The D’Alembert Strategy Explained

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The D'Alembert strategy is one of the most popular betting systems in the world, commonly used on roulette games. It’s a negative progression system named after the French mathematician Jean-Baptiste le Rond d'Alembert, who developed the strategy in the 18th century. 

Based on the idea that winning and losing game rounds occur just as often, the concept behind the D’Alembert strategy is to increase your bet size whenever you lose a game round and decrease it whenever you win. As long as about 40% of game rounds are won, a net profit is secured. 

Unlike other betting systems, the D’Alembert strategy is simple to understand and implement, and of low risk to your bankroll. However, as we will cover in this article, it is not a flawless system

How Does the D'Alembert Strategy Work?

The D’Alembert strategy is typically used for even-money bets in roulette, such as red or black, odd or even, or high or low numbers. However, it can also be used on other games. 

For the strategy to work as intended, you should place bets that pay 1:1 and have as close to a 50% chance of succeeding as possible. In roulette, the aforementioned bets have a 48.65% win rate.

Here's how the strategy is applied in four simple steps:

  1. Start by choosing your initial bet amount, which will be referred to as a unit. This can be any amount you are comfortable with, but starting with a relatively small bet is recommended.
  2. After each game round, decrease your bet by one unit if you win and increase your bet by one unit if you lose. As mentioned above, a unit is equal to your initial bet amount. 
  3. Whenever you win a game round on your initial bet amount, it is not possible to decrease your stake by one unit as that would mean betting nothing. In this case, you just bet the same amount again.
  4. Continue this process for as long as you like, adjusting your bet size based on the outcome of each game round. 

Here’s an example of 18 game rounds using the strategy:

RoundBet (₹)OutcomeCurrent Balance (₹)

The Goal of the D’Alembert Strategy

The core principle of the D’Alembert strategy is that you will win 50% or close to 50% of all game rounds during a gambling session. If this is achieved, you will reach a profit that is equal to your initial stake multiplied by the number of won game rounds. This is illustrated in the example above where we have an initial stake of ₹10, a total of 9 won and 9 lost game rounds and a final profit of ₹90.

What’s interesting though is that you don’t have to win 50% of the game rounds to reach a profit with the D’Alembert strategy. As can be seen in the table, the profit is already reached on the 16th game round with a total of 7 wins and 9 losses. That’s a win ratio of 43.75%. This is below the 48.65% win rate that red/black, odd/even, and high/low bets have in roulette.

Does this mean that the D’Alembert strategy guarantees a profit? In theory, yes. In reality, no.

The Reason the D’Alembert Strategy Doesn’t Work

While it appears to be bullet proof, the simple reason that the D’Alembert strategy doesn’t guarantee a profit is that no gambling session is guaranteed to provide a win ratio of 43.75% or higher. Of course, in the long run, the odds do tell us that of all played game rounds the win ration will be 48.65%. This does, however, not matter on individual gambling sessions.

The D’Alembert strategy fails whenever your gambling session suffers from too many losses compared to winning game rounds. For instance, if you consistently only win a third of the game rounds, the stakes will keep getting higher and higher. Although the stakes only increase by one unit at a time, you will eventually come to a point where the bet is too high for your bankroll to handle or you have reached the maximum betting limit of the game. 

With that being said, many gambling sessions will in fact have a high enough win ratio. That’s why you can expect to end a lot of them in a profit when you apply the D’Alembert strategy. These profits do, however, come at the cost of losing more on those gambling sessions that turn out to be bad. 

Advantages of the D'Alembert Strategy

  • Simple to understand and implement: The D'Alembert strategy is straightforward to understand. It involves increasing or decreasing your bet size based on the outcome of previous bets.
  • Can help manage your bankroll effectively: The strategy aims to minimize losses by increasing bets after a loss and decreasing bets after a win. This allows you to control your bankroll and limit potential losses. 
  • Ends most gambling sessions in a profit: Since you only need to win 43.75% of game rounds to profit, you are likely to end a gambling session with a positive balance as long as you place bets with a higher win chance.
  • Less risky than other strategies: This strategy is often considered conservative. With bets only increasing one unit at a time, there is no risk for the stakes to suddenly become very high.
  • Can add entertainment value: Following a structured betting pattern could potentially make a gambling session more interesting.

Disadvantages of the D'Alembert Strategy:

  • Does not guarantee a win: Although promising on paper, the D'Alembert strategy does not guarantee consistent wins. It is based on the fact that a certain percentage of game rounds are won, but there is always a risk of very long losing streaks.
  • Can lead to significant losses: The D'Alembert strategy is a negative progression system, meaning you increase your bets after a loss. If you encounter a long losing streak, this can lead to larger bets and potential losses.
  • Limited win potential: The strategy's conservative nature means that the potential for big wins is limited. It focuses on small, incremental gains rather than aiming for significant profits.

Bankroll Requirements

To determine the ideal bankroll for the D'Alembert strategy, you need to consider the following factors: 

  1. Betting unit: Decide how much you are comfortable betting as one unit. This could be a percentage of your overall bankroll or a fixed amount. 
  2. Risk tolerance: Assess your risk tolerance level. The D'Alembert strategy is considered low-risk, but it still carries the risk of a prolonged losing streak. Determine how much you are willing to risk losing before reaching your limit. 
  3. Game parameters: Consider the specific game you will be using the strategy on and its betting limits. Different casino games like the Aviator or Poker have different minimum and maximum bet requirements. Ensure that your bankroll sufficiently covers the minimum bets and withstand potential losses.

As with any betting strategy, the bigger the bankroll you have, the more likely it is for you to end your gambling session in a profit. However, a bigger bankroll also means you’re at risk of losing more. 

History of the D'Alembert Strategy

As briefly mentioned in the introduction, the D'Alembert strategy emerges from the intellectual legacy of Jean Le Rond D'Alembert, a distinguished French mathematician and physician of the 18th century. D'Alembert sought to refine the Martingale betting strategy, aiming to mitigate its inherent risks with a more balanced approach.

D'Alembert was inspired by the principle of balance in two outcomes with a 50% probability. He posited that if one outcome occurred repeatedly, the likelihood of the other outcome would correspondingly increase to restore balance over time. 

For instance, in the context of roulette, D'Alembert theorized that a series of game rounds resulting in red would incrementally boost the chances of the next game round being black. Thus, eventually balancing the distribution of red and black outcomes.

This theory, however, is founded on a misunderstanding of probability, as modern understanding confirms that each roulette spin is an independent event. The odds of landing on red or black remain constant, regardless of preceding results. Despite this, the D'Alembert strategy has been influential in the development of betting strategies.

Mattias Fröbrant is a passionate iGaming journalist renowned for his comprehensive reviews of over 300 gambling sites in India. With a remarkable 17-year gambling experience and a background working for industry giants like Betsson Group, Mattias has earned recognition as a leading expert in the Indian online gambling field.

At GamblingBaba, Mattias’s commitment to providing accurate and easily digestible information shines through meticulously researched reviews, guides, and news articles. His strong belief in honesty and transparency ensures that readers receive the most reliable insights on the Indian gambling landscape.

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