Lay Kelly Criterion
Overview
The Kelly Criterion adapted for lay betting. Determines the optimal fraction of bankroll to risk as liability when you have an edge on a lay selection. As with back Kelly, most practitioners should use fractional Kelly.
How It Works
For a lay bet, your “edge” comes from the selection losing more often than the odds imply. Kelly tells you what fraction of bankroll to risk as liability.
Formula
\[f = \frac{q - p \times b}{b}\]Where:
- $f$ = fraction of bankroll to risk as liability
- $b$ = net odds (decimal odds − 1) — this is what you pay per unit won
- $p$ = probability the selection WINS (you lose the lay)
- $q$ = probability the selection LOSES (you win the lay) = $1 - p$
Betfair-adjusted (with commission $c$):
\[f = \frac{q - p \times b}{b \times (1 + c)}\]Example: You estimate only a 30% chance the selection wins. Lay odds are 3.0 ($b = 2$). $f = (0.7 - 0.3 × 2) / 2 = 0.05$ — risk 5% of bankroll as liability.
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
edge |
number | — | Requires true win probability estimate (selection winning = you losing) |
commission |
number | 0.05 | Betfair commission rate |
fraction |
number | 0.25 | Kelly fraction (quarter recommended for lay) |
Risk Assessment
- Risk Level: High (Full), Medium (Quarter)
- Max Drawdown: Significant at full Kelly
- Recommended Bankroll: 200× average liability for quarter Kelly
- Ruin Risk: Higher than back Kelly — lay odds typically longer, meaning more volatility
When to Use
- You can accurately estimate the probability of selections winning (you losing)
- You specialize in lay betting with a proven edge
- Always use fractional (quarter or less)
When to Avoid
- You’re new to Kelly or lay betting
- Your edge estimates are rough
- The recommended fraction exceeds your comfort zone
Betfair Exchange Notes
- The lay Kelly formula differs from back Kelly — make sure you use the right one
- Commission significantly impacts lay profitability at scale
- Consider using Lay % Liability as a simpler, safer alternative
Related Plans
- Kelly Criterion — Back betting equivalent
- Lay % Liability — Simpler proportional lay staking
- Lay Liability — Fixed liability (no edge estimation)
Sources
- Plan catalog reference: The Staking Machine — staking plan software with 50+ plans
- Plan mechanics: Mathematical formulas and plan concepts are in the public domain