Kelly Criterion Calculator
Enter Your Bankroll, Odds and Win Probability - Get Your Stake Size
Use our Kelly criterion calculator for sports betting to work out a stake from your bankroll, the odds and your chance of winning. Choose Full, Half or Quarter Kelly, or enter your own multiplier. The result depends on the probability you enter.
One selection at one price.
Several outcomes of the same event, such as a 1X2 market — not an accumulator.
Enter the whole market as priced at a sharp book such as Pinnacle, not at the bookmaker you are betting with.
The additive method would have given this market a negative probability, which cannot be right. The multiplicative method was used instead, and the label above says so.
The — method has no answer for this market: its model cannot describe prices that add up to less than 100%. The multiplicative method was used instead, and the label above says so.
The implied probabilities add up to less than 100% — that is an arbitrage situation. Removing the vig here inflates the probabilities, which is mathematically correct but usually means one of the prices is wrong. Double-check your odds.
Margin above 20% — the fair probability taken from this market will be a rough estimate at best.
Enter every outcome in the market. The vig cannot be removed from a single price.
Enter the bookmaker odds above to compare the two prices.
Fair price — against — offered: an edge of —.
Fair price — against — offered: no edge (—).
One event, several outcomes, exactly one of which can win — 1X2, a race, an outright market. The calculator works out which outcomes are worth backing and how to split the bankroll between them. Enter your own chance for each outcome; together they should total 100%. It uses the bankroll above and the multiplier and stake limits below.
Derive the probabilities from a sharp market
Enter the same market as priced at a sharp book such as Pinnacle. Removing its margin gives each outcome's fair chance, which is what the table below wants — not the prices you are betting into.
Enter a price for every outcome in the market. The margin cannot be removed from a partial market.
The additive method would have given this market a negative probability, which cannot be right. The multiplicative method was used instead, and the label above says so.
The — method has no answer for this market: its model cannot describe prices that add up to less than 100%. The multiplicative method was used instead, and the label above says so.
These prices add up to less than 100% — an arbitrage. Removing the vig here inflates the probabilities, which is mathematically correct but usually means one of the prices is wrong. Double-check them.
Margin above 20% — the probabilities taken from this market will be a rough estimate at best. A sharp book's market is rarely this wide.
Probabilities filled from the market above. They are ordinary entries now: edit any of them freely.
Outcomes not listed above have no edge at these prices, so Kelly leaves them alone.
These probabilities add up to —. Exactly one outcome can win, so they cannot total more than 100% and there is no valid split to calculate.
Your probabilities add up to —. That is fine if you have deliberately left outcomes out of the market, but if you meant to enter them all, they should total 100%.
This allocation loses money over time. Every leg still has positive expected value, but staking this much of the bankroll on them means the losses compound against a smaller base than the wins build on, so the expected growth rate is negative. Lower the multiplier until the growth figure above turns positive again.
The whole bankroll is committed. The multiplier asked for more than you have, so the stakes were scaled back to fit. That scaling is uniform, which means the multiplier has stopped doing anything at all: raising it further leaves these stakes exactly where they are.
One result takes everything. The bankroll is fully staked and not every outcome is covered, so if one of the outcomes you are not backing wins, nothing comes back. Expected profit above is still positive and that is not a contradiction: an average is finite while the growth rate is not, and it is the growth rate that decides where a bankroll ends up when the bet is repeated. Repeated, this position goes to zero.
These prices are an arbitrage: the selected outcomes can be covered for less than they are guaranteed to return. At a multiplier of 1 that means committing the whole bankroll and holding nothing back; at a lower multiplier you stake that share of it. Check the odds before acting on this.
This puts the whole bankroll on the table. Nothing is held back for the next opportunity, and a single voided leg or a mistyped price leaves nothing to recover with. Bookmakers also notice: stakes like these are the ones that get cut or have accounts limited. Lower the Kelly multiplier if you want the same shape at a size you can repeat.
Limited by the bookmaker's maximum. Kelly asks for — across these outcomes but only — can be placed. The percentages above are the share of the bankroll you are really putting up.
