Kelly Stake

The stake that maximizes long-run growth from your odds and win chance, and what half Kelly gives up.

This sizes one bet against one edge you supply. It does not tell you whether that edge is real, and the sensitivity view below the stake is there because the edge is usually an estimate rather than a fact.

Recommended stake

$50.005.00% of bankroll · half-Kelly

Bankroll$1,000Full Kelly f*10.00%Kelly fraction0.5×Stake$50.00

Growth per bet, by share of bankroll staked

f*, full Kelly: the top of the hillyour stake, lit on the bankroll strip

Your bet

BankrollOdds

Your win probability %

The odds field reads an American price (+150). Switch the format above to enter prices the way your book quotes them, or open the odds converter to see one price in all of them.

Behind the stake

The edge

Implied prob50.0%

Your win probability55.0%

Edge / unit

+10.00%

Break-even odds

1.82

The growth

Growth / bet, full Kelly+0.501%

Growth / bet, your stake+0.375%

vs full-Kelly growth

75%

Full Kelly f*

10.00%

Show how this was computed

The formula this page uses, with your own numbers plugged in at each step. This shows how the stake above was arrived at, not whether it is the right amount to risk.

1. Net odds b
b = decimal odds − 1
b = 2.00 − 1 = 1.0000
2. Win probability p
p = your win % / 100
p = 55 / 100 = 0.5500
3. Loss probability q
q = 1 − p
q = 1 − 0.5500 = 0.4500
4. q / b
q / b
q / b = 0.4500 / 1.0000 = 0.4500
5. Full Kelly fraction f*
f* = p − (q / b)
f* = 0.5500 − 0.4500 = 0.1000
6. Stake fraction at half-Kelly
f = max(0, f*) × multiple
f = max(0, 0.1000) × 0.5 = 0.0500
7. Dollar stake
stake = bankroll × f
stake = 1000 × 0.0500 = $50.00

If your number is wrong

The stake above is sized from one number you typed in, and that number is almost always an estimate. This holds the stake still and sweeps the true win probability across a range instead, so you can see how much of the recommendation survives your estimate being wrong.

Best stake for that edgeYour full-Kelly stakeYour half-Kelly stake

The vertical line and the dot mark the number you entered, and the horizontal line is zero growth: a stake below it shrinks the bankroll rather than building it. Swept: 52.5% to 57.5% win probability. That is a range you picked, not a confidence interval. It says how far off your edge would have to be, not how likely that is. If your estimate came from a countable number of bets, switch to a sample above and get a real interval instead.

What a stake sized on your number earns across the swept range, for full Kelly and half Kelly
Sized on your number	Full Kelly	Half Kelly
Stake	$100	$50
Growth per bet	+0.501%	+0.375%
Share kept, low end	does not grow	100%
Share kept, high end	89%	55%
Stops growing below	52.5%	51.3%

Share kept is what that stake earns at the end of the range, as a fraction of what the best stake for that true win probability would have earned. A hundred percent means the stake you placed turned out to be the right one anyway. Where it says the stake does not grow, it would shrink the bankroll at that end of the range instead, and there is no share of anything left to report.

Read the two share rows together. Being wrong on the low side costs full Kelly far more than being wrong by the same proportion on the high side gives back, because an overestimated edge does not just shrink the reward, it leaves the stake too big for the edge that is actually there. Half Kelly keeps much more of what was available when the estimate was too generous, and gives up some growth when it was too cautious. That trade is the whole argument for betting a fraction, and this is it as numbers rather than as advice.

None of this makes the edge itself more likely to be real. If your number came from a few hundred bets or from a feel for the market, the honest reading is that the stake at the top of this page deserves less confidence than its decimals suggest.

The bankroll race

Same 180 bets · full vs half vs quarter Kelly

Full 2.02× low 0.19×

Half 1.78× low 0.50×

Quarter 1.41× low 0.73×

bar: low to finish · mark: 1.00×, the start

This is one simulated run of 180 bets rather than an average of many. Each line ends at the multiple shown, and “low” is the deepest its bankroll fell at any point along the way. All three plans face the same wins and losses, so they differ by stake alone.

