The question
"If Kelly is the stake that grows my bank fastest, why do professionals stake a half or a quarter of it?"
Because full Kelly is only optimal if you know your edge exactly, and nobody does. This lesson shows what fractional Kelly staking costs you in growth, what it buys you in safety, and why the safety is worth far more than it looks.
The idea in one sentence
Staking a fraction of Kelly gives up a little long-run growth in exchange for much smaller swings and protection against overestimating your edge, the mistake almost every bettor makes.
The picture
We simulated 20,000 bettors, each placing 1,000 bets at odds of 3.0 with a genuine 36% win chance (2% commission), starting with a £2,000 bank. The only difference between the groups is how much of Kelly they staked.
| Staking | Share of bank per bet | Median final bank | Finished below £2,000 | Bank halved at some point | Typical worst fall from a peak |
|---|---|---|---|---|---|
| Quarter Kelly | 0.84% | £3,228 | 9.7% | 0.3% | 24.5% |
| Half Kelly | 1.67% | £4,530 | 13.6% | 8.7% | 44.5% |
| Full Kelly | 3.35% | £5,928 | 22.3% | 40.2% | 72.7% |
| Double Kelly | 6.69% | £2,078 | 48.6% | 80.4% | 96.1% |
Look along the half Kelly row. The typical bettor still more than doubles their bank, their chance of a halving drops from four in ten to under one in ten, and their typical worst fall is 44% rather than 73%.
Now look at double Kelly. Same edge, same bets, and the median bettor finishes almost exactly where they started, after a typical fall of 96%.
| Fraction | Stake per bet | Median final bank | Below start | Halved at some point | Median worst fall |
|---|---|---|---|---|---|
| ¼ Kelly | 0.84% | £3,227 | 9.7% | 0.2% | 24.2% |
| ½ Kelly | 1.67% | £4,530 | 14.1% | 8.3% | 45.3% |
| Full Kelly | 3.35% | £5,928 | 20.2% | 39.2% | 72.2% |
Worked Betfair example
The same bet as Lesson 6.1: backing at 3.0 in Over/Under 2.5, 2% commission, bank £2,000. You believe the win chance is 36%. (Illustrative figures; simulation results are from 10,000 to 20,000 simulated bettors.)
- Full Kelly on your belief. Net odds 1.96, edge 0.36 × 1.96 − 0.64 = +0.0656, Kelly 0.0656 ÷ 1.96 = 3.35%: a £66.94 first stake.
- Half Kelly. 1.67%: a £33.47 first stake. From the table, this keeps about 75% of full Kelly's growth rate.
- Now the twist: your estimate is two points too high. The true chance is 34%, not 36%. The true edge is 0.34 × 1.96 − 0.66 = +0.0064, a tenth of what you thought.
- True Kelly. 0.0064 ÷ 1.96 ≈ 0.33%. Your "full Kelly" of 3.35% is about ten times the right stake.
- What happens to the typical bank over 1,000 bets.
- "Full Kelly" (really 10 × Kelly): median bank £842, below the start 72% of the time.
- "Half Kelly" (really 5 × Kelly): median bank £1,695, below the start 60% of the time.
- "Quarter Kelly" (really 2.5 × Kelly): median bank £1,970, roughly break-even.
- The lesson. A small, completely normal error in p turned full Kelly from the fastest growth into steady decline. Fractional Kelly didn't make a thin edge profitable, but it kept the bank alive while you found out the edge was thin.
Verdict: quarter to half Kelly is the professional range for a reason. Your probabilities are estimates, estimates are usually too optimistic, and overbetting punishes that far harder than underbetting.
The formula
Growth at a fraction of Kelly
- f* is the full Kelly share of bank.
- x is the fraction of Kelly you stake (½ for half Kelly).
- g is the long-run growth rate from Lesson 6.1.
In plain English: half Kelly keeps about ¾ of the growth, quarter Kelly about 44%, and double Kelly about none. The exact figures in our example were 75.2%, 44.0% and 3.5%.
Swings scale with the fraction
- ∝ means "in proportion to".
In plain English: halve your stake and the swings in your bank halve, but the growth only drops by a quarter. That's the best deal in staking.
Chance of your bank ever falling to a share a
- a is the level you're worried about, such as ½ for "halved".
- x is your fraction of Kelly.
In plain English: with no time limit, full Kelly halves your bank at some point with probability about ½¹ = 50%. Half Kelly: ½³ = 12.5%. Quarter Kelly: ½⁷ ≈ 0.8%. Our 1,000-bet simulation came in a little lower (40%, 8.7% and 0.3%) because the clock stopped.
The cost of overestimating
- p_true is the real win chance, which you never observe directly.
In plain English: Kelly is very sensitive to p because the edge is a small difference between two big numbers. Two points off p cut the right stake by 90%. Staking a fraction of your estimate is insurance against that error. Shrinking the estimate itself (Lesson 5.2) is the other half of the cure.
Try it
Set true and believed chance both to 36%, odds 3.0, and run full, half and quarter Kelly. Check the medians land near £5,928, £4,530 and £3,228. Then drop the true chance to 34% and run again, and watch full Kelly's lines sink.
Common mistakes
- Treating full Kelly as the target. It's the ceiling. Above it you lose growth and gain risk; well below it you lose a little growth and gain a lot of safety.
- Assuming your probabilities are right. Almost every model's edges are overstated on paper. A fraction of Kelly assumes that from the start.
- Judging a staking plan on the average. Full Kelly's average bank looks wonderful, dragged up by a few huge winners. The median, the typical bettor, is what you'll actually live through.
- Raising the fraction after a good run. A hot streak is weak evidence of a bigger edge (Lesson 5.2). Change the fraction only on strong, long-run evidence such as sustained closing line value.
- Forgetting the pain. A 45% fall from a peak is normal at half Kelly. If you couldn't sit through that calmly, stake less. See Lesson 6.4.
Staking is only as good as the edge underneath it: why good models still lose money.