This Kelly calculator works out the stake the Kelly criterion puts on one bet. You type four things: your bankroll, the decimal price on offer, your own estimate of the chance (or your own fair price) and the fraction of full Kelly you want.
Kelly is arithmetic, not advice: it treats your estimate of the chance as exact, which it never is, so the stake is worth what the estimate is worth.
How to use the Kelly calculator
Four inputs, in order:
- Bankroll. The money set aside for betting, not your whole account. Every stake is a share of it, so keep it current.
- Odds on offer. The decimal price you can bet at. On an exchange commission comes off your net winnings, not your stake, so type 1 + (price - 1) x (1 - your commission rate).
- Chance it wins, or Fair odds on the other setting. A chance is read as a percentage whatever you type: 50 and 50% are the same, and 0.8 means 0.8%, a fair price of $125.00.
- Kelly fraction. How much of full Kelly to stake: 1, 1/2, 0.25 or 10%.
The tiles show the fair price your chance implies (or the reverse), the edge per $1 staked, the full Kelly share and your stake; the table lists full, half, quarter and tenth Kelly.
Stakes round to the nearest cent, shares to two decimal places. The calculator refuses a bankroll outside $0.01 to $10,000,000, prices outside $1.01 to $10,001, a chance outside about 0.01% to 99%, and a Kelly fraction of 0 or above 1.
The formula behind the stake
- edge = your chance x offered odds - 1
- Kelly share of bankroll = edge / (offered odds - 1)
- stake = bankroll x Kelly share x Kelly fraction
The edge is the expected value of $1 staked, and because the fair price is 1 / chance, it also equals offered odds / fair odds - 1.
On the chance you typed, that share maximises the expected logarithm of the bank. It is only as right as that chance, and on a wrong one it can shrink the bank over many bets. The Kelly criterion derives it.
A worked example on a $1,000 bankroll
Illustrative prices, not a real race. You can bet at $2.70 and rate the runner a 40% chance, a fair price of 1 / 0.40 = $2.50:
- edge = 0.40 x 2.70 - 1 = 0.08, which is 8.00%
- Kelly share = 0.08 / (2.70 - 1) = 0.047059, which is 4.71%
- full Kelly stake = $1,000 x 0.047059 = $47.06, about $47
- half Kelly stake = $47.06 / 2 = $23.53, about $24
Why a short price takes a bigger stake
The divisor is the price minus 1, so the same edge is a far bigger share of the bankroll at a short price than a long one. With illustrative prices on a $1,000 bankroll, each chance is 1 / fair odds and each edge offered odds / fair odds - 1:
| Offered | Fair | Your chance | Edge | Kelly share | Full Kelly stake |
|---|---|---|---|---|---|
| $1.40 | $1.35 | 74.07% | 3.70% | 9.26% | $92.59 |
| $2.70 | $2.50 | 40.00% | 8.00% | 4.71% | $47.06 |
| $4.00 | $3.60 | 27.78% | 11.11% | 3.70% | $37.04 |
| $21.00 | $18.00 | 5.56% | 16.67% | 0.83% | $8.33 |
The $1.40 row has the narrowest edge and the largest stake, 0.037037 / 0.40 = 9.26%, and the $21.00 shot the widest edge and the smallest, 0.166667 / 20 = 0.83%. The share is always below your chance of winning, whatever the edge.
What a Kelly fraction changes
The fraction scales the stake straight down: a quarter of the example's full Kelly is $11.76.
Staking a fraction, often a half or a quarter, is common, because an optimistic estimate inflates the stake far more than the chance: 42% instead of 40% is an edge of 0.42 x 2.70 - 1 = 13.40% and a share of 0.134 / 1.70 = 7.88%, about two thirds more than the 4.71%. Fractional Kelly carries that doubt.
The box refuses a fraction above 1: past full Kelly the expected growth falls away, and at about twice full Kelly it is close to zero.
Risk: Betting involves risk. A Kelly stake is sized off your own estimate of the chance, and the formula sizes a wrong one as confidently as a right one. A +EV bet can still lose, and often does, and there is no guarantee of profit at any stake size. See responsible gambling for limits and support.
When the calculator stakes nothing
Two cases, both of which read $0.00 (illustrative prices):
- No edge. At $2.50 on a 40% chance, edge = 0.40 x 2.50 - 1 = 0, so the share is 0.
- A price shorter than your fair price. At $2.40, edge = 0.40 x 2.40 - 1 = -0.04, which is -4.00%.
The second case has a negative Kelly share, which the calculator floors at zero: a negative share points at the other side of the bet, a lay at a different price. The edge tile still shows the negative number.
Half-typed or out-of-range entries put three dots in every tile and row, and the line under the boxes names the field to fix and its range.
Kelly mistakes that change the stake
Illustrative numbers on a $1,000 bankroll:
| Mistake | What it does to the answer | The fix |
|---|---|---|
| Typing 45% when the chance is really 40% | Edge = 0.45 x 2.70 - 1 = 21.50%, so full Kelly is $1,000 x 0.215 / 1.70 = $126.47, over two and a half times the $47.06 | Stake a fraction, or build the chance with the fair odds calculator |
| Typing 0.4 for a 40% chance | Read as 0.4%, a fair price of 1 / 0.004 = $250.00, so at $2.70 the edge is 0.004 x 2.70 - 1 = -98.92% and the stake nothing | Type 40 or 40% |
| Typing an exchange price before commission | At a 36% chance, $3.00 gives 0.08 / 2.00 = 4%, or $40.00; at an illustrative 5% rate the net $2.90 gives 0.044 / 1.90 = 2.32%, or $23.16 | Type the net price |
When several bets are open at once
The formula sizes one bet as if nothing else were open. Bets on different events come out a little smaller than their single shares when sized together, and the real risk in a batch is estimates that are wrong together, which a smaller fraction allows for.
Bets in one race come out larger, because a win by either covers part of the other's stake. With illustrative prices, two runners you rate at 30% each at $4.00 get (0.30 x 4.00 - 1) / 3.00 = 6.67% of the bank each sized alone, and 10.00% each sized together, from the multi-runner form the fractional Kelly guide works through. Exposure across open bets is a bankroll management question, and the wider plan is betting strategy.
Note: the sum assumes the bet gets on at the price and stake you typed. A bookmaker can cut the price, limit the stake, void the bet or close the account.