D'Alembert Roulette Strategy
D'Alembert is the gentlest negative progression system in common use. The rule is simple: add one unit after a loss, subtract one unit after a win, never go below one unit.
It produces a much smoother bankroll graph than Martingale or Fibonacci at the cost of slower recovery. The long-run expected return is identical.
How D'Alembert works
- Pick a unit size, for example $10. Pick an even-money target.
- Start at 1 unit ($10).
- Loss: next bet = current + 1 unit.
- Win: next bet = current − 1 unit (minimum 1).
Example progression
| Spin | Bet ($10 unit) | Result | Next bet |
|---|---|---|---|
| 1 | $10 | Loss | $20 |
| 2 | $20 | Loss | $30 |
| 3 | $30 | Win | $20 |
| 4 | $20 | Win | $10 |
| 5 | $10 | Win | $10 |
| 6 | $10 | Loss | $20 |
After 6 spins: 3 wins, 3 losses, net result = +$10. D'Alembert produces small profit when wins and losses are roughly balanced, even when individual outcomes are randomly ordered.
Why the math feels favourable - and why it isn't
D'Alembert appears to win whenever wins equal losses, because the last losing bet always exceeds the prior winning bet by 1 unit. That feels like a hidden edge.
It is not. On European, you win 18/37 spins on red - fewer than 50%. Across many sessions, the imbalance compounds and the expected return is the same negative house edge as every other system.
What D'Alembert really does is smooth the volatility. Drawdowns are smaller. Recoveries are slower. Bust risk is lower than Martingale or Fibonacci.
Bankroll requirements
Bankroll to absorb a streak of N losses, starting from 1 unit base:
- 5 losses: 1+2+3+4+5 = 15 units. With $10 base, $150 wagered.
- 10 losses: 1+2+…+10 = 55 units. $550 wagered.
- 15 losses: 120 units. $1,200 wagered.
- 20 losses: 210 units. $2,100 wagered.
Compare to Martingale, which needs $10,230 to absorb just 10 losses. D'Alembert is dramatically easier on a bankroll.
Comparison to other progressions
| System | Escalation pattern | Risk on long losing streak |
|---|---|---|
| Flat | None | Linear |
| D'Alembert | Linear (+1/−1 unit) | Moderate |
| Fibonacci | ~1.618× per loss | High |
| Martingale | 2× per loss | Catastrophic |
Test results
Across 200 spins of $10 D'Alembert on $1,000 bankroll on European:
- ~70% of sessions end with a small profit.
- ~25% end with a small or moderate loss.
- ~5% have meaningful drawdowns of −$200 or worse.
- Bust rate is near zero on a $1,000 bankroll.
- Average final bankroll lands close to the expected loss.
When D'Alembert makes sense
If you want a progression system but cannot tolerate Martingale's bankroll demands or Fibonacci's sequence complexity, D'Alembert is the gentlest option that still has progression logic.
It is also the easiest to track mentally - just add or subtract one unit. No sequence to remember, no exponential growth to monitor.