Full Kelly grows fastest in theory but swings hard and can crater on a bad run, so its low sits well under the others on the same sequence. Half and quarter give up a little growth for far calmer rides, which is why most people bet a fraction. Run the race again for a different sequence.

At these settings, full Kelly finishes behind quarter Kelly on about 29% of runs, swept over the first 400 seeds.

Written and reviewed by Alexander Korsager · last reviewed October 7, 2026 · corrections

The idea

The Kelly criterion gives the stake that maximizes the long-term growth rate of a bankroll. It scales with your edge and shrinks as the odds get shorter: f* = (b·p − q) / b, where b is the odds minus one, p your win probability and q is 1 − p.

Full Kelly is aggressive and assumes your probability estimate is exact.Because it rarely is, most people bet a half or a quarter of the Kelly fraction, giving up a little growth for a large reduction in swings.

FAQ

Questions players ask

What is the Kelly criterion?

A formula for bet sizing that maximizes the expected logarithm of wealth. In practice it produces the fastest sustainable bankroll growth without risking ruin.

Why use half-Kelly?

Full Kelly is very sensitive to overestimating your edge, which causes painful drawdowns. Half-Kelly keeps about three-quarters of the growth with far smaller swings.

What if the calculator returns zero?

It means the inputs imply no edge (or a negative one) at that price. Kelly says the correct stake is nothing, don't bet.

What happens if I bet more than full Kelly?

Growth gets slower, not faster. Full Kelly is the fraction this model calculates as fastest for long-run growth, so any multiple above it is mathematically certain to grow a bankroll slower than full Kelly itself, with bigger swings along the way. Past a certain point it stops being slower growth and becomes certain eventual ruin. The page has a disclosure below the Kelly fraction row to show this on your own numbers.

Methodology

How this is calculated

Three parts, and only the first two come from the formula. The stake is the Kelly criterion for a simple win-or-lose bet: f* = (b·p − q) / b, where b is the decimal odds minus one, p the win probability and q is 1 − p. On the By win % tab, p is the figure you typed.

On the By edge % tab you never type a probability at all: the edge you enter is the expected profit per unit staked, and the tool backs a probability out of it against your price, as p = (1 + edge) / decimal odds.

The two tabs are one input written two ways, which is why a 10% edge at 2.00 and a 55% win probability at 2.00 return the same stake.

The sensitivity view below the stake holds that stake still and re-evaluates the expected log-growth g(f) = p·ln(1 + f·b) + (1 − p)·ln(1 − f) across a range of true win probabilities, comparing it against the growth the best stake for each of those probabilities would have reached.

The bankroll race at the foot of the page is the part that is simulated rather than derived: one sequence of 180 bets drawn at your win probability, replayed against full, half and quarter Kelly so the three lines differ by stake size and by nothing else.

It runs from a fixed seed, so the page opens on the same race for every reader, and Run the race draws a fresh sequence from a new one.

The reversal rate quoted beneath the race is swept across the first 400 seeds at whatever inputs are on the page, recomputed on every input change; the two figures quoted below about the opening race specifically are swept across 2,000, since that count only has to be computed once.

Common misreadings5

A high share kept at the top of the range is not reassurance. The bottom of the range is where the money is at risk, and it is the row worth reading first.
The sensitivity view says what happens if your number is wrong. It does not say your number is right, and no width of range makes an edge real.
Kelly maximizes long-run growth, not comfort. Even the fraction the tool recommends implies drawdowns most people will not sit through, which is what the bankroll race further down the page is for.
A positive edge is not a reason to bet more than you can afford to lose. Growth here is a long-run average over many bets, and any individual bet can lose all of its stake.
The low figure in the race is not a worst case. It is the deepest point of one simulated run, and another run goes deeper often enough to matter: the 0.19× the page opens on at full Kelly is already a harder sequence than most, and 165 of the first 2,000 seeds are harder still, roughly one in 12.

