Does the D'Alembert system work? 100,000 sessions tested
The D'Alembert adds a unit after a loss and removes one after a win. We ran 100,000 simulated single zero roulette sessions to show its real win rate, bust rate, and average result.
What it is and how it works
The D'Alembert raises the stake by one base unit after a loss and lowers it by one after a win, never dropping below the base unit. It is a much gentler staircase than the doubling systems.
The reasoning behind it assumes that wins and losses tend to even out in the short run. They do not: each spin is independent, and the wheel has no memory of what it has already done.
A simple example at a base bet of 5
- Bet 5 on red. It loses.
- Bet 10. It loses.
- Bet 15. It wins, returning 30.
- Bet 10. The stake steps back down one unit at a time.
What our simulation shows
We ran 100,000 sessions of this system against a fair single zero wheel, each session lasting up to 100 spins, starting with 500 virtual points and a base bet of 5. Those are the same defaults the app's Lab starts with. A session ends early if the bankroll can no longer cover the next required bet.
| Sessions simulated | 100,000 |
|---|---|
| Sessions that finished ahead | 54.6% |
| Sessions that finished level | 0.0% |
| Sessions that finished behind | 45.4% |
| Sessions that ran out of money | 30.4% |
| Average result per session | -63.4 points |
| Typical (median) result | +50 points |
| Average total staked in a session | 2,318.1 points |
| Loss predicted by the house edge | 62.7 points |
| Best session seen | +350 points |
| Worst session seen | -500 points |
| Average longest run of losing spins | 6 |
| Longest run of losing spins seen | 16 |
Read that table slowly. The share of sessions finishing ahead is often the number that sells a system, and on its own it is misleading: what matters is the average result, which includes the sessions that went badly.
Why this system cannot overcome the house edge
A single zero wheel has 37 pockets. An even money bet such as red wins on 18 of them and loses on 19, so every point you stake returns 36 of 37 points on average. That is a loss of 2.7027% of everything staked, and it applies to every single bet no matter what size it is or what order the bets come in.
Our simulation shows this directly. Across 100,000 sessions this system staked an average of 2,318.1 points per session. Applying the edge to that amount predicts a loss of 62.7 points. The simulation actually produced an average of -63.4 points.
The staking pattern changed how the wins and losses were spread out. It did not change the total. That is the whole story of every betting system: they move risk around, and nothing more.
Strengths and weaknesses
Strengths
- The stake grows in a straight line rather than exponentially, so it is far easier to survive a bad run than with a doubling system.
- The rule is easy to follow at the table.
Weaknesses
- A long losing run still lifts the stake steadily, and a slow climb over many rounds stakes a great deal in total.
- The idea that results even out in the short run is simply false, and the whole system is built on it.
Who it might suit
The D'Alembert suits players who want their stake to react to results without the violence of doubling. Treat the staircase as a pacing device, not as a recovery mechanism.
Common questions
Does the D'Alembert reduce the house edge?
No. Varying the stake changes how much you put at risk on each spin, not the percentage the wheel keeps. Our simulation shows the average loss tracking the house edge applied to everything staked.
Is the D'Alembert safer than the Martingale?
The stake grows far more slowly, so a losing run is much less likely to end the session abruptly. It still stakes a large amount over 100 spins, which is why its average loss in our data is larger than a flat stake.
Test it yourself
Open the Lab in the app with D'Alembert already selected, set your own budget, base bet, and number of rounds, and watch it play out spin by spin with virtual points.