Kelly Criterion Calculator

This tool finds the mathematically optimal stake for a bet, sized as a percentage of your bankroll, once you already know your edge and the American odds on a US moneyline, spread, or total.

What Is the Kelly Criterion?

The Kelly criterion answers the question expected value leaves open: once you know a bet is +EV, how much should you actually stake? It returns the fraction of your bankroll that maximizes long-run growth — big enough to press a real edge, small enough never to risk ruin. Bet more than Kelly says and your bankroll grows more slowly and swings more wildly; bet less and you leave growth on the table.

Because full Kelly is aggressive and unforgiving of estimate errors, most bettors use a fraction of it instead — half-Kelly or quarter-Kelly — to smooth the ride. The formula does not care how you arrived at your win probability; it only cares that the number you feed it is honest. Feed it an inflated probability and it will happily size a stake too large for the real edge you actually have.

This calculator does not tell you whether a bet is worth making — that is what an edge or expected-value calculation is for. It tells you how much of your bankroll to commit once you already believe you have an edge, returning the full-Kelly stake alongside the half- and quarter-Kelly alternatives.

How the Kelly Criterion Is Calculated

The formula is Kelly fraction = (b x p - q) / b, where b is the decimal odds minus 1 — your profit per $1 staked — p is your win probability, and q is 1 minus p, your probability of losing. Multiply the resulting fraction by your bankroll to get the full-Kelly stake in dollars.

To find b, start from the American odds and convert to decimal. American odds of +120 convert to decimal odds of 2.20, so b is 1.20 — for every $1 staked, a win returns $1.20 in profit on top of the stake back. Plug that b into the formula alongside your win probability p, and it weighs your edge against your decimal payout: a bigger b means the formula tolerates a lower win probability before the bet stops being worth staking on, and a higher p pushes the recommended fraction up.

Once you have the fraction, the dollar stake is just that fraction of your bankroll. A Kelly fraction of 12.0% against a $1,000 bankroll means a full-Kelly stake of $120.00. Half-Kelly and quarter-Kelly simply take half or a quarter of that fraction — and therefore half or a quarter of that dollar stake. The formula itself never adjusts for how confident you are in your probability estimate; that adjustment is what choosing a Kelly fraction below 1.00 is for.

What the Calculator Shows You

Once you enter your American odds, your estimated win probability, and your bankroll, the calculator returns a small set of numbers built to help you decide how much to risk. First is the Kelly percentage — the fraction of your bankroll the formula recommends staking. Next to it is the full-Kelly stake in dollars, which is that percentage applied to the bankroll you entered.

Below that, it shows half-Kelly and quarter-Kelly stakes side by side with the full-Kelly figure, so you can see how much the recommended risk shrinks as you move to a more conservative fraction. There is no separate “should I bet” verdict here — if the underlying fraction comes back at zero or negative, the stake shown is zero, because the bet is not profitable enough at that price and probability to justify risking any of your bankroll.

Worked Example

Take a bet at +120 you rate a 52% chance of winning, with a $1,000 bankroll. The selection is an underdog moneyline. Converting +120 to decimal odds gives 2.20, so b is 1.20 — your profit per $1 staked if the bet wins.

Plug those numbers into the Kelly formula and the fraction comes out to 12.0%. Against a $1,000 bankroll, that fraction is a full-Kelly stake of $120.00. That is the amount the formula says maximizes your bankroll’s long-run growth rate, given that you truly do have a 52% chance of winning at +120.

Most bettors will not stake the full $120.00, though, because full Kelly assumes your 52% estimate is exactly right, and real-world probability estimates rarely are. Trimming to half-Kelly cuts the stake to $60.00 — half the fraction, half the dollar risk — while still capturing most of the long-run growth the full stake would provide. Quarter-Kelly trims further still, down to a $30.00 stake, for bettors who want the edge working without the swings that come with staking more aggressively.

The gap between these three numbers is the whole point of the exercise. Full Kelly, half-Kelly, and quarter-Kelly all stem from the identical 12.0% figure the formula produces from the same +120 price and the same 52% probability; the only thing that changes is how much of that recommended fraction you are willing to put on the line. A bettor confident in their 52% number might lean toward the full $120.00. A bettor who suspects their estimate could be off leans toward the $60.00 or $30.00 alternative, accepting slower growth for a smoother bankroll curve.

