The D’Alembert System was developed in the 18th century by French mathematician Jean-Baptiste le Rond d’Alembert. Originally a mathematical concept rather than a betting strategy, it was later adapted for gambling. While it doesn’t improve the odds, many gamblers still use it due to its structured approach and risk management.
This system is popular for even-money bets, offering a gradual betting progression that avoids the rapid increases of more aggressive strategies. However, it has limitations. Understanding how it works, its advantages, and its drawbacks can help you make informed decisions.
What is the D’Alembert System?
This negative progression gambling strategy is based on a formula created by Jean Baptiste Le Rond D’Alembert. The system was originally developed to prove the Frenchman’s theory regarding equilibrium. However, it is not commonly associated with gambling.
Many have stated that the D’Alembert system falls down due to the fact that it is based on the notion that successes and failures cancel each other out over the long-term. Despite this, it is still a strategy that can be of use to gamblers.
Using the system, you must add to your stake after each losing bet. You will then decrease the stake after a winning bet. The system comes to an end when you find yourself back at your initial stake.
The D’Alembert system is particularly attractive for outside bets on roulette, including red/black and odd/even. The strategy can also be utilized when playing blackjack and is an option for sports bettors.
How Does the D’Alembert System Work?
As a negative progression system, the D’Alembert betting strategy has much in common with other betting systems like the Martingale and Fibonacci systems. However, it’s significantly less aggressive than these alternatives, as D’Alembert requires you to increase your unit bets in a more manageable and conservative way after each loss.
In simple terms, the D’Alembert system compels you to increase your stake by a single bet unit after each loss, something Jean Baptiste Le Rond D’Alembert referred to as waves.
When you win, you’ll decrease your stake by the same amount, creating a simple system that’s also ideally suited to bettors with a small bankroll or relatively balanced betting outlook. But how does this work in practice?
Set a starting bet unit to begin (we’ll use $10 for this example).
Place an initial bet of $10 at even money. This wins, and you bank $10 in profit.
Maintain your $10 bet unit for your next wager. This also wins and earns you $10 profit (+20 total)
Wager $10 again. This is is a losing bet (+$10 total)
Your next stake will be $20, as you move into larger bets. However, this bet is also unsuccessful (-$10 total)
You’ll then bet $30, but this wager loses too (-$40 total)
You’ll now increase your bet unit to $40. This bet wins, and you bank $40 in profit (even total)
After the win, you’ll decrease your stake by a single unit to $30. This wager is successful (+$30 total)
You’ll then close the betting cycle.
At this stage, you’ll have staked $150 in total. You’ll have also made a $30 profit overall, which is an incremental return that’s lower than what you would expect when deploying the Martingale system.
However, you would have wagered $210 while using this system and would have had to commit more of your bankroll chasing individual losses.
Having an end game for your sessions when using the D’alembert strategy is essential. The best way to do this is by setting a stop-win limit. A good target to aim for is around five times your initial unit. Also, having a stop-loss limit is important. Setting a stake limit of around 8 to 10 is also a good plan. This means if your stake ever reaches 8-10 times your original unit. These numbers can be adjusted based on how aggressive you want to be, but the important thing is setting parameters on when to end a session.
Examples of a D’Alembert System
Now that you’ve seen how the D’alambert works in theory, it’s important to consider how it can be applied to specific betting markets and outcomes. Let’s look at how a standard example of the D’Alembert method works. We’ll start with a betting unit of $10 and are playing a game that pays out 1:1.
Bet #
Bet Amount
Outcome
Profit/Loss
+/- Betting Unit
Running Total
1
$10
Loss
-$10
+1
-$10
2
$20
Loss
-$20
+1
-$30
3
$30
Loss
-$30
+1
-$60
4
$40
Win
+$40
-1
-$20
5
$30
Win
+$30
-1
+$10
6
$20
Loss
-$20
+1
-$10
7
$30
Win
+$30
-1
+$20
8
$20
Win
+$20
-1
+$40
9
$10
Loss
-$10
+1
+$30
10
$20
Loss
-$20
+1
+$10
11
$30
Win
+$30
-1
+$40
12
$20
Win
+$20
-1
+$60
13
$10
Win
+$10
-1
+$70
14
$10
Loss
-$10
+1
+$60
15
$20
Win
+$20
-1
+$80
As you can see, we made a decent profit of $80 in just 15 rounds. However, we were fairly lucky and didn’t go on any substantial losing streak. In the table below, you can see how quickly your bankroll can get depleted if you are on a cold streak.
