13 | 19% | Very conservative — close to flat staking with an edge tilt. |
Where it breaks
- Correlated bets. Kelly assumes one bet at a time. Two bets on the same match are one position — backing the home win and under 2.5 goals are not independent, and staking each at its own Kelly fraction is a much larger bet than either number suggests.
- A moving bankroll. The fraction is of your current bankroll. Recalculating after every result is what makes Kelly self-correcting; sizing off a peak figure from a month ago is not Kelly.
- Longshots. At long odds the formula returns a tiny fraction, which is correct — but a small error in
pis proportionally enormous there, so those stakes are the least trustworthy the formula produces. - Bookmaker limits. A stake Kelly asks for and a stake the book will accept are different numbers, and the gap widens exactly as your account becomes profitable.
Kelly cannot rescue a negative edge
If the probability estimate is wrong in the wrong direction, staking is a loss whatever the sizing rule. Kelly is a tool for deciding how much, never for deciding whether — that question belongs to the expected value calculator.
Frequently asked questions
What is the Kelly criterion formula for betting?
For decimal odds, the fraction of bankroll to stake is (p × odds − 1) / (odds − 1), where p is the true probability. The numerator is the edge, so the formula is simply edge divided by (odds − 1). If the edge is zero or negative the formula returns zero — Kelly never stakes on a bet without an edge.
Should I use full Kelly?
Almost certainly not. Full Kelly maximises long-run growth only if your probability estimate is exactly right, and yours is an estimate derived from a bookmaker's line. Being slightly too optimistic makes full Kelly overbet badly, and the resulting drawdowns are severe. Most disciplined bettors use a quarter or a half.
How much growth does quarter Kelly give up?
More than most write-ups admit. Staking a fraction k of full Kelly keeps k(2 − k) of the maximum growth rate, so quarter Kelly keeps about 44% of it and gives up roughly 56%. What you buy is a quartering of volatility and — the real reason — protection against your probability estimate being wrong, which full Kelly assumes it is not.
What if I have several bets at once?
The simple formula assumes one bet resolved before the next. Simultaneous bets on independent events should be sized down relative to their individual Kelly fractions; simultaneous bets on the same match are correlated and must not be summed at all — backing both over 2.5 and the home team is one position, not two.
Is flat staking better than Kelly?
Flat staking is more robust to a wrong probability estimate and much easier to execute, which is why many bettors use it. Kelly is better if your estimates are well calibrated. In practice fractional Kelly is a middle path: it scales with edge, but not so aggressively that a mis-estimated edge is ruinous.
For research, not betting advice. Positive expected value is an edge across many bets, never a prediction about one. Bet only what you can afford to lose. 18+.