In one sentence
The Kelly criterion tells you what share of your current bank to stake on a bet so that your bank grows as fast as possible over the long run, based on your estimated edge and the odds on offer.
How it works
Stake too little and a real edge makes money slowly. Stake too much and losing runs knock your bank down so hard it never recovers, even though every bet was value. Kelly finds the sweet spot.
It does this by maximising the average growth rate of your bank rather than the average profit of each bet. Because stakes are a percentage of the current bank, stakes shrink after losses and grow after wins, so in theory you never go completely bust.
The catch is that Kelly assumes you know your true win probability. You never do, and that single weakness drives almost everything in the pitfalls section below.
The maths
- f* is the fraction of your current bank to stake.
- b is the net odds: decimal odds minus 1 (what £1 wins if the bet lands).
- p is your estimated probability that the bet wins.
- q is the probability it loses, which is 1 − p.
Kelly is the stake that maximises the expected log of your bank:
- G(f) is the average growth rate of your bank per bet when staking fraction f.
- ln is the natural logarithm.
In plain English: stake your edge divided by the net odds, and if the edge is zero or negative, stake nothing.
Worked betting example
You rate Brentford at 44% to beat Fulham and can back them at 2.50 on Betfair's Match Odds market. Your bank is £2,000. The 44% is an illustrative model figure.
- Net odds b = 2.50 − 1 = 1.5.
- Edge per £1 staked: 0.44 × 1.5 − 0.56 = +£0.10, a 10% edge.
- Kelly fraction: (1.5 × 0.44 − 0.56) ÷ 1.5 = 0.10 ÷ 1.5 = 6.67%.
- Stake: 6.67% × £2,000 = £133.33.
- If it wins, the bank becomes £2,200. If it loses, the bank becomes £1,866.67, and the next stake is 6.67% of that smaller figure.
Now add Betfair commission, which is charged on net winnings. At 2% the effective net odds become 1.5 × 0.98 = 1.47, and Kelly drops to 5.90%, a stake of £118.10. That is about 11% less than the stake before commission, because commission takes a slice of the edge itself.
Before commission, growth per bet at full Kelly is 0.00330 in log terms. Half the stake still gives 0.00248, about 75% of the growth. Double the stake (13.3%) gives only 0.000085, almost no growth at all, and anything beyond roughly 13.4% of the bank shrinks it over time despite the 10% edge.
Where it's good
- Deciding stake size when you have a well-tested model with a measurable edge.
- Comparing bets: it naturally puts more on bigger edges and less on long shots.
- Showing why overbetting a real edge can still lose money.
- Laying: treat your liability as the stake, use 1 ÷ (lay odds − 1) as b and the chance the selection loses as p.
Limitations and pitfalls
- It is only as good as your probability estimate. Overstating your edge makes Kelly overbet, and overbetting by 2× wipes out the growth entirely.
- Full Kelly is a rough ride: halving your bank at some point is very common, even with a real edge.
- It assumes one bet at a time. Several bets running at once, or bets in the same match, need the simultaneous version.
- Commission must be included in b, otherwise you stake too much on every bet.
- Market prices are usually well calibrated, so a large calculated edge is more often a model error than a real opportunity.
How to build it
- A few lines of Python or a spreadsheet cell is enough; no library needed.
- Use calibrated probabilities from a model tested out of sample, not your gut feel.
- Always compute b after commission.
- Practical tip: start at a quarter or half Kelly until you have a few hundred bets of evidence that your edge is real.
Related methods
- Fractional Kelly – the safer, more common way to use Kelly in practice.
- Simultaneous Kelly – Kelly for several bets at once.
- Expected value – the edge that goes into the formula.
- Risk of ruin – what happens when you stake too much.
- Commission-adjusted EV – getting the net odds right.