Assumptions6

One bet, two outcomes, at fixed decimal odds. Your whole stake is either lost or returned with the profit, with no partial settlement, no push and no correlated second leg.
The bankroll is re-sized before every bet, which is what makes the answer a fraction rather than an amount, and what the growth figure compounds.
Growth per bet is the expected logarithm of the bankroll multiple, shown as a percent. Kelly maximizes that quantity, which is why the stake it picks is the one at the peak of the curve.
Where the range comes from a sample, it is the 95% Wilson score interval on a win probability estimated from that many independent bets, and the figure you enter is treated as the sample your probability was estimated from.
Where the range is a what-if instead, it scales the edge per unit staked by the multiplier you chose and converts back to a win probability. It is a range you selected, and carries no claim about how likely any point in it is.
The opening race is the same one every time, and at the shipped defaults of 55% at 2.00 it is this one: full, half and quarter Kelly finish at 2.02×, 1.78× and 1.41×, having fallen to 0.19×, 0.50× and 0.73× on the way. Those figures are pinned in race.test.ts, so the page and the race it describes cannot come apart.

Limits8

The Wilson interval assumes your bets were independent draws at one underlying probability. A win rate measured across changing prices, changing opposition or a run of correlated events is not that, and the interval will read narrower than the uncertainty you actually face.
A what-if range is an arbitrary width. Nothing in it says your edge is more likely to sit inside than outside.
Kelly assumes you can stake any fraction and that the odds are available at the size you want. Minimum and maximum stakes, and a price that moves when you bet into it, are outside this model.
Share kept compares against the best stake for that true probability, which is a benchmark nobody can bet, since knowing it would mean the estimate was never uncertain.
The race is one sequence, not a distribution, and 180 bets is short. Across the first 2,000 seeds at the page defaults, full Kelly finishes behind quarter Kelly on 578 of them, close to 29 in 100, so the order the opening view happens to show is a common result rather than the expected one. Run the race a few times before reading anything into where the lines end.
Low in the race is measured against the bankroll you started with, so it never reads above 1.00× and it understates a fall that started from a peak. A plan that doubled and then halved shows no fall at all.
The race caps what it actually stakes at 98% of the bankroll, whatever f* comes to. That only matters at the far edge of the inputs this page accepts: the win-probability field tops out at 99%, and at that figure with a long enough price, f* prints above 98% (99% at 3.00, for instance, is f* = 98.5%). The Full line in the race then risks less than the f* shown above it, capped rather than left to stake nearly the whole bankroll on one bet. Everywhere else in the range this page's inputs reach, the two agree exactly.
A full Kelly fraction at or below 0.05% of the bankroll is reported as no edge rather than as a stake, and the sensitivity view is withheld with it. That is a display floor rather than a maths result: an estimate that fine cannot be told apart from zero, and the stake it implies rounds away at any bankroll likely to be entered here.

Evidence

The Kelly fraction and the log-growth function are the standard results, covered in math.test.ts alongside the sensitivity maths: that the break-even probability returned for a stake really does give it zero growth, that the best-available growth is never beaten by any other stake, that the Wilson interval matches the published figure for 50 wins in 100 and always contains the estimate it was built from, and that a stake sized on an edge overestimated by half keeps far less of what was available than the same stake keeps when the edge was underestimated by half.

The race is covered separately in race.test.ts, which is where every figure quoted about it above is derived rather than written down: the six finishing and lowest multiples of the opening race, that one drawn sequence of wins and losses is what all three plans face, that a smaller stake never falls further than a larger one on the same sequence (checked on 2,000 of them, without exception), the 578 sequences in 2,000 on which full Kelly finishes behind quarter Kelly, and the 165 that fall deeper than the opening race does, plus the 98% stake cap itself: that 99% at 3.00 gives an f* above it and that the race clamps its Full line there rather than staking the uncapped figure.

The caption under the race on the page itself sweeps the same reversal question at the reader's current inputs, over a much smaller run of seeds (RACE_SWEEP_N in race.ts), pinned at two settings in race.test.ts rather than one. A passing test means the code matches the model, not that the model fits every real market.

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