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The Kelly criterion and bankroll sizing
Arbs research desk · Updated 2026-11-01 · Reviewed 2026-11-01 · 3 min read
The short answer: Kelly stakes (b × p − q) ÷ b of your bankroll, where b is decimal odds − 1. At even money with a 55% win chance that is 10%. Because probability estimates are never exact, most bettors stake a quarter to a half of that.
The formula
f* = (b × p − q) ÷ b = (p × d − 1) ÷ (d − 1)
The second form says Kelly is your EV divided by the net odds. No edge means no bet; a bigger edge or a shorter price means a bigger stake.
| Odds | Win chance | Full Kelly | Quarter Kelly |
|---|---|---|---|
| +100 | 55% | 10.0% | 2.5% |
| +150 | 45% | 8.3% | 2.1% |
| −150 | 65% | 12.5% | 3.1% |
| Polymarket 45¢ after fee | 50% | 7.0% | 1.75% |
Why Kelly
Staking a fixed share of your current bankroll means you bet more after wins and less after losses. Kelly picks the share that maximises the expected growth of the bankroll’s logarithm, which is the same as the fastest long-run growth:
G(f) = p × ln(1 + b × f) + q × ln(1 − f)
| Stake | Fraction of Kelly | Growth per bet | Share of the maximum |
|---|---|---|---|
| 2.5% | Quarter | 0.22% | 44% |
| 5% | Half | 0.38% | 75% |
| 10% | Full | 0.50% | 100% |
| 20% | Double | −0.01% | below zero |
Double Kelly grows no faster than not betting at all, with far more risk. Past that, a +EV bet shrinks your bankroll.
The catch
Full Kelly is only optimal if your win probability is exactly right. If you overestimate your edge, you overbet, and overbetting is what turns +EV bets into a shrinking bankroll.
Worked example: You think 55%, the truth is 52%
- Your full Kelly: 10% of bankroll
- True full Kelly: 4%, so you are betting 2.5 times too much
- True growth at 10%: 0.52 × ln 1.1 + 0.48 × ln 0.9 = −0.10% a bet
- At your quarter Kelly, 2.5%: +0.07% a bet
Quarter Kelly still grows; full Kelly on the same bets loses money.
Drawdowns are the other cost. In the standard continuous approximation, the chance of the bankroll ever falling to a fraction x of its peak, betting a fraction c of Kelly, is:
P(drawdown to x) = x raised to (2 ÷ c − 1)
- Full Kelly: a 50% chance of halving at some point
- Half Kelly: 12.5%
- Quarter Kelly: under 1%
Several bets at once
Kelly assumes one bet at a time. When several games run at once, each stake comes out of the same bankroll, and the combined risk is larger than any single bet suggests. A simple rule is to scale every stake down so the total on the board stays within what one full Kelly bet would be.
Simulate before you choose
The Kelly calculator runs 2,000 simulated paths of 100 bets at full, half and quarter Kelly so you can see the range of outcomes, not just the average.
Try it: Kelly calculator
Frequently asked questions
What fraction of Kelly should I use?
A quarter to a half is the common range. Use less when your probabilities are uncertain.
Does Kelly work for parlays?
Yes, with the parlay’s true probability and its odds. The edge on parlays is usually smaller than it looks, so Kelly stakes are small.
What if I bet several games at once?
Simultaneous bets compete for the same bankroll. Scale each Kelly stake down so the total stays sensible.
Should I recalculate after every bet?
Yes. Kelly is a share of your current bankroll, so stakes grow after wins and shrink after losses.