Re-worked around the bookmaker's maximum. Kelly asks for — across these outcomes and your maximum will not take it. Cutting every stake to the limit is not the answer: the outcomes held at the limit no longer offset the others, so the right stake on the rest is smaller — and on some of them it is nothing. The stakes above are the best allocation your limit allows, — in total.
Some stakes fall below the bookmaker's minimum of —. Those bets cannot be placed at all, so they are shown as zero rather than as a recommendation. Raising them to the minimum would be overbetting.
The stakes above are unchanged, deliberately. Unlike a single bet, a market cannot simply be made pessimistic: the probability you take off the outcomes you are backing has to land somewhere, and once it lands on an outcome you are not backing it creates value there. Re-solving that market would hand you a larger bet for a wider error, which is not a conservative answer. So the allocation is held exactly as recommended and re-valued against the pessimistic case instead. Expected profit under it is —.
An error that size would sink this position. If every outcome you are backing is — less likely than you think, the allocation above loses money over time rather than growing. It absorbs — of error before that happens.
Every outcome in this market is being backed and the probabilities total 100%, so there is nowhere for a pessimistic shift to go. That is the arbitrage case, where the payoff does not depend on your probability estimates at all.
The stakes are unchanged, and that is correct. An abandoned event returns every stake, so that branch neither grows nor shrinks the bankroll and it drops out of the optimisation entirely. A chance of postponement is not a reason to stake less. What it does change is what the position is worth: the expected profit and growth above are both scaled by the chance the event is actually played.
Your probabilities total —, which is almost exactly the chance of the event being played. That suggests the abandonment is already priced into them. This field expects the opposite: enter each outcome's chance of winning given that the event happens, so that they total 100%. Until they do, the edge in this market will be understated.
The stakes were recalculated for a smaller set. An outcome you cannot back is no longer there to offset the others, so the right stake on the rest is lower than it would be if the whole market were covered. The figures above are for the outcomes actually being backed.
Nothing here can be backed at your stake limits. There is an edge in this market, but once the outcomes that fall short are removed the remaining stakes shrink below the limits as well. This is not a market with no value; it is a bankroll too small to take the value at these limits.
Some stakes round away to nothing at the rounding step you have chosen. Use a finer step or a larger bankroll to back those outcomes.
Enter odds and a probability for at least two outcomes.
No outcome in this market has an edge at these prices. Kelly says stake nothing.
Quarter Kelly is the default on purpose. Full Kelly is the fastest-growing stake, and every error in your probability estimate pushes you past it.
Kelly assumes your probability is exactly right, and it never is. On a single bet this prices the pessimistic end of your range and tells you whether the edge survives it. On a market it asks what your allocation would be worth if every outcome you are backing were that much less likely. Leave it at 0 to work from the point estimates alone.
Exchange commission, pushes and stake rounding
Fill in your bankroll, the odds and your probability estimate to see a recommended stake.
Some of the numbers above cannot be used. Fix the highlighted fields and the stake will reappear.
Your estimate of — is below the break-even probability of — for these odds, so there is no edge to bet into. Kelly's answer is to stake nothing. You would need to believe this outcome wins more than — of the time before a bet is justified.
Your estimate of — beats the break-even probability of —, so the bet has positive expected value at this price.
The multiplier is 0, so no stake is recommended. Raise it to see the Kelly fraction applied.
Kelly asks for —, but your rounding step of — takes that down to nothing. There is an edge here; the bet is just too small to place at this rounding. Use a finer step or a larger bankroll.
On these numbers losing is impossible: your win and push probabilities leave nothing for a loss. The formula responds by staking everything it is allowed to. That is arithmetic rather than a recommendation — check the estimate before acting on it.
At the pessimistic end of your own range the probability is —, which sits at or below the break-even point of —. The edge does not survive your own margin of error, so this bet rests entirely on your estimate being right rather than merely close. The conservative stake below is —.
Kelly backs — of these outcomes and holds the rest of the bankroll in reserve.
No outcome in this market is priced generously enough to back. Kelly's answer is to stake nothing.
Capped at the whole bankroll. The formula asks for — of your bankroll, which is more than you have. Staking everything on one bet means a single loss ends the series. A number this large almost always means the probability estimate is too high.
Nothing here can lose. Your win probability and your push probability together account for the whole event, so the formula sees no losing outcome and stakes accordingly. Real bets have a losing side; check the two probabilities.
