The D'Alembert Progression


How the D'Alembert Progression works

The D'Alembert betting strategy is named after the French mathematician and roulette theorist Jean le Rond D'Alembert who lived in the 18th century. Just like the Martingale it is based on a progression after each loss, meaning that the bet is being increased after a losing round. The original D`Alembert progression for the even money chances follows an arithmetic row:

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - ...

It always starts with a base bet of 1 unit. After a loss the bet size in the next stage is raised 1 unit and after a win the bet size for the next stage is reduced by 1 unit. As a result of the flatter progression, one winning coup does usually not cover all losses that were made before.If wins and losses are balanced, the D`Alembert wins 1/2 unit per spin.

The disadvantage of the normal D`Alembert is that the higher the bets become, the recovery force of the progression gets weaker and weaker. This is always the case, when the spin run is imbalanced over a longer period. The draw downs can get pretty frightening and furthermore losses due to zero / double zero are almost impossible to regain. However the chances are much smaller that the player goes bankrupt or reaches the table limit before he can make up for previous losses than by using the Martingale. The aggressive mode of this progression avoids most of the above disadvantages. Instead of lowering the bet size after a win, it remains at the same level until a new loss is encountered. Then the bet size goes up 1 unit as usual. Nevertheless the D'Alembert system definitely has its pitfalls when it comes to its practical use.

The Contre D'Alembert Betting Strategy

As a result of the disadvantages that come with the D'Alembert roulette system – which mostly arise from progressing after lost coups, some mathematicians came up with a Contre version. The roulette Contre D'Alembert system basically works like the regular D'Alembert, only the other way around - instead of progressing after a lost round, the player increases the bet after a win. So after every round you win, you have to add one chip to your total bet, and after you lose, you take one chip away – unless you are already playing with just one chip, then you just leave it at that. The advantages compared to the regular D'Alembert roulette system are that the player needs even less money to use it. If you happen to have a long losing streak, you don't have to try compensating it by betting more and more chips.

RNG and Live Dealer Tests of the D'Alembert Strategy for 32000 bets

For demonstration purpose we have tested a simple roulette system. The rules are just to bet on Low using the D'Alembert. The first test run shows the results for the D'Alembert Strategy if there was no zero on the roulette wheel for the purpose of demonstration how it work for real 50:50 chance games. Hence you know what to expect if you use the strategy e.g for bets on Player at Baccarat. The almost equal distribution of High/Low results with 15994/16006 gives a profit of 14466 units seeing a maximum drowdown to -14622 units. The highest bet amount is just 194 units.

The results for single zero roulette wheels are shown in the other two tests. As you can see in the charts the bet amounts continuously climb up to a maximum of 936 units observing a longest losing streak of 18 spins and a longest winning streak of 15 spins in the RNG test with 15543 wins and 16457 losses. The Live Dealer test shows a maximum bet amount of 878 units a longest losing streak of 15 and a longest winning streak of 11 spins with 15574 wins and 16426 losses.

Live Dealer Tests Results without Zero

RNG Tests Results

Live Dealer Tests Results