D'Alembert Strategy in Roulette

D'Alembert Roulette Strategy

The betting system D'Alembert bears the name of its creator, the French scientist and mathematician Jean Le Rond D'Alembert (1717-1783). This strategy has been known for a long time and applies not only to roulette and similar games, but also to bets in general and the stock market. The great advantage of the D'Alembert system is the simplicity of its rules. Simple odds are played with payments of 1 to 1, which in roulette means betting on red/black, odd/even or low/high. The player determines the value of their base bet, considering their bankroll and the bet limits of the table. They then choose what they are going to bet on and make their first base bet.

How D'Alembert works

According to the D'Alembert strategy, in case of profit it is necessary to increase the next bet by one base bet, while in the case of a loss they must subtract the amount of one base bet.

It is a progressive betting system, in other words, the bet of the player increases or decreases in relation to the different situations of the game. This is done in an arithmetical way with amounts equivalent to the base bet.

Unlike the progressive Martingale system, in which the bets are increased geometrically, in the D'Alembert strategy, the fluctuations of the bet size occur more slowly.

Since the bankroll is spent more sparingly, especially if there are a series of unfortunate runs, the D'Alembert system is recommended for all new roulette players, since possible beginner errors will not be so expensive if this system is used. As the rules are simple and the strategy easy to follow, it will be difficult to make mistakes.

D'Alembert vs Martingale Strategies

The following table allows you to compare the strategies of D'Alembert and Martingale with the examples of the increase of the bet in the case of a series of 7 non winning spins:

1 1 1
2 2 2
3 3 4
4 4 8
5 5 16
6 6 32
7 7 64
TOTAL 28 127

In mathematical terms, in this table we compare the arithmetic and geometric progression. The difference is only noticed in the third unfortunate roll where the player who follows the Martingale system spends one more base bet.

However, with each of the following unfortunate rounds, the difference in game costs grows significantly. It is difficult not to see how in a series of 7 losses, the player who follows the D'Alembert system spends a total of 28 base bets. On the next roll, the eighth, when increasing by one, the next bet must be 8 times the base bet plus the size of the base bet with which the game started. To continue playing after seven consecutive unfortunate runs, the player will need a total balance of 36 (28 + 8) initial base bets.

With the Martingale system, in the same situation on the eighth roll, the player would need a fund of 255 base bets.

So, playing according to the Martingale strategy, the player aspires to win the entire lost balance with a single roll. If they have just one successful roll, they can come out with a win amount of a considerable size.

When winning the eighth roll, the player according to D'Alembert strategy, recovers only 8 of the 28 losing bets and reduces them by just one quarter, so you can see that using this lower cost strategy also affects the winnings.

Whoever plays roulette according to the D'Alembert betting system does not need a large bankroll as can be seen from the calculations in the previous table, around 36 base bets is sufficient to sustain a series of eight runs that are consecutively non winning, which gives an advantage. Of course, the bigger the player's opening balance compared to the base bet, the better.

In relation to this, online casinos offer more advantageous conditions. In physical casinos the average minimum bet is 10, so 36 base bets equals 360, in the large online casinos you can find tables with minimum bets of 1. Therefore, with the same financial fund of 360, on the internet the player gets the chance to play with a bankroll that exceeds the base bet by two zeros.

Another even more significant advantage of the D'Alembert roulette strategy is its relatively lower dependence on the betting range, often limited by the casino. The minimum and maximum of bets for the simple odds at any table usually vary between 30-50 in the different establishments and less frequently there are tables with a wider range of limits for the player.

As shown in the table and previous examples, playing at a roulette table with betting limits of between 10 and 500, the player according to the Martingale system will, by the sixth round, have problems making the bet of 640, which would exceed the maximum allowed by casino rules.

Under the same conditions, the player who is following the D'Alembert strategy, would only have problems with the maximum limit if they had 50 consecutive non winning rounds.