Bet #
Bet Amount
Outcome
Profit/Loss
+/- Betting Unit<
Running Total
1
$10
Loss
-$10
+1
-$10
2
$20
Loss
-$20
+1
-$30
3
$30
Loss
-$30
+1
-$60
4
$40
Loss
-$40
+1
-$100
5
$50
Loss
-$50
+1
-$150
6
$60
Loss
-$60
+1
-$210
7
$70
Win
+$70
-1
-$140
8
$60
Win
+$60
-1
-$80
9
$50
Loss
-$50
+1
-$130
10
$60
Loss
-$60
+1
-$190
Using the D'Alembert System for Sports Betting
When using the D’alembert system for sports betting, it’s essential to pick outcomes that are as close to even money as possible. However, in sports, this is made more complicated by the commission (or vigorish) charged by online sportsbooks, which equates to a 4.77% house edge on the wagers that they take.
This is why you’ll rarely see sports betting outcomes priced at +100 online. Instead, you’ll find many markets priced at around -110. So, when using the D’alembert approach for sports wagering, you’ll often have to focus on selecting outcomes that are as close to even money as possible.
In most cases, this will be spreads and totals, but occasionally you’ll find moneylines and prop bets offering these types of odds.
As a result, you’ll have to place winning bets around 55% of the time while relying on detailed match and competitor analysis to make the most informed selections possible.
D'Alembert Betting Strategy at a Blackjack Table
The D’alembert system is also popular among blackjack players. This is because some iterations of blackjack boast a return-to-player (RTP) rate that’s in excess of 99%. In fact, the theoretical RTP rate for classic blackjack is 99.41%, equating to a $99.41 return for every $100 wagered.
In blackjack, all winning bets are also even money and paid at 1/1. The blackjack payout is marginally higher at 3/2, but generally speaking, you’ll either lose or double your money with each wager. This simplistic payout structure suits the D’alembert system, as does the implied probability of winning each hand.
However, there are rules in blackjack that may introduce complications. For example, when you double down or split cards, you are required to double your stake in the hand. You could simply avoid these options when employing D’alembert’s formula, but if you are following blackjack basic strategy, you don’t want to do that as this increases the house edge.
Instead, what you should do is increase your bet by two units if you double down and lose and decrease the unit by two if you win. If you split and lose both hands, increase the unit by two, if you win both, decrease by two; and if you win one and lose one, treat it as a push and keep the same bet. Here’s an example:
Round
Bet Amount
Outcome<
Double/Split?
Profit/Loss
+/- Units
Running Total
1
$10
Loss
No
-$10
+1
-$10
2
$20
Loss
No
-$20
+1
-$30
3
$30
Win
No
+$30
-1
$0
4
$20
Win
No
+$20
-1
+$20
5
$10
Loss
Double Down
-$20
+2
$0
6
$30
Loss
No
-$30
+1
-$30
7
$40
Win
No
+$40
-1
+$10
8
$30
Win
No
+$30
-1
+$40
9
$20
Loss
Split (One win one loss)
$0
0
+$40
10
$20
Loss
No
-$20
+1
+$20
D’Alembert Roulette Strategy
As we’ve already discussed, the D’alembert system is ideally suited to even money bets. This is why it’s synonymous with roulette, which features a number of so-called “outside bets” that pay at 1:1. These include Red/Black, Odd/Even, and High (19-36) / Low (1-18), which essentially afford you a 50% chance of winning.
While there are ample bet choices when wagering on roulette and deploying the D’alembert system, this is an incredibly fast-paced game. This means that you’ll have to place a high volume of wagers within a relatively short period of time. We’d recommend starting with a minimal bet unit of around $1.
Your choice of roulette game and iteration is also important for the effectiveness of the D’Alembert roulette system. For example, European roulette only features a single zero groove and offers an RTP rate of 97.30% Conversely, the RTP for American roulette is almost double at 94.64%, due to the addition of a second zero groove on the wheel.
So, picking European roulette iterations enables you to naturally retain more of your starting bankroll and optimize the efficiency of the D’alembert betting system.
Dozens and Columns D’alembert Roulette System
If you’re a less risk-averse player, you might consider applying the D‘alembert formula on roulette dozens and column bets. These wagers pay 2:1, allowing you to build profits faster. However, the odds of winning a single dozen or column bet are just 32.43%.
To reduce risk while still betting on dozens or columns, you can wager on two dozens per spin (e.g., 1-12 and 13-24). This increases your winning chances to 64.86%, but each win only returns half your total stake. This approach is ideal for those who prefer a lower-risk and are comfortable with a grind.
D'Alembert Strategy for Craps
Craps is another casino game that’s suited to the D’alembert betting strategy. Once again, however, it’s important to focus on the game’s even money bets, namely Pass/‘Don’t Pass’, ‘Come/Don’t Come,’ and Odds.
