The D’Alembert Roulette System Explained: Tips for Consistent Play

Jean-Baptiste le Rond D’Alembert was a French mathematician who was something of a Renaissance man.  He studied science, Latin, mathematics and music during the mid- to late 1700s. 

While he certainly won ‘the best name for a French mathematician’ award, the system named after him, the D’Alembert Roulette System, is now seen as being based on a fallacy.

The D'Alembert system, sometimes written as the dalembert system, is a negative progressive system that he set up to reflect his belief that if you lose, you should increase your bet as you’re more likely to win going forward.

His theory has been debunked but, in his time, he was a highly respected figure and his theory was well-regarded.

Once you have read through this article, you will know what the D’Alembert system is, how it works, how to bet it and when it might work for you.

What is the D’Alembert System?

The D’Alembert roulette system is a low-risk betting strategy where you increase your bet by one unit after a loss and decrease it by one unit after a win. It aims to balance losses and wins over time, reducing risk compared to other systems like Martingale.

How the D'Alembert System Works

The D’Alembert Betting Strategy is a simple system to understand and to follow.  It can be used on even money roulette bets like Red/Black, High/Low and Odd/Even.  

In this article, we’re going to look at two different philosophies. 

The first is if you start with a two-unit bet of $10.  Then we’ll look at what happens if you start with the lowest amount, the one-unit $5 bet.

The reason we’re going to start with a two-unit bet of $10 is if you start with a $5 bet and your first spin wins, you cannot reduce your bet because you’re already at your lowest amount.

As you can see, the D’Alembert works very well for even money bets like Red and Black on Roulette. 
(As a sidebar, it also works great on other even money bets like the Player or Banker bet in Baccarat, or the Pass Line or Don’t Pass Line in Craps).

Here are two tables of the results of 12 spins from a free roulette game I found online. 

I started with a two-unit bet of $10. 

I increased or decreased my bet by one unit ($5) after each spin.

Here's the system in action starting with a $10 bet on Red.

And here's the system in action starting with a $10 bet on Black.

As you can see, the outcomes were significantly different depending on the number of wins or losses incurred.

The Bet on Red Table had 8 wins out of 12 and a total win of $45.

The Bet on Black Table had 8 losses out of 12 and a total loss of $50, for a $95 total variance between the two.

What is interesting to note is that the system becomes less volatile if you start with a $5 bet, versus the $10 bet.  

It doesn’t seem like there would be much difference, does it?

The two tables below show you how the numbers change based on starting with a $5 bet instead of a $10 bet. 

Here's the system in action starting with a $5 bet on Red.

And here's the system in action starting with a $5 bet on Black.

The Bet on Red Table had 8 wins and a total win of $40.

The Bet on Black Table had 8 losses and a total loss of $30, for a $70 total variance between the two.

Reverse D'Alembert Strategy

The Reverse D’Alembert is a simple system to understand in that you do the exact opposite of the D’Alembert System. 

You increase your bet by one unit if you win, and you decrease your bet by one unit if you lose.

Essentially, it becomes like a Paroli Light – you’re betting the winnings back but not all of the winnings, so you’re riding the winning streak, but still taking some profit along the way.

Advantages and Disadvantages of the D’Alembert System

The advantages of the D’Alembert system are that it is a low-risk, easy-to-implement system that is also easy to understand and execute. 

While it is based on the fallacy that the roulette wheel wants to come up red after a few black spins in a row (it doesn’t), the system requires that you reduce your bet by one unit if you win and increase it by one unit if you lose.

The main disadvantages of the D’Alembert betting strategy are that it can lead to significant losses if you run into a long losing streak.  

Even though you are only increasing your bet by one unit, with a 7 or 8 spin losing streak, your bet can get to $35 or $40.  

And the cumulative effect of that is that you may lose $150+ by the end of the streak.

The other disadvantage is that once you get to a $40 bet and hit a winner, you only win $40.  Which means you are still losing $100+ after your losing streak. So the system doesn’t allow you to catch up quickly like the Martingale, for example.

Best Situations to Use D'Alembert

The best time to use the D’Alembert is if you want to play for a long time, have a smaller bankroll, and want to play a low-risk strategy with the opportunity for some small wins. 

You will probably be able to build up some comp value along the way, but you won’t have much opportunity to hit a big winner because you’re reducing your bet as you win.