100% certainty does not exist. At a probability of 100% the formula believes losing is impossible and stakes accordingly. Check the input.
You are overbetting. Above a stake of — of the bankroll the expected growth rate turns negative — betting this much loses money over time even though each individual bet has positive expected value. Lower the multiplier.
An edge of — is extraordinary. Edges above 20% are very rare in real markets and usually mean the odds were mistyped or the probability estimate is optimistic.
Below the bookmaker's minimum stake. Kelly asks for — but the minimum is —. Staking the minimum instead would be overbetting; the disciplined move is to pass on this one.
Limited by the bookmaker's maximum. Kelly asks for — but the maximum accepted is —. You will be staking — of your bankroll instead of the — the formula wanted, and every growth and drawdown figure below reflects that smaller bet.
Rounding has taken a bite. Kelly asks for — and your rounding step brings that down to —. The figures below describe the rounded bet.
Very short odds. At a price this close to 1.00 the Kelly fraction swings wildly on tiny changes in your probability estimate. Treat the number above as indicative.
Commission eats this price. After commission the net odds are almost nothing, so the stake calculation is unstable.
Full breakdown
Risk of drawdown
| Bankroll falls to | Chance it happens |
|---|---|
| 75% | — |
| 50% | — |
| 25% | — |
| 10% | — |
These are exact for this bet repeated forever at the same fractionthis market repeated forever with the same shares, on a bankroll you can always stake a fraction of. They say nothing about how long a drawdown lasts, and nothing about a bet you place onceone event on its own.
At a stake this small the chance of any of these falls rounds to nothing.
Nothing is being staked here, so the bankroll cannot fall at all.
Every outcome is covered for more than it costs, so there is no settlement that leaves the bankroll lower than it started. The risk in a position like this is not arithmetic — it is a void, a palpable-error rule or an account limit.
This stake has no positive growth rate, so in a long enough run the bankroll reaches every level below — not with some probability, but eventually. That is what overbetting means in practice.
Simulate a run of this betSimulate a run of this market
Repeats the same bet at the same price and multiplier, resizing the stake off the bankroll as it moves and applying your rounding step and stake limits each time, then does the whole run thousands of times over.
Repeats this whole market: every time, the allocation above is re-staked across the outcomes, one of them settles, and the bankroll moves by the net. Each leg is resized off the bankroll as it moves, through your rounding step and stake limits. The shares stay as they are on screen — re-solving the allocation on every one of millions of steps is not something a page can do, and legs that fall under your minimum are simply left off that event.
—
The simulation settings above cannot be read. Fix the highlighted fields and run it again.
There is no edge to simulate. With a stake of zero the bankroll never moves, so the run would be a flat line.
Fix the calculator inputs above before running a simulation.
At this bankroll the recommended stake is already below your minimum stake, or rounds to zero. There is no first bet to simulate.
Nothing in this market is worth backing at these prices, so there is no allocation to repeat.
Every stake in this market comes out at zero once your limits and rounding are applied. There is no first event to simulate.
—
Every event re-stakes —.
| Percentile | Final bankroll |
|---|---|
| 5th (bad run) | — |
| 25th | — |
| 50th (median) | — |
| 75th | — |
| 95th (good run) | — |
If your estimate is wrong
The same stakes, sized on your estimate, run against the pessimistic end of your range instead. This is the realistic failure: you staked as though you were right, and you were not.
| If the true probability is | Median finish | Chance of finishing up |
|---|---|---|
| your estimate | — | — |
| the pessimistic end | — | — |
Bankroll went bust in — of runs. It fell far enough that no legal bet could be placed: the stake dropped below your minimum, or rounded away to nothingno leg of the market could be backed any more: every stake dropped below your minimum, or rounded away to nothing.
Bankroll paths
5th–95th percentile band Median path Individual runs Starting bankroll
The vertical axis is logarithmic, because a bankroll compounds. The dashed line is where you started.
What the simulation assumes. It takes your probability estimate as exactly right and every betevent as independent of the last. The first of those is never true in practice, which is why real results come in worse than the chart suggests.