Full-Kelly Stake at +120 on a $1,000 Bankroll by Your Win Probability

The Kelly percentage, and therefore the dollar stake, is driven by your win probability once the price is fixed. Holding the price at +120 and the bankroll at $1,000, small changes in your estimated win probability move the recommended stake substantially, which is why an honest probability matters more than the formula itself.

Full, Half and Quarter Kelly on the $120 Full Stake

Once the calculator produces a full-Kelly stake, the remaining decision is which fraction of it to risk. The table below takes the $120.00 full-Kelly stake from the worked example and shows what each standard fraction reduces it to in dollar terms.

Kelly’s Blind Spot: Bad Probability Estimates

Kelly is only as trustworthy as the probability you feed it, and it punishes over-confidence harshly: overestimate your edge and full Kelly over-bets, which drags long-run growth down and can dig a deep hole fast. The formula has no way of knowing whether the probability you enter reflects a genuine edge or wishful thinking — it treats whatever you type in as gospel and sizes the stake accordingly.

That sensitivity is exactly why fractional Kelly is the norm rather than the exception. Half-Kelly captures about three-quarters of the growth that full Kelly would produce, with far less than half the volatility — a trade most bettors find worth making once they have watched what a run of bad variance does to a full-Kelly bankroll. Quarter-Kelly trims volatility further still, at the cost of some growth, for bettors who would rather grind steadily than chase the theoretical maximum.

Two other rules matter just as much as the fraction you choose. First, if the formula returns zero or a negative number, the bet is not +EV at that price and probability, and Kelly’s answer is to stake nothing at all. Second, Kelly assumes you can re-bet a growing or shrinking bankroll many times over; it is built for repeated wagering, not a single wager you will never repeat. For a one-off bet or a fixed bankroll you cannot compound, the aggressive full-Kelly stake makes less sense than it would for a bettor placing this same kind of bet week after week. Treat the number the calculator returns as a ceiling on what you might stake, never a target you are obligated to hit.

When the Kelly Criterion Makes Sense

The Kelly criterion is built for bettors who already have a process for estimating win probabilities and who bet repeatedly over time, letting a bankroll compound across many wagers. If you can produce an honest, disciplined probability estimate for a bet — not just a hunch — and you plan to keep betting with the same bankroll going forward, Kelly gives you a principled way to decide how much of that bankroll a given edge deserves.

It makes less sense where either condition breaks down. If your probability estimates are shaky or you are new to handicapping a particular sport or bet type, feeding an uncertain number into the full Kelly formula can produce a stake far too large for the confidence you actually have — which is precisely why half- or quarter-Kelly exists as a safer default. If you are placing a single, one-off bet rather than a long series of similar ones, the long-run growth argument behind Kelly does not really apply, since Kelly’s advantage is a statistical one that shows up over many repeated bets, not a guarantee on any individual wager.

Bankroll size and risk tolerance matter too. A bettor with a large, stable bankroll and a genuine, well-tested edge is in the best position to use full Kelly or something close to it. A bettor working with a smaller or less certain bankroll, or one who simply cannot stomach the swings that come with an aggressive stake, is generally better served sticking to half- or quarter-Kelly regardless of how strong the edge looks on paper.

Common Mistakes

Feeding in an inflated win probability makes Kelly over-bet, since the formula cannot detect an estimate that is too optimistic. Using full Kelly when your edge is genuinely uncertain adds unnecessary risk instead of choosing a safer fraction built for that uncertainty. Staking anything when the formula returns a zero or negative fraction ignores Kelly’s own signal that the bet is not worth making. Forgetting to recompute the stake as the bankroll grows or shrinks means later bets are sized against a figure that is no longer accurate.

Full Kelly vs Fractional Kelly

Full Kelly maximizes theoretical growth but carries very high volatility, a hard combination when your probability estimates are less than perfect. Half-Kelly and quarter-Kelly trade some of that growth for a much smoother bankroll curve.