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The D'Alembert System For Roulette - A How To Guide

The illegitimate son of a prominent French artillery officer, Jean-le-Rond D'Alembert was effectively abandoned as a child, and grew up in relative poverty - although his father did forward sums of money to the foster parents so that D'Alembert could be given a good education. He threw himself into maths and became famous for a series of mid-18th century works that explored and developed the ideas of Newton. One of his lines of inquiry led him to experiment with a gambling system - now named after him. We'll take a look at this system, and see if it still holds water.

How It Works

 The system is relatively simple to explain, and will be mostly straightforward to implement - just as long as you can hold a number in your head. As with the numerous other systems, it's assumed that you'll be betting repeatedly on a 50/50 selection - such as Red/Black or Odd/Even.

The system works using 'units'. A unit can be as small or as large as you wish, but you will end up having to bet lots of units at some point, so you shouldn't make an individual unit higher than 1% of your total fund - 0.5% or 0.33% would be safer still. For the sake of our demonstration, we'll assume one basic unit is worth £1.

The theory behind the D'Alembert System is that you gradually increase the amount being bet when you're doing badly, and gradually decrease it when you're doing well. So you start off by betting one unit (£1) on red. If it wins, then you simply repeat the process. If that first bet loses, though, you increase the number of units by one. If you lose a second time, you add another unit. And so on.. If you win, on the other hand, you decrease the number of units again - until, eventually, you get back down to one unit. A typical start to a game might look like this:

- Bet £1. Lose
- Bet £2. Lose
- Bet £3. Lose
- Bet £4. Win
- Bet £3. Win
- Bet £2. Lose
- Bet £3. Win (the next bet would be £2, and so on..)

There is no 'get out' point. You simply keep on betting and betting until you have had enough. Some times you would be facing considerable losses, but you carry on regardless.

The flaw in the original rules

Using the outline above, it quickly became clear that the system, as propounded by D'Alembert himself, doesn't actually work very well. In testing, we were regularly losing lots of money - typically in excess of 30K over the course of 10,000 spins! A little think about the system, though, explains why the original set of rules were defective. When the number of units is relatively low, increasing them by one unit makes for quite an impact - the difference between betting two, three or four units is considerable. However, play the system for a considerable period, and you'll find that there are stages where you're betting much larger numbers of units - 20 or 30, for instance. It makes little real difference whether you're sticking on 30, or increasing it to 31 units. Hence, the system becomes largely invisible, and the winning odds become the dominant factor instead - and, as we know, even on a European-style table, the odds are against you.

The poor odds mean that you're consistently losing over time. But the D'Alembert system magnifies this, gradually increasing the number of units in line with your worsening financial situation. Betting one unit a time on a losing system is painful, but betting 30 units a time makes it utterly disastrous. If we take away the house edge, the system effectively breaks even - even though you would still get some significant losing runs in there. But with even a small house edge working against you, it's a no-hoper.


 In fairness to D'Alembert, he didn't have the access to the sophisticated computers that we have today. If he had, he may well have examined his system, and come up with a better version. There aren't too many possible variations, but we've come up with a couple that may make for interesting reading.

Clearly, the important thing is to change the unit subtraction so that you don't build up those large 20, 30+ sequences that never come down again. Winning must have a greater effect on the number of units. We started off by having the simple rule that, when you win, the number of units gets reset to one. The effect here was dramatic, with the system losing, but only losing small sums. The house edge means that we still lose, but without the magnification effect of the original system, we only lose small amounts. Indeed, given the way it accounts for losing sequences by adjusting the number of units, the system actually compensates for many of the losses. Without the house edge, this is a profitable system. With it, it's a fairly marginal loser, dropping around £600 on average every 10,000 spins.

What about a less dramatic version of the original system? We tried doubling the rate at which the number of units comes down. A loss still increased the number of units by one, but a win now resulted in the number of units being reduced by two. A brief run of wins would quickly cut the number of units back to its starting position. This turned out to be the best move of all, getting the losses down to around £500 on average. Without the house edge, this was a more than profitable system overall - over the long term, we made many four figure sums for every 100,000 spins. (Note: That does say 100,000 and not 10,000) Even here, there were some four figure losses, but overall, the system worked.

Buoyed by this success, we tried decreasing the number of units (after wins) by larger amounts. This was to little avail, though. Increasing it to three units slightly dampened the profitability, and the system started doing much less well at four units and above. Keep it to a 2:1 ratio, however, and you seem to get optimum results.

The best system?

We didn't find many drawbacks with the modified 2:1 system. Unlike the Martingale System, the rate at which bet size goes up is relatively modest. Obviously though, you can still find yourself having to place some sizeable bets before things improve. Over the course of a long run, you should expect to find yourself betting 10 or 11 units a number of times. Using units of £1, this meant we could find ourselves £60 to £70 down at some points. Forays above 11 were rare, although they do happen over a very long period. Over the course of 100,000 spins, for instance, the worst extreme we saw was a betting unit tally of 19 - a fall in our bank account of £179. If you were playing on a table with no house edge, and weren't likely to face problems with table/bet limits, a bank of £300 or £400 would generally allow you to negotiate even lengthy losing runs while playing with £1 units. This wouldn't insulate you against lengthy general losing runs, though, and those can still get up to four figures.

Clearly, the biggest problem is that the system can't overcome the house edge - in fairness, negative expectation is a killer for essentially any system. Even with no edge working against you, it's possible to find yourself several thousand down over the course of 100,000 spins, so this isn't a surefire route to riches. However, our modified version performed better than any system we've seen. With a little bit of skill, or access to a no house edge table, this could be an excellent system. You'll still need a handsome bank, but for a relatively pain-free way of playing - and quite possibly coming out ahead after a few hours at the casino - D'Alembert works.


- Modified systems profitable if you remove the house edge
- Bet sizes never get too high
- Relatively straightforward to play


- Original set of rules useless
- Can't offset the house edge
- With no house edge in play, the system would be profitable over the
very long term, but could still see four figure losses in the medium
- No jumping out point