How to Use the Kelly Criterion Calculator
Keep Single bet selected for one selection. Then follow these steps:
- Enter your bankroll: the money you have set aside for betting.
- Enter the bookmaker odds: the price available for your selection.
- Enter your win probability: in Direct % mode, type 55 for a 55% chance. Typing 0.55 means 0.55%.
- Choose your Kelly multiplier: Quarter Kelly is the default. Half, Full and Custom are also available.
- Check the stake, its share of your bankroll and any warnings.
The Kelly calculator updates as you type. The odds field accepts decimal, American and fractional odds. For example, 2.00, +100 and 1/1 describe the same price. American odds need a sign, such as +150 or -110. An unsigned 150 means decimal odds of 150.00.
Update the Bankroll field as your balance changes.
How Kelly Calculates Your Stake
Kelly uses your odds and estimated win probability to calculate a share of your bankroll. It aims to maximise long-term growth as you resize bets with your changing balance. This principle comes from Kelly’s original paper.
For a bet with no commission or push (a result where your full stake is returned):
Full Kelly fraction = (p × d − 1) ÷ (d − 1)
Here, p is the win probability as a decimal and d is the decimal odds.
With a $1,000 bankroll, 2.00 odds and a 55% win probability:
(0.55 × 2.00 − 1) ÷ (2.00 − 1) = 0.10
Full Kelly is therefore 10% of the bankroll. Fractional Kelly reduces that amount:
| Setting | Multiplier | Share of bankroll | Stake |
|---|---|---|---|
| Full Kelly | 1.00 | 10% | $100 |
| Half Kelly | 0.50 | 5% | $50 |
| Quarter Kelly | 0.25 | 2.5% | $25 |
Quarter Kelly uses 25% of the Full Kelly stake. In this example, that means risking 2.5% of your bankroll.
Smaller fractions reduce the amount at risk, but also reduce expected growth when your estimate is correct. They can still lose money if you overestimate your chance of winning.
Custom accepts multipliers from 0 to 2, including entries such as 0.3, 1/3 or 30%. Values above 1 request more than Full Kelly and can produce negative long-term growth.
At 2.00 odds, with no commission or push, a win probability of 50% or less gives a zero stake. Changing the multiplier cannot create an edge.
Where Your Win Probability Comes From
The calculator offers three input modes:
- Direct %: enter your own estimated win chance. Base it on data or a model, and check how past estimates matched results.
- Fair odds: enter a price with the bookmaker margin already removed. With no push, fair decimal odds of 2.00 mean a 50% win chance.
- Remove vig: enter the prices for every outcome in a reference market to remove the bookmaker margin, also called vig. Then select your outcome. Keep the price you can bet at in the separate Bookmaker odds field.
If you do not have your own probability model, a complete reference market gives you a starting estimate through Remove vig. The result still depends on how accurately that market reflects the event.
The default multiplicative method reduces implied probabilities in proportion until they total 100%. Additive, Shin and Power use different assumptions, as explained in research on removing bookmaker margin. If a method cannot produce a valid result, the tool uses the multiplicative method and shows a notice.
Removing margin does not prove the true win probability or guarantee a profitable bet.
Understanding Your Results
Start with these five figures:
| Result | Meaning |
|---|---|
| Recommended stake | The calculated amount after the multiplier, maximum stake and rounding |
| Actually staking | The stake as a percentage of your bankroll |
| Break-even probability | The win chance needed for zero expected profit, allowing for commission and a push |
| Edge | Expected net profit per unit staked, shown as a percentage |
| Expected profit | Average net profit at this stake if your estimate is correct |
Our Quarter Kelly example gives a $25 stake, a 10% edge and $2.50 expected profit. A win earns $25 net profit; a loss costs $25. The $2.50 figure is the average across repeated bets with those chances.
The gap between a 55% estimate and a 50% break-even probability is 5 percentage points. The 10% edge measures expected profit on the stake.
The full breakdown also shows expected bankroll growth, which accounts for resizing stakes as your balance changes. Error this stake absorbs shows how far your win estimate can fall before that stake’s modelled growth reaches zero. It does not measure how accurate your estimate is. The overbetting threshold shows the stake fraction where modelled growth falls back to zero.
Read the notices too.
