D'Alembert system
The D'Alembert system raises your bet slowly after losses and lowers it after wins. Here is how it works and what the tester shows when you run it.
How the D'Alembert system works
The D'Alembert system is a betting progression for even-money bets like red or black, odd or even, and high or low. Each one pays 1 to 1.
You pick a base bet, called one unit. Then you follow these steps:
- Start with a bet of one unit.
- If you lose, add one unit to your next bet.
- If you win, take one unit off your next bet.
- Never go below one unit.
- Repeat until you reach your goal, run out of money, or stop.
That is the whole rule. The bet goes up by one unit or down by one unit, never more.
The D'Alembert system only changes how much you bet. It never changes the odds of the next spin.
A short example of a D'Alembert roulette session
Here is how the bets move in a short run on red. One unit is one chip.
- Bet one chip on red – you lose. Next bet: two chips.
- Bet two chips – you lose. Next bet: three chips.
- Bet three chips – you win. Next bet: two chips.
- Bet two chips – you win. Next bet: one chip.
You had two losses and two wins. You lost three chips and won five chips, so you are up two chips.
This is the main idea: when wins and losses are equal, you end up a little ahead. Each pair of one loss and one win adds about one unit to your result.
The catch is that on a roulette wheel, wins and losses are not equal. The green zero tips the balance toward losses.
Run the D'Alembert system in the tester above
The tester at the top of this page is already set to the D'Alembert system. Press run and watch many sessions play out in a few seconds.
The default run uses these settings on the European wheel with 37 pockets:
- Bankroll: 200 chips
- Goal: win 50 chips, then stop
- Spin limit: up to 300 spins
- Table maximum: 500 chips
- Number of sessions: 20,000
Here is what the default run shows:
- Sessions that reached the goal: 68.0%
- Sessions that finished ahead (any profit): 68.1%
- Sessions that lost the whole bankroll: 31.5%
- Average result per session: -28.2 chips
- Result the house edge predicts: -28.2 chips
Now change the settings. Try a bigger goal, a smaller bankroll, or switch to the American wheel. You will see the numbers move, but the average result stays below zero.
Look at the last two lines first. The average result lands very close to the house-edge prediction; small gaps are just random variation.
Why it wins small often and loses big sometimes
Most sessions end with a small win. That happens because the bets stay low, and a few wins in a row can bring you back up to the goal.
A smaller group of sessions ends with a big loss. Here is why:
- On the European wheel, red wins 48.65% of the time – a bit less than half.
- So over many spins, losses tend to outnumber wins.
- Each extra loss pushes the bet up by one unit, and the bet keeps climbing.
- After a long bad stretch, the bets are large and the bankroll drains fast.
The many small wins and the few big losses add up to the same thing: an average loss.
The idea that a win is "due" after several losses is the gambler's fallacy. Each spin is new, and the wheel does not remember the last one.
A good-looking win rate can hide a bad average. Always check the average result, not just how often you finished ahead.
D'Alembert strategy vs the house edge
The D'Alembert system is gentler than the Martingale. Martingale doubles the bet after a loss, while D'Alembert adds just one unit. Your bets grow more slowly.
But slower is not better odds. On the European wheel, the house edge is 2.70% on every bet. No order of bets can change that.
- Your average loss is the total amount you bet times the house edge.
- D'Alembert keeps you at the table for many spins, so you bet a lot in total.
- That is why the average result of -28.2 chips lands very close to the prediction of -28.2 chips.
The D'Alembert system does not beat roulette. To compare it with other progressions, try the Fibonacci, Labouchere, or Paroli pages, or read can you beat roulette.
Treat the D'Alembert as a way to pace your bets, not a way to win. The house edge stays the same whatever you do.
Questions
What is the D'Alembert system in roulette?
It is a betting progression for even-money bets. You add one unit to your bet after a loss and take one unit off after a win, never going below one unit.
Does the D'Alembert strategy work?
No. It changes how much you bet, not the odds. In the default tester run the average session result was -28.2 chips, very close to the -28.2 chips the house edge predicts.
Is the D'Alembert safer than the Martingale?
Its bets grow more slowly, since it adds one unit instead of doubling. It can still lose the whole bankroll – in the default run that happened in 31.5% of sessions.
Why do most D'Alembert sessions end with a small win?
Bets stay low and a few wins can bring you back to the goal, so many sessions finish slightly ahead. The few sessions with long losing runs lose much more, which makes the average negative.
What is the house edge when using the D'Alembert system?
It equals the house edge of the even-money bet you use. That is 2.70% on the European wheel and 5.26% on the American wheel.