It is a conservative system, but you may be able to hit a few winners and build them up into enough to cash out a small win.

The D’Alembert is not the best system to play if you’re looking to hit a home run winner. 

It is a conservative system and is designed to be low risk, so the opportunity to win big isn’t built into this system.

Managing Your Bankroll with D'Alembert

Bankroll Management is one of the most important parts of being a successful player of any casino game. 

Having a separate bankroll for gambling is critical, and it needs to be kept totally separate from your ‘real life’ bankroll.

Your real-life bankroll has your paycheck going into it, and your rent and car payment and food budget etc coming out of it.

The gambling bankroll needs to be kept in two parts.  One is ‘today’s session’ bankroll, and the other is ‘lifetime bankroll’.

Your session bankroll should be 100 times your unit bet. So with a $5 unit, your ‘today’s session’ bankroll should be $500.  However . . .

How to Set Betting Limits and Unit Sizes

Because you are playing roulette and using the D’Alembert system, your bankroll can be reduced to $300 or so. 

The reason is because the D’Alembert is a very conservative system, and you are certainly going to experience some small wins along the way.

If you were playing blackjack, or craps, I would suggest the $500.  But because it’s roulette and the D’Alembert, you can reduce it to $300. 

Please go here and read my article on Bankroll Management. It’s specifically written for blackjack, but the main points translate perfectly to roulette.

Comparing D'Alembert with Other Systems

The D’Alembert System is a more conservative betting system than the Martingale, and the Martingale is quite high-risk. 

The D’Alembert is much less volatile than the Martingale system, because the Martingale requires that you double your bet with a loss, until you finally win. 

When you do so, you win back all your losses, recouping them all at once. 

The Martingale can also get you into deep water quickly, and you may find yourself with a very large bet to win only a small amount. 

You may also run into the table maximum before you hit the winning bet that returns all your losses to you.

The LaBouchere System

This system requires that you decide how much you would like to win and divide that amount into a sequence. 

The Fibonacci Sequence

This is a well-known sequence of numbers that often appears in nature. 

The numbers come from adding the previous two numbers together and adding the sum to the sequence.

You start with one unit, and you bet through the sequence if you continue to lose. 

If you win, you go back two numbers in the sequence and start again from there. 

You can read my other guide to find out more about these betting systems (and others) that you may find of value.   

Realistic Expectations and Limitations

Let’s talk about probabilities and how Jean-Baptiste thought about them. 

At first glance, it seems to be logical that there should be an equal number of red and black outcomes on a roulette game.  And that’s what he thought, too.

Except that the roulette wheel and ball are inanimate objects.  Neither has any recollection of what happened last spin.  Or the spin before that.  Or ten spins ago.  Or fifty spins ago.

Which means that if we have ten black spins in a row, the odds of red coming up next are exactly the same as before any other spin.

No matter how many black spins have shown up in a row, the odds of red (or black) coming up next are unchanged. 

So even though Jean-Baptiste was a bright, well-educated guy, he didn’t understand that the odds of black coming up don’t change if red has hit 6 times in a row.

Understanding the Statistical Odds and House Edge

There are 37 numbers on a European roulette wheel (1 – 36 and a single zero), and 38 on an American wheel (1 – 36 and single and double zero).

The House Advantage on a European wheel is 2.7%, and on an American wheel it’s 5.26%, almost double. 

So it makes sense that you should always try to play on a European wheel, doesn’t it?

And if you add in the ‘La Partage’ or ‘En Prison’ rule, it drops the HA on the even money bets like Red and Black to 1.35%. 

These two rules are only available on a European wheel and when zero hits, they give 50% of a losing bet on Red/Black, High/Low or Odd/Even back to the player.

Final Thoughts & Best Practices

Never mix your ‘real life’ bankroll and your gambling bankroll.  It’s a recipe for disaster.

If you’re looking to play roulette with a low-risk conservative system, to pass the time and perhaps generate some decent comp value, then the D’Alembert might be exactly the system you are looking for.

Always try to find a European wheel that has the La Partage or En Prison rules in place and play there, not on the American wheel.  It’s definitely worth the effort to do so.

Always have an amount you’re willing to win when you go to the casino or login online, and when you get there, cash out and walk away.