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 applies to all even-money bets in roulette and works well with any even-odds bets in other casino games. With this strategy, roulette players raise their bet after each loss and decrease it after each win.
Before describing this strategy in detail, we should look at its origins to better understand it. It is still unclear who created the D’Alembert system, when, or 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 mathematical theories and equations, along with 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 wrongly argued that the more times a coin lands on tails, the more likely it is to land on heads in the future. The system that bears his name is also based on the idea that a string of red results and a string of black results in roulette will eventually balance out. In fact, many betting systems rely on this false belief.
So why are they so popular, and why do gamblers still use them despite knowing that roulette is random and each outcome is independent of past and future ones? Today, such strategies, including the D’Alembert, are used for money management rather than decision-making. As a matter of fact, many roulette players find the D’Alembert system very effective for producing small but consistent winnings.
How It Works
This system is often listed as a type of 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 the stake every time the player loses, while the D’Alembert system offers a flatter progression in which the bet increases by only a single unit. Thus, players who choose it avoid the steep rise in stakes found in the Martingale, but they will need longer sessions to regain their losses.
As mentioned above, the D’Alembert is designed for even-money bets where two possible outcomes are equally probable. These include the red/black, even/odd, and high/low bets in roulette. The chances are not exactly 50/50 because of 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 eventually even out, allowing players to recoup previous losses.
Knowledgeable roulette players know, however, that this balance is intuitive rather than factual. Still, they can use the system to try to regain lost money by increasing their bets after a loss and waiting for a winning bet large enough to offset those losses. To start using the system, players need to determine the basic unit they will wager on every spin. This could be $5, $10, $20, or more, but setting a cap is a good idea. To adjust it to each individual bankroll, keep the cap at up to 5% of the bankroll. Players who are new to the system are advised to start with the table minimum, $5 for example.
They wager $5 on red and lose, so they increase the bet by one unit to $10 on the second spin. If they lose again, the bet rises 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 cover the earlier losses and players will still be down $10. If the following bet wins, however, the net profit will be $5 after only two wins and three losses. This can be 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, but they might also prove 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 most players should avoid because several huge wins might be needed to recover the losses.
When using the D’Alembert Strategy, players will notice that the number of winning spins does not have to exceed the number of losing ones 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
Similar to other betting strategies such as the classic Martingale, the D’Alembert system has an opposite counterpart. The Reverse D’Alembert is a positive progression where players increase their bet after a win and decrease it after a loss. This system is usually applied to even-money bets in roulette, and a basic unit of only a few percent of the bankroll is used at the start. As you can see, this method is as simple to use as the original D’Alembert, but it prevents players from exhausting their bankroll even if a long losing streak occurs. After a few losses, the progression simply ends because 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. Once again, the bets are raised or lowered by one unit only. As mentioned above, it is almost impossible to lose large amounts of money using this system. However, players could still lose everything if they experience several losing streaks. This method is 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.
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 a single losing bet can erase those gains. As the table below shows, 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
Interestingly, when using the classic D’Alembert strategy and registering an equal number of winning and losing bets, the net profit will equal the number of basic units with which we started. It is impossible to predict how many spins we will win or lose, but this point is interesting to consider, especially during longer sequences. In reality, this strategy is more useful in the short term. 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, gamblers need to score roughly the same number of wins and losses. While in theory such an outcome is expected, because the odds for even-money bets in roulette are close to 50%, reality can be very different. Each spin is a random and independent event, so we cannot assume that after a long streak of red, the ball will land on black. Even if we do, the house edge of 2.70% to 5.26% means that, eventually, players will end with more losses than wins.
The real danger when using the D’Alembert system is a long losing streak, which can greatly increase the amount wagered per spin. In some cases, the bet could reach the table limits, meaning we can no longer continue the progression and hope to regain the money we have lost. In the example below (using the same basic unit), 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 use it rather than rely on uncertain future winnings to compensate them. A good solution is to determine a stopping point for the sequence: for instance, do not bet more than five times your initial stake. Although this method cannot guarantee winnings, it can limit losses to more acceptable levels. Note that while losing $125 on roulette may not sound like much, this loss was incurred with an initial bet of only $5.
Advantages and Disadvantages of the D’Alembert Strategy
Compared 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 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 applying it in real-life casino games, and players who use it will not be immediately noticed by the security staff.
Having a safe betting system, however, is not always useful, because it means players have fewer chances to recover the money they have lost. Indeed, with the D’Alembert strategy, the bets increase at a slower rate than in the Martingale, but they also lack the potential to fully offset large 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 may be 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 accumulated losses rise, and the player then needs to win several spins in a row to secure even a minimal profit.
Conclusion
Clearly, the D’Alembert casino strategy has gained popularity, especially among roulette players. Some argue that it is not trustworthy because of Jean-Baptiste D’Alembert’s flawed ideas about probability. Even without the gambler’s fallacy, however, 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 bets in roulette and other games.
Moreover, the D’Alembert system is a good option for casino players who are just discovering the wide range of betting systems on offer. They can try it with smaller bets and shorter sequences to avoid losing a lot of money quickly. It is always recommended to start with the table minimum and gradually 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 again. Overall, the D’Alembert is not a perfect betting system and it certainly has its faults, but it can be a convenient tool for managing your bankroll and optimizing your play.