How it works
The Kelly criterion gives the share of a bankroll to stake that grows it fastest over many bets, if your chance is exactly right. It stakes more on a bigger edge, and nothing when there is no edge.
Your chance is never exactly right, and full Kelly punishes an overestimate hard, with big swings and deep drawdowns. So this calculator, like Unitley, never stakes full Kelly. Each risk profile stakes a fraction of it and caps any one bet at a share of the bankroll:
- Conservative: ¼ Kelly, and at most 2% of the bankroll on one bet.
- Balanced: ⅓ Kelly, and at most 3% of the bankroll on one bet.
- Aggressive: ½ Kelly, and at most 5% of the bankroll on one bet.
With no edge, full Kelly comes out at zero or below, and the stake is $0.
The formula
b = decimal − 1 (the profit per $1), p = your chance, q = 1 − p
Full Kelly = (b × p − q) ÷ b
Stake share = the smaller of full Kelly × fraction and the capAnd 0 when full Kelly is 0 or less.
Stake = bankroll × stake share
A worked NFL example
A $1,000 bankroll on the Balanced profile. You give an NFL underdog at +130 a 46% chance to win.
- b: 2.30 − 1
- 1.3
- Full Kelly: (1.3 × 0.46 − 0.54) ÷ 1.3
- 4.46%
- ⅓ Kelly: 4.46% × ⅓
- 1.49%
- Under the 3% cap, so the stake is
- $14.87
A bigger edge meets the caps. At +100 with a 55% chance, full Kelly is 10% of the bankroll. A quarter of it, 2.5%, is held to Conservative’s 2% cap; a third, 3.33%, to Balanced’s 3%; and half is exactly Aggressive’s 5%.
| Profile | 46% at +130 | 55% at +100 |
|---|---|---|
| Conservative, ¼ Kelly | $11.15 | $20 |
| Balanced, ⅓ Kelly | $14.87 | $30 |
| Aggressive, ½ Kelly | $22.31 | $50 |
Common mistakes
- Staking full Kelly. Even with a real edge it swings hard, and with a chance that is too high it overbets every time. That is why no profile uses it.
- Overstating your chance. Kelly is sensitive to it. At +130, 48% instead of 46% takes full Kelly from 4.46% to 8.00%, close to double. The fraction and the cap blunt that.
- Sizing several bets as if each stood alone. Kelly sizes one bet at a time. Bets placed together, above all on the same game, share their risk, and sized one by one they can add up to more than you meant to stake.
- Treating it as a stop rule. Kelly says how much to stake, not when to stop. A loss limit does that: see bankroll management.
In Unitley
In Unitley you set a bankroll, a unit size and a risk profile. Suggested stakes use these same fractions and caps, never full Kelly, within stake caps and daily and weekly loss limits. See bankroll and limits.