Kelly criterion calculator
Enter your probability, the price, and your bankroll. This sizes one stake, handles several outcomes from the same market together, and shows what a smaller Kelly fraction gives up in exchange for a shallower drawdown.
Worked example — Full Kelly stake at 55% on an even-money bet: 10.0%. 55% probability, decimal 2.00 (even money), the textbook illustration
3-way market example: The joint-outcome showcase this calculator opens with.
| Outcome | Price | Implied | Your probability | Edge | Kelly on its own | Kelly solved together | Stake at 0.50 Kelly |
|---|---|---|---|---|---|---|---|
| Outcome A | 2.10 | 47.6% | 50.0% | +2.4 pts | 4.55% | 10.61% | $530.49 |
| Outcome B | 3.40 | 29.4% | 31.0% | +1.6 pts | 2.25% | 6.67% | $333.54 |
| Outcome C | 4.00 | 25.0% | 19.0% | -6.0 pts | 0.00% | refused | no stake |
An outcome is admitted when its expected return, probability times price, beats the reserve implied by the outcomes already admitted, which here is 82.72%. That reserve is also the share of the bankroll left unstaked at full Kelly. Outcomes are tested in order of expected return, so a refused outcome is not merely a losing bet, it is one that would take money away from a better one.
Growth per bet is the exact expected log return of the stated allocation. The continuous approximation column is the textbook shape, growth scaling as lambda times (2 minus lambda), printed beside the exact number because it is the argument for half Kelly rather than the answer. A multiple above 1 can ask for more than the whole bankroll, and a stake you cannot place has no growth rate, so those rows say so instead of printing a number. In plain English: larger fractions grow faster only until the extra swings overwhelm the edge. The continuous-time drawdown expression is a2/λ − 1, the chance of the bankroll ever touching that level, not the chance at any one moment. It assumes you keep betting the same edge forever and never reduce size, so treat it as a floor on the discomfort rather than a forecast.
What is the Kelly criterion formula?
For one bet at decimal odds o with probability p, the growth-optimal fraction is (p(o-1) - (1-p)) / (o-1), the familiar (bp - q)/b. At 55% on an even-money bet (decimal 2.00), that is (0.55 times 1.00 minus 0.45) over 1.00, which comes out to 10.0% of the bankroll. It comes from maximising the expected logarithm of wealth, and log wealth is not a preference chosen for elegance: it is what compounding does to a sequence of multiplicative bets, so the fraction that maximises it is the fraction with the highest long-run growth rate with probability one. The assumption underneath is that p is correct. Everything difficult about using Kelly follows from the fact that it never is.
What does half Kelly give up?
On the default 3-outcome market on this page, full Kelly stakes 17.28% of the bankroll and grows it 0.465% a bet. Half Kelly keeps 73.8% of that growth rate while staking half as much and cutting the chance of ever halving the bankroll from 50.0% to 12.5%. The case for betting a fraction of the answer is not caution, it is arithmetic: growth falls off quadratically as you move away from the optimum, while risk falls off linearly, so the first half of the stake you give up costs almost nothing and removes a great deal. Under the continuous approximation, growth at fraction lambda is lambda times (2 minus lambda) of the maximum, which says half Kelly keeps 75% of the growth; the exact discrete number on this market is 73.8%, printed beside the approximation in the calculator's own frontier table because the approximation is the argument and the exact figure is the answer.
How much can I lose betting full Kelly?
A bettor with a real edge, sizing correctly at full Kelly, will at some point see the bankroll cut in half. Not as a tail risk: the probability of ever touching half is exactly 50%, and of ever touching a quarter is 25%. At half Kelly those fall to 12.5% and 1.6%. Most people do not abandon a strategy because the maths was wrong, they abandon it inside a drawdown that the maths said to expect, and no other Kelly calculator on this query prints the number. It comes from the continuous-time result: the chance of ever falling to fraction a of the bankroll is a raised to the power (2/lambda - 1).
Each outcome, sized on its own vs sized together
Sizing three outcomes of one market with the one-bet formula three times gets the wrong answer, because the formula assumes the rest of the bankroll is idle. Solving the outcomes together instead recognises that the outcomes are mutually exclusive: the losing branches overlap, so the pair carries far less risk than two independent bets of the same size, and it can stake more for more growth.
| Sizing method | Total staked | Growth per bet |
|---|---|---|
| Each outcome on its own | 6.80% | 0.283% |
| All outcomes solved together | 17.28% | 0.465% |
Solving jointly stakes 10.5% more of the bankroll for 64% more growth per bet on this market. The direction of the error depends on the correlation between the outcomes, which is exactly why the one-line formula cannot be reused for a market with more than one outcome: order the outcomes by expected return, probability times price, and admit them one at a time while that number beats the reserve implied by the outcomes already admitted. It is a closed form, not a search, and this page checks it against a projected gradient ascent on the same objective before shipping.
What this does not model, and what I would do
It does not model estimation error in your probabilities, which is the dominant risk and the reason the honest answer is smaller than the formula's. It assumes bets settle in sequence, that the bankroll is the whole bankroll, that stakes are unlimited and unrounded, and that there is no commission. Simultaneous bets across different events are not covered: enter one market at a time. My position is half Kelly or less, and I would go to a quarter on any edge derived from your own model rather than from a price difference you can see. You lose a quarter of the growth and remove three quarters of the drawdown, and the growth you gave up was calculated from a probability you guessed. If you want to test whether your edge is real before sizing it, measure it against the closing line first.
The next question after this one
Risk of ruin calculatorCalculatorKelly maximises growth and accepts deep drawdowns to get it. This puts a probability on the drawdown you would have to sit through.Open nextOther questions
All 130 calculatorsHow JMM sources and checks its numbersWhat stays free, and what early access would add
More calculators for the same question
The arbitrage calculator sizes the case where every outcome is covered for a certain profit, and the odds calculator carries a single price into an expected-value estimate before you size it here.