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Kelly criterion calculator
Work out the Kelly stake from your probability and the price, then scale it to half or quarter Kelly and see what the smaller stake costs and saves.
The short answer
The Kelly criterion stakes the fraction f = (bp − q) ÷ b of your bankroll, where b is the profit per £1 at the price (decimal odds minus 1), p is your probability of winning and q is 1 − p. A result of zero or less means no bet.
At 9/4 with a 32 per cent chance, full Kelly is 1.78 per cent of the bank. Most bettors stake a fraction of that: half Kelly here is 0.89 per cent, or £8.89 from £1,000.
Type your probability and the price you can get, choose a fraction, and the calculator gives the stake, the edge, and what the smaller fraction gives up and saves. Nothing is stored or sent.
Worked example
You rate a side at 32 per cent to win and the best price on offer is 9/4, which is 3.25 in decimal odds. The price implies 30.77 per cent, so you think it is too long.
- Profit per £1: b = 3.25 − 1 = 2.25. Losing chance: q = 1 − 0.32 = 0.68.
- Edge: 0.32 × 3.25 − 1 = 0.04, so +4.0p per £1 staked on average.
- Full Kelly: (2.25 × 0.32 − 0.68) ÷ 2.25 = 0.04 ÷ 2.25 = 0.0178, or 1.78 per cent of the bank.
- Half Kelly: 0.89 per cent, which is £8.89 on a £1,000 bankroll. Quarter Kelly: 0.44 per cent, £4.44.
| Fraction | Stake, share of bank | Stake on £1,000 | Growth kept (exact) | Chance the bank ever halves |
|---|---|---|---|---|
| Full Kelly | 1.78% | £17.78 | 100.0% | 50.00% |
| Half Kelly | 0.89% | £8.89 | 75.2% | 12.50% |
| Quarter Kelly | 0.44% | £4.44 | 44.0% | 0.78% |
Growth kept is the exact expected growth of the bankroll’s logarithm at that stake, as a share of the full Kelly figure. The halving column uses Ed Thorp’s approximation, x2/c − 1 with x = 0.5 and c the fraction, for a long run of bets at a genuine edge.
Why almost nobody stakes full Kelly
Full Kelly grows a bankroll fastest in the long run only if your probability is right. It rarely is exactly. Suppose the side’s real chance in the example is 30 per cent, not 32. At 9/4 that bet is worth −2.5p per £1, a loser, and the full Kelly stake of 1.78 per cent now shrinks the bankroll’s expected log growth by 0.000790 a bet. Half Kelly loses 0.000309, well under half as much. A two-point mistake in your estimate is easy to make, and the smaller stake is what protects you from it.
The table makes the trade plain. Halving the stake keeps about three quarters of the growth and cuts the chance of ever seeing the bank halved from one in two to one in eight. Quarter Kelly keeps a little under half the growth and makes a halving rare.
A quicker way to the same number
With decimal odds d, the formula rearranges to (p × d − 1) ÷ (d − 1): the edge divided by the profit per £1. A 4 per cent edge at 3.25 is 0.04 ÷ 2.25 = 1.78 per cent. The same edge at evens would be 0.04 ÷ 1 = 4 per cent, so for the same edge Kelly stakes less on longer prices, because they lose more often.
Where your probability should come from
Kelly is only as good as p. The honest sources are your own model, checked against results, or a sharp bookmaker’s price with the margin taken out using the margin remover. The value bet calculator tells you whether there is an edge at all; this page tells you how much to stake once there is. To see what a staking plan does over a whole season, try the season simulator, which runs fractional Kelly as well as level stakes.
Chapter 29 of The Stat Man, How Much to Stake: Kelly Is Responsible Gambling in Disguise, sets out the argument that a fraction of Kelly is the most responsible way to stake, and the chapter 29 worked solutions take its exercises step by step.
Questions
Frequently asked questions
What is the Kelly criterion formula?
Stake the fraction f = (bp − q) ÷ b of your bankroll, where b is the profit per £1 at the price (decimal odds minus 1), p is your probability of winning and q = 1 − p. With decimal odds d it is the same as (p × d − 1) ÷ (d − 1): your edge divided by the odds. If the answer is zero or negative, the formula says do not bet.
What Kelly fraction should I use?
Most people who use Kelly seriously stake between a quarter and a half of it. Half Kelly keeps about three quarters of the long-run growth of full Kelly for far less risk, and it leaves room for the fact that your probability is an estimate. If you are unsure how good your estimates are, start at a quarter.
Can I use Kelly for several bets at the same time?
The simple formula assumes one bet is settled before the next is placed. With several bets running at once, sizing each one at full Kelly overstakes the bankroll as a whole. Use a smaller fraction for each and keep an eye on the total you have at risk at any one time.
Does the calculator store anything?
No. It runs in your browser, sets no cookies and sends nothing anywhere. Your inputs are written into the page address after the # so you can bookmark a calculation; that part of an address never reaches a server.
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