D’Alembert Strategy for Roulette

One of the simplest and safest betting systems in gambling is the D’Alembert Strategy, a negative progression that is incredibly popular, especially among roulette players. It is applied to all even-money bets in roulette, but it functions perfectly with any kind of even-odds bets in other casino games, as well. With this strategy, roulette players raise the amount of their bet each time they lose, while after winning, they decrease it.

Before describing this strategy in detail, we should pay attention to its origins in order to better understand it. It is still unclear who created the D’Alembert system, when and why, but it is named after the French mathematician, physicist, and philosopher Jean-Baptiste le Rond d’Alembert. He lived in the 18th century and is widely known for his various mathematical theories and equations, several principles and interesting paradoxes.

Known as the co-editor of the Encyclopédie along with Diderot, D’Alembert also believed in the gambler’s fallacy. The prominent mathematician falsely argued that the more times a coin flips tails, the more likely it is to land heads in the future. The system bearing his name also lies on the idea that a string of red and a string of black numbers in roulette will eventually balance out. In fact, the majority of betting systems are based on this false belief.

So why are they so popular and why do gamblers still use them despite knowing well that roulette is random and each outcome is independent of the past and future occurrences? Today, such strategies, including the D’Alembert, are used for money management rather than for decision-making. As a matter of fact, many roulette players find the D’Alembert system very effective in providing them with small but consistent winnings.

How It Works

How It WorksThis system is often listed as a type of a Martingale and it could be fairly described as such because it increases the bet after a loss and decreases it following a win. There is one substantial difference between the two systems, however – the classic Martingale doubles up the stake every time the player loses, while the D’Alembert system represents a flatter progression where the bet is increased by a single unit. Thus, players who decide to opt for it would avoid the steep rising of the stakes in the Martingale. Yet, they will need to play longer sessions in order to regain their losses.

As mentioned above, the D’Alembert is designed for even-money bets where two possible outcomes are equally probable. Of course, these are the red/black, the even-odd, and high/low bets in roulette – the chances here are not 50/50, but they are as close to this as possible. The reason for this is the zero (or zeros in American roulette), which is neither red nor black, neither even nor odd, and neither high nor low. The logic behind the D’Alembert concept is that such outcomes will inevitably even out and players will be able to recoup all losses from the previous spins.

Knowledgeable roulette players know, however, that such a balance is simply based on intuition and not on actual facts. Still, they can use the system to successfully regain lost money by increasing their bets after a loss and wait for a winning bet, whose amount will be enough to offset the losses. In order to start using the system, players need to determine the amount of the basic unit they will be wagering on every spin. This could be $5, $10, $20 or even more but a setting a cap for it is a good idea – ito adjust it to each individual bankroll, let’s keep the cap in percentages, up to 5% of the bankroll. Of course, players who are new to the system are advised to start with the table minimum – $5, for example.

So, they wager $5 on red and they lose, in which case, they increase the bet with another unit, i.e. $5 to wager $10 on the second spin. If they lose again, the bet increases to $15 and to $20 if they lose three times in a row. Now, even if the next bet ($20) wins, the payout will not be sufficient to compensate for the losses and players will still be -$10 in the red. If the next bet wins, however, this will change and the net profit will be $5 after such a short session and after only two wins compared to three losses. This can be easily seen in the following table:

Spin Bet Outcome Payout Profit
1 $5 Lose $0 -$5
2 $10 Lose $0 -$15
3 $15 Lose $0 -$30
4 $20 Win $40 -$10
5 $15 Win $30 $5
Total Bet Amount: $65 Total Payout: $70 Net Profit: $5

Longer sessions could be riskier, however, but they could also turn out to be more profitable. As long as players start with a relatively small basic unit, they should be able to turn a nice profit eventually. However, long losing streaks could result in very high bets, which is certainly something most players should avoid. The reason is very simple – several huge wins might be needed for the losses to be recuperated.

When using the D’Alembert Strategy, players will notice that the number of winning spins does not have to be higher than the number of losing ones in order to turn a profit. Sometimes, you can generate decent winnings even though you have lost more spins than you have won. To demonstrate this, we have tried the system in the following example:

Spin Bet Outcome Payout Profit
1 $5 Lose $0 -$5
2 $10 Win $20 $5
3 $5 Lose $0 $0
4 $10 Win $20 $10
5 $5 Lose $0 $5
6 $10 Lose $0 -$5
7 $15 Win $30 $10
8 $10 Lose $0 $0
9 $15 Lose $0 -$15
10 $20 Win $40 $5
11 $15 Win $30 $20
Total Bet Amount: $120 Total Payout: $140 Net Profit: $20

D’Alembert Roulette Strategy Gameplay


Reverse D’Alembert System

Reverse D’Alembert SystemSimilarly to other betting strategies such as the classic Martingale, the D’Alembert system has its opposite counterpart. The Reverse D’Alembert is a positive progression where players increase their bet after a win and decrease it after a loss. Of course, this system is usually applied to the even-money bets in roulette and a basic unit of only several percents of the bankroll is used in the start. As you can see, this method is just as simple and easy to use as the original D’Alembert but it prevents the exhausting of one’s bankroll even if a long losing streak occurs – after a few losses, the progression simply ends as the player has reached the initial betting unit.

