D’Alembert System

While the Martingale system makes a player increase his bets extremely rapidly to recover his losses as soon as possible, the D’Alembert betting system aims to take a bit longer than one winning spin to make a profit. It uses even money outside bets and is based on the idea that a player is just as likely to win as he is likely to lose.

History of the D’Alembert Roulette System

In the late 18th century, a time of many discoveries in mathematics and physics, the Italian-French scientist Joseph Louis Lagrange, and later the French mathematician Jean le Rond d’Alembert, worked on a statement of the fundamental laws of motion. They concluded that "the sum of the external forces acting on a body and the inertial forces are a system in equilibrium". This is a generalization of Newton’s Second Law and it is called the D’Alembert Principle.

When this law of equilibrium is applied to games of chance, it leads to the belief that future outcomes will be more likely to balance unlikely variations in the past. This means that, for instance, after a long streak of black, red becomes a more likely outcome. As such it is simply a rephrasing of the gambler’s fallacy and not true. However, it means that the D’Alembert system is based on the player winning as often as he loses.

How the D’Alembert System works

The system is based on the belief a player is as likely to win as he is to lose, and when D’Alembert is used it will generate a profit if the player wins as often as he loses (or more). It is a negative progression system, upping the ante after every loss. It is also called the Pyramid System because it uses increases and decreases of 1 unit for losses and wins, respectively.

The D’Alembert roulette system works as follows: start by betting an initial amount on an even money outside bet. After a loss, increase the bet by 1. After a win, decrease the bet by 1. Once the player has won exactly as many times as he has lost, the system is sure to deliver a net profit. Of course, this can happen earlier as well.

An example of D’Alembert

Here is how the system would work if we start by betting 3 chips and would have the following sequence of wins (W) and losses (L): LLWWLW.

  1. We bet 3 chips. We lose.
    Net: -3
  2. We lost, so we increase the bet by 1. We bet 4 chips and lose again.
    Net: -3-4 = -7
  3. Another loss, so increase to a bet of 5. We win!
    Net: -3-4+5 = -2
  4. After a win we decrease the bet to 4. We win again.
    Net: -3-4+5+4 = +2
  5. We won, so we decrease the bet to 3. We lose.
    Net: -3-4+5+4-3 = -1
  6. After this loss we increase the bet to 4. We win once more.
    Net: -3-4+5+4-3+4 = +3

As you can see, after winning and losing both 3 times, the net profit is 3 chips. This is true, regardless of the initial stake, so the initial bet should be 1 chip. This is why: in this example, we needed 12 chips to win 3, whereas if we had started with betting just 1 chip, we would require only 6 to win the same amount.

Also, the final profit, after an equal number of wins and losses, is exactly the number of winning spins.

Advantages and drawbacks

The single biggest advantage to this system in comparison to others is that the potential losses it generates increase very slowly. The immediate drawback related to this is that it requires a player to win just as often as he loses; the only system to go even slower is Oscar’s Grind. However, this is a very simple system, making it easy to use.

A big disadvantage to this system lies in the fact that it indeed requires a player to win as many times as he loses. But remember that in roulette, the even money outside bets do not have a win chance of 50% (or 1 in 2), but of 18 in 37 (or 18 in 38 for American roulette). This means that in a long streak of wins and losses, statistically a player will lose more often than he wins, which will make him less likely to recover lost money.