D’Alembert Staking Plan
Overview
A moderate negative progression system: increase stake by 1 unit after a loss, decrease by 1 unit after a win. Much less aggressive than Martingale or Fibonacci. Based on the (mathematically false) “law of equilibrium” — the belief that wins and losses eventually balance out.
How It Works
- Start with a base stake (e.g., 1 unit)
- After a loss: Increase next stake by 1 unit
- After a win: Decrease next stake by 1 unit (never below base stake)
- Theory: over time, wins and losses should roughly balance, and each win-lose pair produces +1 unit profit
\[S_{i+1} = \begin{cases} S_i + 1 & \text{if bet } i \text{ lost} \\ \max(S_i - 1, 1) & \text{if bet } i \text{ won} \end{cases}\]
Parameters
| Parameter |
Type |
Default |
Description |
base_unit |
number |
1 |
Starting and minimum stake |
increment |
number |
1 |
Amount to increase/decrease (default 1 unit) |
Risk Assessment
- Risk Level: Medium
- Max Drawdown: Linear growth — 10 consecutive losses = 55 units lost (1+2+3+…+10)
- Recommended Bankroll: 100–200 units
- Ruin Risk: Medium — slower stake growth than Fibonacci, but still vulnerable to long losing streaks
When to Use
- You want a progression system but find Martingale/Fibonacci too aggressive
- Your system has a roughly 50% strike rate
- You have a moderate bankroll
When to Avoid
- Low strike-rate systems — even linear growth becomes unsustainable over many losses
- High-odds betting — wins are infrequent and the “1 unit per pair” profit logic breaks down
- You’re uncomfortable with any form of loss-chasing
Betfair Exchange Notes
- For lay betting, be cautious: increasing stake after a loss means increasing liability. At odds of 5.0, each additional unit of stake = 4 additional units of liability.
- Commission on wins reduces the net profit from win-lose pairs — the 1-unit-per-pair profit may become ~0.9 units after commission
Comparison
| Plan |
Stake After 5 Losses |
Stake After 10 Losses |
Recovery Style |
| D’Alembert |
6 units |
11 units |
Linear |
| Fibonacci |
8 units |
89 units |
Exponential-ish |
| Martingale |
32 units |
1,024 units |
Doubling |
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