d'Alembert Betting System

The d’Alembert betting system is a wagering system that emphasizes adjusting the amount of your stake on even-money wagers. It is similar to the Martingale method in that both systems involve negative progression models to determine ideal wager amounts.

Here, we’ll explain how the d’Alembert system applies to sports and casino betting. We will also discuss the pros and cons of using the d’Alembert, highlight common misconceptions, and emphasize the importance of risk management.

What is the d’Alembert Betting System?

The d’Alembert system is named after French mathematician Jean-Baptiste le Rond d’Alembert, who first posited the idea in 1754 in Croix ou Pile (translated to “Cross or Tails”).

The system centers around the outcome of a coin toss, given the odds of either result should be 50-50 on each toss. d’Alembert theorized that when choosing the outcome of a coin toss, bettors should increase their stake by one unit after each loss and decrease their stake by one unit after a successful wager.

His work relies on an exploitation of the Gambler’s Fallacy, which is the belief that in an event where either outcome has an equal chance of occurring and one outcome has occurred less frequently that it is more likely to occur on subsequent occasions. In other words, the fallacy implies the more times heads comes up consecutively on a coin toss, the more likely tails will come up on the next toss (mathematically, this is false – it’s still 50-50 as an independent outcome, even though it’s statistically unlikely).

Hypothetically, this system could be used to recoup large amounts of losses on consecutive winning wagers. However, in practice, it can lead to chasing losses, which is a risky gambling behavior that can lead to financial ruin.

Understanding the d’Alembert Betting System

The d’Alembert system relies on using a system with a 50-50 probability of winning or losing. Even a change to 51-49 is enough to cause the entire system to fall apart.

Using this system, d’Alembert claimed it would be better to increase the amount of your stake by one unit (as decided in advance by the gambler) after a loss and decrease by the same amount after a winning wager. Let’s take a look at a practical example, where the bettor is calling “Tails” on each toss and wins the full amount of their stake after a win.

Over the course of these 10 tosses, heads and tails each came up five times, reaching a 50-50 split. This resulted in ranging from being down $60 in losses to up $50 in winnings.

However, profitability in this scenario relies heavily on the exact 50-50 distribution of each result. Let’s use the same results as before but change the result of Toss 4 to result in four consecutive “heads” results to start the sequence of 10 tosses and keep all others the same.

By changing just one result in the sequence, our gambler went from winning $50 to only winning $10 over 10 coin tosses. The system is imperfect because while 50-50 long-run results are a mathematical certainty over time, the result doesn’t alternate in its distribution in the short term.

Application in Sports Betting

In sports betting, the most useful application for the d’Alembert system is in wagering on moneylines, spreads, and totals bets where the payout is the same for either result. At most U.S. sportsbooks, this occurs with -110 odds on each side.

However, this also doesn’t result in a true “even money” scenario, as the vigorish, or “vig,” ensures the sportsbook will still make a profit regardless of the end result (this is why a $10 wager at -110 odds wins $9.09 rather than doubling your money with a $10 profit). The vig is a “fee” for winning and handling the bet, though the exact vig percentage will vary by sportsbook.

Application in Casino Games

One of the most famous casino applications of the d’Alembert system occurred at the Monte Carlo Casino in August 1913. Roulette players were stunned as the ball landed on black 26 times in a row; the odds of such an occurrence are around 1 in 66.6 million.

Bettors had continued to up their stakes thinking “Surely red will come up next!”losing millions in the process. They also anticipated a long streak of red outcomes would follow, though this was not the case.

While blackjack does not feature a 50-50 win/loss likelihood, the d’Alembert system can still be used somewhat effectively, with the bettor raising their stake after a loss, keeping in the same after a draw, and reducing the stake after a win. However, even by perfectly implementing “basic strategy” (the strategy putting the highest odds in the player’s favor), the dealer is still expected to win 49% of the time with a roughly 9% push rate.

In baccarat, this same strategy of raising stake amount after a loss and lowering the stake after a loss. However, because a “tie” in hand value is an outcome you can bet on, it is still somewhat impractical to apply d’Alembert in this way, as even by factoring out the tie bet, the dealer is still expected to win about 51% of the time.

Pros and Cons of the d’Alembert Betting System

To help you decide if the d’Alembert betting system is right for you, please consider the following pros and cons.

Pros

• The strategy is simple to understand and easy to follow.
• Variance isn’t as high as for other negative progression strategies, meaning losses aren’t as rapid.
• Lower risk of hitting a table limit while gambling at a casino
• Incremental gains and decreases lead to better bankroll management and lower volatility.

