The Kelly criterion is a formula for sizing a bet when you think the odds are bigger than they should be. It says how much of your betting bankroll to stake, based on the odds and your estimate of the chance.
It sounds precise. However, it depends entirely on that estimate. This guide shows the maths, a worked example, and why most people who use it scale it down or stick with flat stakes.
Read the transcript
How much should you stake on a value bet? Here are the main approaches.
Flat staking means the same small amount every bet, like one or two per cent of your betting budget. It's simple and steady.
Kelly staking sizes each bet by your edge. At odds of two point three with a forty-seven per cent chance, full Kelly says six point two per cent of your bankroll.
But Kelly assumes your forty-seven per cent is right. If you overestimate your edge, full Kelly swings hard, and stakes far too much.
That's why many people use a quarter of Kelly. Here, that's about one point six per cent.
Whatever you choose, only bet money you can afford to lose, and never chase losses. Please bet responsibly.
The short version
- The Kelly criterion stakes a share of your bankroll in line with your edge.
- Formula: (b × p − q) ÷ b, where b = decimal odds − 1, p is your chance and q = 1 − p.
- At odds of 2.30 with p = 0.47, full Kelly is about 6.2% of your bankroll.
- Most people use quarter or half Kelly, because your estimate of p is never exact.
- No staking plan can create an edge that isn’t there.
The Kelly criterion formula
The formula needs three inputs. First, b is your net odds, which is the decimal price minus 1. Next, p is your estimate of the chance the bet wins. Finally, q is the chance it doesn’t win, so q = 1 − p.
Kelly stake = (b × p − q) ÷ b
The top half of the sum, b × p − q, is your expected value per £1 staked. So if that number is zero or below, the formula says do not bet. If it is positive, the stake grows with your edge and shrinks as the odds get longer.
The idea comes from a 1956 paper by John Kelly at Bell Labs, and it aims to grow a bankroll as fast as possible over the long run. You can read the background on the Kelly criterion page on Wikipedia.
A Kelly criterion worked example
Worked example
You find odds of 2.30 (13/10). You believe the true chance is 47%, so p = 0.47.
- b = 2.30 − 1 = 1.30
- q = 1 − 0.47 = 0.53
- b × p = 1.30 × 0.47 = 0.611
- b × p − q = 0.611 − 0.53 = 0.081, which is an 8.1% edge
- Kelly = 0.081 ÷ 1.30 = 0.0623, or about 6.2% of your bankroll
With a £1,000 betting bankroll, full Kelly is about £62. Half Kelly is about £31, and quarter Kelly is about £16.
Also note that the bookmaker’s price of 2.30 implies a chance of about 43.5%. That is why the implied probability is the first thing to check. Your 47% has to be right for any of this to work.
Use the calculator below to try your own odds, chance and fraction.
Kelly stake calculator
Why most people use fractional Kelly
Full Kelly is wild. For example, stakes of 5% or more of a bankroll mean that a normal bad run can cut it in half. Also, even with a real edge, the swings can be hard to live with.
So most people use a fraction instead. Half Kelly stakes half the formula’s figure, and quarter Kelly stakes a quarter. As a result, the ups and downs shrink a lot. In theory, half Kelly keeps about three quarters of the long-run growth rate, while cutting the swings roughly in half.
In the example above, that means about 3.1% at half Kelly, or about 1.6% at quarter Kelly. As a result, those figures are far easier to sit through during a bad month.
The danger of overestimating your edge
The biggest risk with the Kelly criterion is not the formula. Instead, it is the p you feed into it. Most people overrate their own judgement, and so the formula punishes that.
Worked example
Same bet at 2.30. You think p = 0.47, but the true chance is 0.44.
- True edge: 0.44 × 2.30 − 1 = 0.012, so only 1.2%
- True Kelly: (1.30 × 0.44 − 0.56) ÷ 1.30 = about 0.9% of bankroll
- You staked 6.2%, which is almost 7 times too much
If the true chance were 0.43, the edge would be negative. Then the right stake would be nothing at all.
Kelly theory also shows that staking more than about twice the true Kelly figure tends to shrink a bankroll over time, even when the edge is real. Therefore, when you are not sure of p, it is safer to bet too little than too much. Fractional Kelly gives you that margin for error.
For this reason, a good check is to compare your prices with sharp ones. If you cannot beat the fair price on Betfair Exchange or the close, your p is probably too high. Our guide to closing line value explains how to test this.
Flat staking: the simple alternative
Many careful bettors skip the Kelly criterion and use flat stakes. That means the same stake on every bet, often 1% to 2% of a starting bankroll. For example, with £500 set aside, a flat stake of 1% is £5 a bet.
Flat staking has real benefits:
- It does not depend on a precise estimate of p.
- It keeps your records simple, so profit, ROI and yield are easy to read.
- It is hard to overbet by mistake.
- It makes bad runs easier to plan for.
On the other hand, flat stakes do not lean into your best edges. However, for most people that is a fair price for less risk. Our guide to bankroll management covers flat units in more detail.
Using the Kelly criterion responsibly
The Kelly criterion is a sizing tool, not a promise. It assumes you have an edge. Even with a real edge, results swing a lot, as our guide to betting variance shows.
Only ever use money you can afford to lose, kept apart from bills and savings. If you are unsure, flat stakes of 1% are a calm place to start, and stopping is always an option.
Related guides
18+ only. Betting should be fun, and every bet can lose. Set a budget you can afford to lose and stick to it. For free, confidential support, visit BeGambleAware.org or call the National Gambling Helpline on 0808 8020 133.