The question
"I think I've found value. Do I stake £10, £50 or £500?"
Most punters stake by feel, and feel is exactly what goes wrong after a few wins or losses. The Kelly criterion for betting gives a precise answer: the stake, as a share of your bank, that grows it fastest over the long run.
The idea in one sentence
Stake a share of your bank equal to your edge divided by your net odds: bigger when the edge is bigger, smaller when the odds are longer, and nothing at all when there's no edge.
The picture
Imagine betting the same edge over and over, each time staking a fixed share of whatever your bank is at that moment. Plot the long-run growth rate of the bank against the share you stake, and you get a hill.
- Too little and your bank grows, but slowly. You're leaving money on the table.
- Exactly Kelly sits at the top of the hill: the fastest long-run growth possible.
- Too much and growth falls away quickly. At about twice Kelly, growth is back to zero. Beyond that, a bettor with a genuine edge goes backwards.
That last point surprises everyone. Overbetting a real edge can lose money over time, not because the bets are bad but because the losses bite harder than the wins help.
For the example below (36% at odds of 3.0, 2% commission):
| Stake size | Share of bank | Growth v Kelly |
|---|---|---|
| Quarter Kelly | 0.84% | 44% |
| Half Kelly | 1.67% | 75% |
| Full Kelly | 3.35% | 100% |
| Double Kelly | 6.69% | 4% |
| Triple Kelly | 10.04% | negative |
Half Kelly keeps three quarters of the growth with half the stake size. That trade is the subject of Lesson 6.2.
Worked Betfair example
Over/Under 2.5 Goals, backing the over at 3.0. Your model says 36%. Bank £2,000. (Illustrative figures.)
- Net odds after commission. A £1 winning bet makes £2.00, less 2% commission: b = 2.00 × 0.98 = 1.96.
- Your edge (expected value per £1). 0.36 × 1.96 − 0.64 = 0.7056 − 0.64 = +£0.0656, about +6.6%.
- Kelly share. Edge ÷ net odds: 0.0656 ÷ 1.96 ≈ 3.35% of your bank.
- Stake. 3.35% × £2,000 ≈ £66.94.
- What happens next. Win and your bank rises to £2,000 + 66.94 × 1.96 ≈ £2,131.20. Lose and it falls to about £1,933.06. The next stake is 3.35% of the new figure.
- Commission's effect. Without commission the Kelly share would be (0.36 × 2 − 0.64) ÷ 2 = 4.0%. The 2% charge cuts the stake by about a sixth.
- What most pros would stake. Half Kelly: about £33.47. Lesson 6.2 explains why.
Laying with Kelly
Laying at odds O is the same as backing "it won't happen" at net odds of (1 ÷ (O − 1)) × 0.98, with the stake measured as your liability.
Say you lay a team at 3.0 believing they win only 30%:
- Net odds on the lay. (1 ÷ 2) × 0.98 = 0.49. Risk £1 of liability to win £0.49.
- Edge per £1 of liability. 0.70 × 0.49 − 0.30 = +£0.043.
- Kelly share of liability. 0.043 ÷ 0.49 ≈ 8.78% of bank: £175.51 of liability on £2,000.
- Lay stake. Liability ÷ (O − 1) = 175.51 ÷ 2 ≈ £87.76.
The formula
The Kelly stake
- f* is the share of your current bank to stake.
- b is your net odds: (decimal odds − 1) × (1 − commission).
- p is your estimated win chance, and q = 1 − p.
In plain English: the top line is your expected profit per £1 staked. Divide it by what a win pays per £1, and you have the stake. No edge, no bet: if bp − q is zero or negative, Kelly says stake nothing.
Why it's the growth-maximising stake
- g(f) is the average growth of the log of your bank per bet when staking share f.
- ln is the natural logarithm.
In plain English: growth compounds, so what matters is the average of the log of each result. A win multiplies your bank by (1 + fb) and a loss by (1 − f). Kelly is the f that makes this average as large as possible. At full Kelly here, g ≈ 0.001087 per bet, so over 1,000 bets the typical bank grows about e^1.087 ≈ 2.96 times.
Laying
- p is your chance the selection wins (so 1 − p is your chance the lay wins).
- O is the lay odds and c the commission rate.
In plain English: a lay is a back of "not this outcome" at short odds. The formula is the same; the stake is your liability.
Try it
Enter 36%, odds 3.0, bank £2,000, commission 2% and fraction 1.0. Check you get a stake of about £66.94. Then drag the probability down to 34% and watch the stake collapse to about £6.50: a two-point error in your estimate cuts the right stake by 90%.
Common mistakes
- Plugging in an overconfident probability. Kelly is only as good as p. Overestimate your edge and full Kelly becomes overbetting. Shrink your estimates first (Lesson 5.2).
- Staking full Kelly. Even with the right p, full Kelly has brutal swings: in our simulations, about 40% of full-Kelly bettors saw their bank halve at some point within 1,000 bets. See Lesson 6.2.
- Forgetting commission. Use net odds. At 3.0, 2% commission turns a 4.0% Kelly stake into 3.35%.
- Using Kelly on the starting bank forever. Kelly re-sizes to the current bank after every result. Staking a fixed £67 regardless of wins and losses is level staking, which is a different plan with different risks (Lesson 6.3).
- Treating several open bets as one. Bets running at the same time share one bank. Staking full Kelly on each overbets the total (simultaneous Kelly).
Why even correct staking can't save a flawed edge: why good models still lose money.