What is the Kelly criterion in betting?
The Kelly criterion is a formula that sizes a stake as a share of your bankroll when a price looks generous: (b × p − q) / b, where b is the odds minus 1, p your estimated chance and q = 1 − p. It relies on your probability being right, so many bettors stake a fraction of it.
Where does the Kelly criterion come from?
The formula was published by John L. Kelly Jr. in 1956. It aims to grow a bankroll as fast as possible over many repeated bets, assuming the true probabilities are known. In football (soccer in the US) betting, nobody knows the true probabilities. You only have an estimate, and that gap is the most important thing to understand about Kelly.
This guide explains the maths. It is not advice on how much you should stake.
How do you calculate a Kelly stake?
Use decimal odds. The formula has three inputs:
- b = decimal odds − 1 (the profit per £1 staked if the bet wins)
- p = your estimated probability that the bet wins
- q = 1 − p, the chance it loses
Kelly fraction = (b × p − q) / b
Hypothetical example: Over 2.5 goals is priced at 2.10 and your estimate is 52%.
- b = 2.10 − 1 = 1.10
- p = 0.52, q = 0.48
- b × p = 1.10 × 0.52 = 0.572
- 0.572 − 0.48 = 0.092
- 0.092 / 1.10 = 0.0836, or about 8.4% of the bankroll
The bookmaker’s price implies 1 / 2.10 = 47.6%, so on your numbers the price is generous. The top line of the formula, 0.092, is your expected profit per £1 staked (0.52 × 2.10 − 1 = 0.092). Kelly divides that edge by b, so the same edge earns a smaller stake at longer odds.
If the result is zero or negative, Kelly says do not bet. At 2.10 with an estimate of 45%: (1.10 × 0.45 − 0.55) / 1.10 = (0.495 − 0.55) / 1.10 = −0.05, so no stake.
Why is full Kelly considered aggressive?
Full Kelly stakes are large. In the example above, 8.4% of a £500 bankroll is £41.82 on one match. Many bankroll management plans use 1% to 2%, so full Kelly can be four to eight times bigger, and a normal losing run causes deep drops.
The bigger problem is sensitivity. Kelly treats your estimate as the truth. Look at how the suggested stake moves at the same odds of 2.10 when the estimate changes by a few points:
| Your estimate (p) | b × p − q | Full Kelly stake | On a £500 bankroll |
|---|---|---|---|
| 48% | 0.008 | 0.7% | £3.64 |
| 50% | 0.050 | 4.5% | £22.73 |
| 52% | 0.092 | 8.4% | £41.82 |
| 55% | 0.155 | 14.1% | £70.45 |
A 3-point difference in your estimate, from 52% to 55%, raises the stake by about two-thirds. If your 55% was really 48%, you would be staking £70.45 on a bet where Kelly suggests £3.64.
What is fractional Kelly?
Fractional Kelly means staking a set share of the full Kelly figure, often half or a quarter. It cuts the size of swings and gives some protection against over-optimistic estimates.
| Approach | Share of bankroll (52% at 2.10) | Stake on £500 |
|---|---|---|
| Full Kelly | 8.36% | £41.82 |
| Half Kelly | 4.18% | £20.91 |
| Quarter Kelly | 2.09% | £10.45 |
The same maths works in dollars. Quarter Kelly here lands near the 1% to 2% range of many flat staking plans, while still giving more weight to bigger estimated edges.
How does Kelly compare across different odds?
Three hypothetical goals bets:
| Market | Odds | Your estimate | b | Kelly fraction |
|---|---|---|---|---|
| Over 1.5 | 1.50 | 70% | 0.50 | (0.35 − 0.30) / 0.50 = 10.0% |
| BTTS Yes | 2.10 | 52% | 1.10 | 0.092 / 1.10 = 8.4% |
| Over 3.5 | 3.00 | 38% | 2.00 | (0.76 − 0.62) / 2.00 = 7.0% |
Over 3.5 has the biggest edge per £1 (0.38 × 3.00 − 1 = 0.14) yet gets the smallest share, because it loses more often. To find edges in the first place, see how to spot value in goals markets.
What are the limits of the Kelly criterion?
- Garbage in, garbage out. The formula is only as good as p. A probability built from a few games of team goal stats carries a lot of uncertainty.
- It ignores bets running at the same time. Several Kelly stakes on one weekend add up to a large share of the bankroll.
- It does not make anything certain. A positive Kelly figure means a price looks generous on your estimate, not that the bet will win.
Where PRO Betting Tips fits
PRO Betting Tips, an iOS and Android app made by MICOM TECH, uses a Kelly criterion score to rank its Pro Picks. A pick needs a probability of at least 50% and odds between 1.20 and 3.50, and is ranked by its Kelly score, normally 0.08 or more; the chosen picks are then listed by kick-off. The score is a way to rank value, not an instruction on how much to stake. The learning centre covers bankroll, value and staking. The app is free with an optional premium plan, for adults 18+, and is not a bookmaker.
18+. Betting involves risk; no prediction is guaranteed. If gambling stops being fun, visit BeGambleAware or call 1-800-GAMBLER in the US.