While the classic version starts once a loss has been registered, the reversed variation starts after the first winning spin. Of course, the raising and decreasing of the bets is by one unit only, once again. As mentioned above, it is almost impossible to lose large amounts of money using this system. However, players could still end up losing everything if they experience several losing streaks. This method will be suitable for shorter sessions and lower bets – players who prefer high-stakes games might easily lose their entire bankroll if they choose to bet more than 5% of the total budget.

So, let us see an example of the Reverse D’Alembert using $5 as our basic unit. After two successful spins, we have $15 in net profit, but it takes just one losing bet to come out with nothing. As you can see in the table below, after 13 spins of the wheel, we have won only $5. Still, this is one of the positive possible scenarios with this method.

Spin Bet Outcome Payout Profit
1 $5 Win $10 $5
2 $10 Win $20 $15
3 $15 Lose $0 $0
4 $10 Win $20 $10
5 $15 Win $30 $25
6 $20 Win $40 $45
7 $25 Lose $0 $20
8 $20 Lose $0 $0
9 $15 Lose $0 -$15
10 $10 Lose $0 -$25
11 $5 Win $10 -$20
12 $10 Win $20 -$10
13 $15 Win $30 $5
Total Bet Amount: $175 Total Payout: $180 Net Profit:$5

Risks to Consider with the D’Alembert System

Mobile rouletteInterestingly, when using the classic D’Alembert strategy and register an equal number of winning and losing bets, the net profit will be equal to the number of basic units we have started with. It is impossible to predict how many spins we will win or lose, but it is an interesting idea to ponder on, especially when playing longer sequences. In reality, this strategy is more useful in the short term but in longer sessions, it cannot prevent big losses once a losing streak occurs.

This is probably the biggest risk of using the system and players should be very careful when applying it. To turn a profit with it, gamblers would have to score approximately the same number of wins and losses. While in theory, such an outcome is to be expected as the odds for even-money bets in roulette are close to 50%, in reality, things could be very different. As each spin is a random and independent event, we cannot assume that after a long streak of red, the ball would hit black. Even if we do, the house edge of 2.70% to 5.26% means that eventually, players would end with more losses than wins.

The real danger when using the D’Alembert system is to have a long losing streak, which could increase the amount we wager per spin. In some cases, the bet could reach the table limits, which would mean that we can no longer continue the progression and hope to regain the money we have lost. In the example below (the same basic unit is used), you can see how this relatively safe betting system could cost players a lot of money:

Spin Bet Outcome Payout Profit
1 $5 Lose $0 -$5
2 $10 Lose $0 -$15
3 $15 Win $30 $0
4 $10 Lose $0 -$10
5 $15 Win $30 $5
6 $10 Win $20 $15
7 $5 Lose $0 $10
8 $10 Lose $0 $0
9 $15 Lose $0 -$15
10 $20 Lose $0 -$35
11 $25 Lose $0 -$60
12 $30 Lose $0 -$90
13 $35 Lose $0 -$125
Total Bet Amount: $205 Total Payout: $80 Net Profit: -$125

There is a way to avoid such losses and some players prefer to apply it than to rely on uncertain future winnings that are supposed to compensate them. A good solution is to determine a stopping point for the sequence – for instance, you should not bet more than 5 times your initial stake. Although this method cannot guarantee winnings, it can be used to cut the losses to more acceptable levels. Note that while losing $125 on roulette may not sound so much, this loss has been incurred with an initial bet of only $5.

Advantages and Disadvantages of the D’Alembert Strategy

Advantages and DisadvantagesCompared to other betting systems, the D’Alembert method is much safer and easier to use. It does not involve any complex calculations as players are only required to either increase or decrease the amount of their stake, depending on the outcome of each spin. The simplicity of this system is a great advantage when it comes to applying it in real-life games in casinos where players who use it will not be immediately noticed by the security staff.

Having a safe betting system, however, is not always useful for the players because it means that they have fewer chances for recovering the money they have lost. Indeed, with the D’Alembert strategy, the bets increase at a slower rate than in the Martingale but, at the same time, they do not have the potential to compensate you for the losses. In contrast, some systems enable players to recover their losses with a single bet.

Another thing to consider before using the D’Alembert casino strategy in roulette games is that it could be somewhat useful in short sequences where the number of winning bets is close to the number of losing ones. Whenever more than three consecutive losses occur, the bet and the lost amount increase and the player needs to win several spins in a row in order to make even a minimum profit.


Roulette TableClearly, the D’Alembert casino strategy has gained some popularity, especially among roulette players. Others suggest that it is not a trustworthy system because of Jean-Baptiste D’Alembert’s wrong ideas about probability. But even if we remove the gambler’s fallacy out of the equation, the strategy still has its strengths and benefits – it is simple, easy to understand and apply, and it can be used with various even-money or even-chances bets in roulette and in other games.

Moreover, the D’Alembert system is a good option for casino players who are just discovering the great abundance of betting systems on offer. They can try it out with smaller bets and shorter sequences to avoid losing a lot of money in a short period of time. It is always recommended to start with the table minimum and slowly increase your stakes with this system until you turn a small profit or register several losses in a row. Then, you can start the pattern all over again. Overall, the D’Alembert is not the perfect betting system and it certainly has its faults but it could be a convenient tool to manage your bankroll and optimize your play.