Short answer: D'Alembert looks gentle, adding just one unit after each loss, but it doesn't beat roulette. In 100,000 simulated sessions it wiped out a €100 bankroll more than half the time and lost 2.7% of everything wagered, exactly the house edge.
How D'Alembert works
- Bet one unit on an even-money bet such as red.
- After a loss, add one unit to your next bet.
- After a win, take one unit off (but never go below one unit).
It's named after the 18th-century mathematician Jean le Rond d'Alembert. The idea behind it is that wins and losses should "balance out", so after a run of losses a win is "due". That is the gambler's fallacy: the wheel has no memory, and every spin has exactly the same odds.
Why it feels safer than Martingale
Martingale doubles after every loss, so 7 losses in a row turn a €1 bet into €128. D'Alembert only climbs one step at a time: after 7 losses your bet is €8. No single spin is terrifying.
The catch is what happens over a long bad stretch. Every loss adds a unit and every win only removes one. Because red loses slightly more often than it wins (19 of 37 pockets), the stake tends to drift upwards over a session. You end up betting larger amounts on many spins, and the house edge takes 2.7% of all of it.
We simulated 100,000 sessions
Using the same engine as our free roulette simulator: bets on red, €500 table maximum, a fair wheel, 100,000 sessions per row. "Lost whole bankroll" means the session ended because the money ran out.
| Setup | Sessions in profit | Lost whole bankroll | Average result |
|---|---|---|---|
| D'Alembert, €1 base, €100 bankroll, 200 spins | 41.2% | 52.9% | −€24.75 |
| D'Alembert, €1 base, €100 bankroll, 1,000 spins | 6.8% | 93.1% | −€67.79 |
| D'Alembert, €5 base, €100 bankroll, 200 spins | 12.3% | 87.5% | −€37.43 |
| D'Alembert, €1 base, €500 bankroll, 200 spins | 54.6% | 6.7% | −€47.65 |
| D'Alembert, €1 base, €100 bankroll, 200 spins, American wheel | 29.4% | 64.8% | −€46.69 |
And for comparison, same wheel and bankroll, €1 base, 200 spins:
| Strategy | Sessions in profit | Lost whole bankroll | Average result |
|---|---|---|---|
| Flat €1 on red | 32.5% | 0.0% | −€5.42 |
| Martingale | 44.5% | 50.7% | −€14.12 |
| D'Alembert | 41.2% | 52.9% | −€24.75 |
What the numbers show
- "Gentle" doesn't mean safe. Over 200 spins D'Alembert lost the whole €100 slightly more often than Martingale, and lost more on average.
- It puts a lot of money on the table. An average 200-spin session wagered about €925, more than four times the flat-betting total of €200. 2.7% of €925 is about €25, which is exactly the average loss.
- Long sessions are brutal. Over 1,000 spins, only 6.8% of sessions finished ahead and 93% ran out of money.
- A bigger bankroll only reshapes the losses. With €500 behind you, busts drop to 6.7%, but the average loss nearly doubles because you can keep betting bigger for longer.
- The wheel matters. On an American wheel the average loss almost doubles again.
The core problem: D'Alembert changes how much you bet, never the odds of each bet. Every euro you wager still loses 2.7% on average, so any system that makes you wager more makes you lose more.
If you enjoy playing D'Alembert
- Set a maximum bet before you start, for example 5 units, and stop the progression there.
- Keep sessions short. The longer you play, the further the stake tends to drift up.
- Play European or French roulette, never American.
- Decide your loss limit in advance. See how to set a roulette budget.
Want to see it for yourself? Choose "D'Alembert" in the roulette simulator and run 1,000 sessions, or compare it with every other system in our strategy comparison.