D’Alembert Betting System

The D’Alembert is among the easiest betting systems, applicable to the game of roulette. In fact, this system ranks second in terms of popularity after the Martingale. It bears many of the characteristics of the Martingale, which is not surprising considering the fact both systems are based on negative betting progressions. Therefore, the D’Alembert dictates that players should increase the size of their stakes after a loss and decrease it after each winning bet.

The origins of the D’Alembert system can be traced back to the 18th century, when the French mathematician Jean le Rond D’Alembert began his work on a statement of the fundamental laws of motion. The mathematician came to the conclusion that the external forces acting on a body and the inertial forces are a system which exists in equilibrium. This conclusion laid the foundations of Newton’s Second Law and became known as the D’Alembert Principle.

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How Does the D’Alembert Betting System Work

When applied to games of chance like roulette, D’Alembert’s law of equilibrium inspires the idea that future outcomes of wheel spins can balance less likely variations in the past. According to D’Alembert, the chances of a coin landing on tails increase if it has already landed on heads several consecutive times.

In other words, if the ball lands in red pockets several times in a row, black is due to be spun and becomes a more likely outcome. This concept is also known as the Gambler’s fallacy. However, this serves as an indication that the D’Alembert system is based on the idea that players, who place even-money bets, will generate a profit if they win as often as they lose or more.

The D’Alembert system is quite simple to learn, even by roulette novices. The first thing you need to do is set a base betting unit depending on the overall size of your bankroll. It is important to mention your betting unit should not exceed 5% of your bankroll for the session. A betting unit of 2% is considered the safest option.
The D’Alambert system dictates you should start by placing an even-money bet of precisely one betting unit. If your luck fails you on the first spin and you lose, you need to increase your next wager with one betting unit. You keep increasing your wagers with a single betting unit after each loss.

After each winning bet, you are required to reduce your next stake with one betting unit. If your first bet is a winning one, you continue wagering with the same base betting unit until you lose. The idea here is that if a given player wins and loses roughly the same number of times, they will eventually turn a profit.

It would be best to demonstrate how the D’Alembert works in practice by providing an example. Let’s assume your bankroll is £250 and your betting unit is £5 or 2% of the overall sum you intend to join the roulette table with. You bet £5 on Red and lose. You increase your next wager with one betting unit, so you bet £10 on Red and lose again. At this point, you have lost £15.

You increase your next wager on Red to £15 and win this time, collecting £15 in net profit. After this success, you are supposed to reduce the next wager with one betting unit to £10. You bet on Black and win again, generating a net profit of another £10. It becomes clear you have won £25 with your last two bets and have lost only £15 with your two losing wagers – your net profit for this betting session is £10.

As you can see, the D’Alembert system works efficiently as long as the number of winning bets coincides with or exceeds that of losing bets. Of course, there is the option to set a limit at which you will stop increasing the stakes after a loss and reduce the betting unit to its initial size to start from scratch. This modification can help you minimise your losses if you happen to enter a longer losing streak.

The D’Alembert System
Spin Bet (units) Outcome Total Profit
1 5 LOSS -5
2 10 LOSS -15
3 15 WIN 0
4 10 WIN 10
5 5 WIN 15
6 5 LOSS 10
7 10 LOSS 0
8 15 WIN 15
9 10 WIN 25
10 5 LOSS 20
11 10 WIN 30
12 5 WIN 35
13 5 WIN 40

The Reverse D’Alembert

Similarly to the Martingale, the D’Alembert system has its positive-progression counterpart, known as the Reverse D’Alembert. This variation works on the same principle but the other way around, and is suitable for even-money bets in roulette.

Players are again recommended to choose a base betting unit which should range between 2% and 5% of their overall bankrolls. Your first even-money bet should be one betting unit. According to the Reverse D’Alembert, players should increase their stakes by one betting unit after each winning bet.

So if your first bet of £5 on Red wins, your second bet should be no more than £10. If you are successful again, your next wager needs to be £15 and so on. When players lose a bet, they are required to decrease their next stake by one betting unit. So if you lose your third bet of £15, you reduce the next wager to £10.

One major advantage of the Reverse D’Alembert is that it enables players to minimise their losses and generate greater profits. Those, who implement the Reverse D’Alembert, are less likely to exhaust their bankrolls when they experience a lengthy losing streak. Besides, implementing this variation may prove to be rather profitable if the player wins several bets in a row.

The Reverse D’Alembert System
Spin Bet (units) Outcome Total Profit
1 5 WIN 5
2 10 WIN 15
3 15 LOSS 0
4 10 WIN 10
5 15 WIN 25
6 20 LOSS 5
7 15 LOSS -10
8 10 WIN 0
9 15 WIN 15
10 20 LOSS -5
11 15 WIN 10
12 20 WIN 30
13 25 WIN 55

Advantages of the D’Alembert Betting System

Without question, the biggest advantage the D’Alembert system has to offer is its very simplicity. It does not require players to take notes like some other systems do. On the contrary, the system is quite easy to learn and incorporate at the roulette table.

Another advantage results from the fact there is no steep increase of the bet size with this negative progression system. As wagers are increased with a single betting unit after each loss, a longer losing streak is less likely to drain your bankroll completely. The D’Alembert system also enables those who follow it to generate a consistent profit.

The size of the wager after each loss is increased slowly which renders the system suitable for players who do not have sizable bankrolls to play with. Besides, the risk of reaching the table limit on a lengthy losing streak is much smaller if you implement the D’Alembert.

Disadvantages of the D’Alembert Betting System

Similarly to the other betting systems we have discussed so far, the D’Alembert has a few faults. The system is most effective when it comes to generating short-term profits. Though consistent, the winnings will be far from life-changing which is to be expected from a system that involves a relatively low degree of risk.

Then again, in order to turn a profit at all, players are expected to win and lose roughly the same number of times. Unfortunately, there is no guarantee that this will happen since the chances of winning and losing with even-money bets in roulette are not exactly 50%. The scales are tipped in favour of the casino because of the introduction of the zero pocket on the wheel. Even more so, if one plays American roulette, where there is an additional double-zero pocket, which further increases the house edge. Statistically speaking, players lose more often than they win which would make it more difficult for them to recover from their losses.

Entering a longer losing streak is not that unlikely, either. If a given player suffers five or six losing bets in a row, there is no guarantee they will succeed in winning the same number of times to offset the losses. Essentially, players need to remember that neither the D’Alembert nor any other betting system can reduce the house edge or influence the spins. This is so because the outcome of each spin is not affected by the previous numbers which had been spun on the wheel.