Cons

• Reliance on losing to increase the stake can still lead to big losses over time that burn through a player’s bankroll
• Longer losing streaks can increase the temptation to chase losses and bet even larger amounts to recoup.
• The cautious nature of the method means the probability of “winning big” is lower.

Comparison with Other Betting Systems

The d’Alembert system offers a slower, less risky progression than other negative progression strategies. Below, we compare it with popular betting systems to highlight key differences.

Compared with the Martingale betting system

One of the most similar betting systems to the d’Alembert is the Martingale betting system, which is also a negative progression strategy. In the Martingale system, players double their stake amount after a loss rather than increase by one unit; they also reset to their original bet amount following a winning wager.

Compared to the above table where we earned a $50 profit on 10 coin tosses with five correct predictions, the Martingale strategy would play out like this:

We still reached the same $50 profit total but had greater variance in our results (lowest deficit was -$70 instead of -$60). For this reason, the Martingale is a riskier overall method than the d’Alembert.

Compared with the Fibonacci betting system

Another comparable method is the Fibonacci betting system, which again relies on betting units. You can calculate the next number in the Fibonacci sequence by adding together the previous two totals (so the sequence begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… etc.).

When Fibonacci betting, you move up one order in the sequence after a win but down two steps in the sequence after a loss. Thus, we would end up with a betting system as follows:

Notice that the Fibonacci had a smaller variance than either the d’Alembert or the Martingale system. The profits weren’t as high, but the losses weren’t as low. 

The Fibonacci system can be more of a hassle to follow since it relies on moving down multiple unit totals following a win rather than simply adding or subtracting a unit like the d’Alembert. This makes the d’Alembert an easier option for novice gamblers to get used to bankroll management and unit betting. 

Risk Management and Bankroll Considerations

Risk management is the most important element of the d’Alembert betting system. Careful consideration of your bankroll will ensure you aren’t wagering more than you can afford to lose. 

Without proper safeguards and bet tracking along the way, it can be easy to blow through your entire bankroll if you hit an extended streak of losses. We strongly encourage anyone using the d’Alembert to set limits on the maximum amount they can wager per bet as well as weekly/monthly limits where applicable.

Cumulative losses aren’t just a possibility while employing the d’Alembert strategy; they are a mathematical certainty. Knowing when to stop betting and walk away is an important element of self-discipline that is essential for d’Alembert success. 

Common Misconceptions about the d’Alembert Betting System

There are several misconceptions about the d’Alembert betting system that we need to address to ensure you’re doing it properly. 

#1: The d’Alembert system eliminates the house edge.

Reality: There is no betting system that fully eliminates the house edge. It can be “reduced” in some ways, but a system that eliminates the house edge would put casinos and sportsbooks out of business. 

#2: The d’Alembert system guarantees profits.

Reality: Similar to the last point, there isn’t a betting system that guarantees a profit. By its very nature, the d’Alembert relies on consecutive losses to increase winning amounts, leading to low profit growth over time with no guarantee of breaking even. 

#3: You can change your unit amount at any time.

Reality: Changing your unit amount is a dangerous option as it can break the system and make it harder to track your results especially if you want to increase the value of your unit. If you are going to make a change to your unit amount, we recommend starting from scratch, resetting your bankroll, and doing so at a time where you aren’t at a negative net. 

Legal and Ethical Considerations

Whether you’re betting at an online sportsbook or an in-person casino, the d’Alembert system is legal to use. However, in-person facilities may prohibit you from using a phone app or notebook to keep track of the bets you’re making; mobile devices are frowned upon in nearly every gambling facility. 

Casinos and sportsbooks are frequently audited by local oversight agencies to ensure all gambling is conducted in a fair manner. However, offshore sportsbooks are not subject to these same reviews, and as such, they should be avoided at all times. 

Wherever and however you decide to gamble, you should only make your bets through licensed, regulated operators. 

Conclusion

Now that you understand the d’Alembert betting system, you’re ready to apply the strategy to your next gambling venture. Remember to decide on a unit amount and stick to it, increasing your bet amount after a loss, decreasing after a win, and walking away before emptying your bankroll. 

It takes discipline and focus to employ the d’Alembert successfully, but with practice and patience, you can use the strategy in what we hope is a profitable manner!

Good luck, have fun, and always gamble responsibly!