- No edge means the estimate does not support a positive single-bet stake.
- Below minimum means the amount is too small to place.
- Rounds to zero means rounding removes the whole stake.
A single-bet result below the minimum can still display a calculated amount. Increasing it to the minimum changes your chosen stake size. With a maximum stake set, an Overbet label can refer to the amount before the cap.
Kelly Betting on Multiple Outcomes
Choose Multiple outcomes for different results of one event, such as a football home win, draw or away win. The listed outcomes must not be able to win together. This mode does not calculate accumulators or bets on separate events.
Enter two to eight outcomes, each with odds and an estimated probability. A complete market should total 100%. A lower total leaves a chance that none of your listed selections wins. A total above 100% is invalid.
For a $1,000 bankroll and Quarter Kelly:
| Outcome | Odds | Estimated probability | Calculated stake |
|---|---|---|---|
| Home win | 2.10 | 50% | $25 |
| Draw | 3.50 | 30% | $15 |
| Away win | 4.00 | 20% | $0 |
The total stake is $40, leaving $960 unbet. With no commission:
- A home win returns $52.50, giving $12.50 net profit after both stakes.
- A draw also returns $52.50, giving $12.50 net profit.
- An away win loses both bets, for a $40 loss.
The calculator sizes these bets together because a win on one means the others lose. A zero stake can reflect the odds, your limits or the best split across the market.
Advanced Settings and Stake Limits
| Setting | How to use it |
|---|---|
| My estimates could be off by | Enter an error range in probability points. A value of 3 tests a 55% estimate from 52% to 58% |
| Exchange commission | Enter the charge on winning profit; leave at 0 when there is no separate charge |
| Push / void probability | For a single bet, enter the chance of a full stake return |
| Chance the event is abandoned | For multiple outcomes, enter the chance that all stakes are returned. Outcome probabilities describe the event if it is played |
| Round stake down to | Set the rounding unit, such as 0.01 or 1.00 |
| Bookmaker min stake | Set the smallest accepted stake. Smaller amounts get a warning or are left out in market mode |
| Bookmaker max stake | Set the largest accepted stake per selection |
The error range is your assumption, not a measured confidence interval. For a single bet, it shows a conservative stake using the lower probability; it does not replace the main stake. For multiple outcomes, it tests the existing allocation with less favourable probabilities.
For a single bet that can push, use Direct %. For example, with a 40% win chance, 20% push chance and 40% loss chance, enter 40 for wins and 20 for pushes. Win and push probabilities together cannot exceed 100%. The current Fair odds and Remove vig modes do not adjust for a push. Half-win and half-loss settlements on quarter Asian lines are not supported.
In multiple-outcome mode, the tool applies commission to each winning selection separately. Betfair charges commission on net profit for the whole market, after losses on other selections. The field therefore does not reproduce Betfair commission when you back several outcomes in one market.
Understanding Bankroll Risk and Simulations
Risk of Drawdown
The calculator’s Risk of drawdown table shows theoretical upper bounds for the chance of reaching a share of your starting bankroll. Falling to 75% means losing 25%; falling to 50% means losing half.
The bounds assume the same odds, probabilities and stake fraction are repeated indefinitely, without changing limits or rounding. The actual chance within that model can be lower than the displayed bound. These are not exact probabilities or guarantees about real betting. See the research on Kelly drawdown bounds.
Reading the Simulation
The simulation runs a fixed number of independent bets or events at the same odds and probabilities. Stakes change with the bankroll, and your limits and rounding apply each time. Multiple-outcome runs keep the original allocation fractions.
- Average and median finish: the average can rise because of a few large wins; the median is the middle result.
- 5th and 95th percentiles: lower and upper points in the results, not the worst and best possible finishes.
- Chance of finishing up: how often the final bankroll exceeds the starting amount.
- Chance of halving: a fall to half the starting bankroll during a run. The worst fall from a peak measures a drop from the highest balance reached, so it uses a different starting point.
- Going bust: the calculated stakes become too small to place. Money can still remain.
With an error range set, the extra simulation keeps the original stake fractions but uses less favourable probabilities. Use it to see how an overestimated win chance affects the bankroll. Review your estimates, balance and available odds before each new calculation.
