D'Alembert system in roulette

What the D'Alembert system is

The D'Alembert is the mildest of the popular negative progressions. You pick a unit, say £5, and start by betting one unit on an even-money bet. Each time you lose, the next bet is one unit bigger. Each time you win, the next bet is one unit smaller, down to a floor of one unit.

Compared with the Martingale, which doubles after every loss, the D'Alembert grows in a straight line: £5, £10, £15, £20 rather than £5, £10, £20, £40. That gentler slope is its whole appeal. Wizard of Odds' D'Alembert analysis (opens in a new tab) describes the same add-one, take-one rule and tests it on single-zero even-money bets.

It's almost always played on red or black, odd or even, or high or low, all of which pay 1 to 1 and win on 18 of the 37 pockets.

D'Alembert system rules, step by step

1. Decide your session budget and a unit size, for example £5 from £200.
2. Pick an even-money bet on a single-zero table, preferably one using La Partage.
3. Bet one unit.
4. After a loss, add one unit to your next bet.
5. After a win, take one unit off your next bet, but never bet less than one unit.
6. Many players stop when they're a set number of units ahead, or when the stake reaches a cap they chose in advance.
7. Stop at your budget or time limit regardless of where the sequence is.

Worked D'Alembert example at £5 a unit

Here's an imagined ten-spin session on red with exactly five wins and five losses, mixed in an ordinary way.

Five wins, five losses, and the session is £25 up: one unit for every win. That's no fluke of this particular order. As long as the stake never hits the one-unit floor, equal numbers of wins and losses always leave a D'Alembert player one unit ahead per win. Each loss raises the next stake by a unit and each win lowers it, so every win-loss pair nets one unit whichever order it comes in.

That neat result is exactly why the system is so persuasive. The problem is the assumption hidden inside it: that wins and losses will come out equal.

The equilibrium idea behind the D'Alembert system, and why it fails

The D'Alembert is built on a belief that outcomes balance out: after a loss, a win becomes more likely, so it makes sense to bet more. That's the gambler's fallacy. A roulette wheel has no memory, and the chance of red on the next spin is 18 in 37 whatever happened before. Each spin is an independent event.

Worse, the wheel isn't even balanced to begin with. On an even-money bet there are 18 winning pockets and 19 losing ones, because zero loses too. Over 37 spins the average is 18 wins and 19 losses, not an even split. Over 370 spins, it's 180 wins and 190 losses. Each extra loss pushes the stake up one unit, so the system ends up betting more just as the balance tips against it.

The law of large numbers does say results drift towards the true probabilities over many spins. But that true probability is 48.65% wins, not 50%, and the drift happens by sheer weight of numbers, not because the wheel corrects past results.

D'Alembert odds: what the simulations show

Wizard of Odds ran simulations of the D'Alembert on single-zero even-money bets with a range of session goals and limits. The headline findings are worth spelling out because they show how a system can feel like it works and still lose money:

• The session goal was reached in between 89.81% and 99.26% of sessions, depending on the settings.
• Despite that, the expected result was negative in every case.
• The loss as a share of total money bet matched the 2.703% house edge.

How can a system that hits its target nine times out of ten or more still lose? Because the target is small, a handful of units, while the failures are large, the sessions where a long losing drift drove the stake up and the budget ran out. Many small wins plus a few big losses add up to the house edge. It's the same pattern Wizard of Odds describes across all betting systems (opens in a new tab): the ratio of money lost to money bet always heads towards the edge.

How a losing run builds with the D'Alembert system

The straight-line climb is gentle, but losses still add up quickly because each bet is bigger than the last. Here's ten straight losses at £5 a unit.

The chance that the next ten even-money spins all lose on single zero is (19/37)¹⁰, about 0.13%. Straight runs like that are rare, but the D'Alembert doesn't need a straight run to hurt. A session that goes 40 losses and 30 wins leaves the stake ten units above where it started, with a deficit to match. The system lets the hole grow slowly, which makes it easy not to notice.

D'Alembert vs Martingale vs Fibonacci

All three are negative progressions, raising stakes after losses. They differ in how steeply.

After six losses the Fibonacci system has lost slightly less than the D'Alembert, because its first steps are smaller (£5, £5, £10), but from there it climbs much faster. The Martingale is in another league. The edge column is the one that never changes. Our roulette betting systems guide compares the full set.

Best roulette tables for the D'Alembert

Since no staking plan alters the odds, the cheapest way to play is to pick the cheapest game. French roulette with La Partage returns half of a losing even-money bet when zero lands, which cuts the edge on those bets to about 1.35%. Standard European tables are 2.70%. American roulette, with its double zero, is 5.26% and tilts the win-loss balance even further: 18 wins against 20 losses per 38 spins.

For a £5-unit D'Alembert session that puts £500 through the wheel, that's an average cost of about £6.75 at La Partage, £13.50 on a European table and £26.30 on an American one. Our cost per hour guide shows how to work this out for any game.

D'Alembert on UK online and live roulette

Single-zero RNG and live roulette have the same maths, so the D'Alembert behaves the same on both; live games are slower, which means fewer bets and a lower hourly cost. In the UK, autoplay has been banned on all online casino games since 17 January 2025, so you'll be placing each bet yourself. Non-slot games must allow at least 5 seconds per game cycle, and your net spend and time played must be on screen.

Casinos must prompt you to set a financial limit before your first deposit, and offer time-outs and reality checks. If adding a unit after every loss starts to feel like a way of getting money back, that's a sign to stop; chasing losses explains why. You can talk to GamCare (opens in a new tab) or call the National Gambling Helpline on 0808 8020 133, free and 24 hours a day.

Common D'Alembert mistakes

• Believing a win is due after a loss. The odds of the next spin don't change.
• No stake cap. Without one, a slow losing drift can push stakes far higher than planned.
• Using a large unit. A £25 unit reaches £250 bets after nine net losses.
• Ignoring the zero. It means losses outnumber wins over time, which the system has no answer to.
• Seeing frequent small wins as proof it works. Frequent small wins and rare big losses are exactly what the edge looks like with this system.

For a plain-English look at why none of this can be engineered away, read can you predict roulette numbers, or go back to the roulette hub for every bet explained.

Where to play roulette with the D'Alembert system

Our partner offers are general welcome deals, mostly slot-based, and they don't make any staking system more effective. Roulette and other table games are often excluded from bonus wagering or count for less, so always read the terms. 18+ and terms apply.

• Casumo: 50% bonus up to £100 for new customers who opt in; minimum first deposit £20, bonus wagered 10x within 7 days, £5 maximum bet while active, game, play and payment restrictions apply.
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To see what each lists for table games, try Coral blackjack and roulette.

18+. Every casino game has a built-in house edge, so over time you should expect to lose what you stake. Set a budget before you play and stop when it’s gone: safer gambling tools and support. Free, confidential help: National Gambling Helpline 0808 8020 133.