These are just a few of the many bets available in craps. However, D’alembert is far less suited to other options, including ‘Hardways’ and ‘Any 7’, which have higher payouts but higher house edge and much lower probability of occurring.
D’Alembert Strategy for Baccarat
Like roulette, the game of baccarat is incredibly fast-paced and frenetic. The game’s ‘Banker’ and ‘Player’ bets also boast respective RTP rates of 98.94% and 98.76%, meaning that it has obvious similarities with blackjack too. As a result, there’s some value in leveraging the D’alembert baccarat system when playing baccarat.
Once again, the key is to target the right wager types. The player or banker’s bet is the way to go; both payout at 1:1. However, a banker bet has a 5% commission as it is slightly more statistically likely to win due to the drawing rules.
D’Alembert System Pros and Cons
However you look to deploy the D’Alembert betting system, it’s important to understand this strategy’s unique advantages and disadvantages. These include:
Pros:
Low variance and relatively minimal losses
Conservative stake progression aids bankroll management
Losses are gradual and don’t scale too quickly
Can be used for both casino and sports betting verticals
Simple progression is suited to new or risk-averse players
Cons:
Requires you to chase losses
Recovers a losing bet much slower than other negative progression systems
The Reverse D’Alembert
It is common for gambling systems that have a “reverse” option. This is the case with D’Alembert. The Reverse D’Alembert system works in the opposite way to the traditional D’Alembert method. It is known as a positive progression strategy.
This means that you are required to increase your stake by one unit after a win. Your stake is decreased by one unit following a loss. This allows you to raise the stakes using money made and means there is no need to chase losses.
The reverse D'alembert also works best when placing even money wagers. However, there are arguably superior positive progression strategies available. The ‘Paroli system’ (or reverse Martingale) is capable of delivering more significant returns while simultaneously avoiding sustained losses.
Tips for Using the D’Alembert System
By now, you should have a good understanding of D’Alembert betting and how it works in relation to different verticals. But what steps can you take to optimize your chances of success and apply this betting system optimally?
Set Your Ideal Bet Unit
While the D’Alembert system may be conservative, it can still decimate your bankroll during losing streaks. So, it’s important that you set a bet unit that you can comfortably sustain during a predetermined timeframe. You may also want to minimize this when playing fast-paced games like roulette.
Understand the Impact of Negative Progression Systems
This is another key consideration, as all negative progression systems require you to actively chase losses. This can place a significant strain on modest bankrolls, and you must be able to sustain losses in the pursuit of maximized returns. Losing streaks happen, but with the D’Alembert approach, a losing streak is seen as an opportunity to succeed.
Prioritize Even Money Bets
There’s a reason why the D’Alembert system is synonymous with roulette, as it features a lot of even money bets. This is crucial as it optimizes your chances of winning and recovering previous losses. It’s important to always prioritize wagers that are as close to even money as possible.
Use Insight and Analysis to Optimize Sports Wagers
Remember, most sportsbooks charge a commission that makes it tough to access even money wagers. So, you’ll often have to back outcomes with odds of +110 or greater. It’s important that you use detailed datasets and form analysis to make the most informed picks possible.
Stick to The System in a Session
If you choose to use the D’Alembert strategy, it’s important to stick with it for the entire session, as switching strategies midway undermines its purpose. However, if you find that D’Alembert isn’t working for you, it’s perfectly fine to reassess and try a different approach after the session.
Alternatives to the D’Alembert Betting System
In this guide, we’ve referenced several alternatives to the D’Alembert betting system. Some of these may be more suited to your outlook, appetite for risk and starting bankroll. So, let’s take a closer look at some of the more popular strategies available.
The Martingale System: In terms of negative progression systems, the Martingale system is undoubtedly the best known. It’s also the highest risk and needs a big bankroll, as it requires you to double your next bet every time a bet loses.
The Fibonacci System: When it comes to risk and reward, the ‘Fibonacci System’ sits between Martingale and D’Alembert. Based on the mathematical Fibonacci sequence, this negative progression system compels you to scale your next bet after a loss by adding to your two previous stakes together.
The Labouchere System: The Labouchere system requires you to create an initial number sequence of at least three numbers. You set your base unit by adding the first and last digits in the sequence. Previous losing stakes will subsequently be added to the end of the sequence, while winning wagers will see the first and last numbers removed.
Conclusion
Like most betting systems the D’alambert strategy does not give you an edge over the house, in fact it does not alter your chances of winning at all. What it can do is provide a structured framework for your betting, help you recoup losses and reduce bad habits like impulsive betting.
It’s a less aggressive system than many others available and it will suit some players more than others. The best way to see if it suits you is to try it out after a few sessions and see the results and if you think it enhances your experience overall. Just don’t get carried away with the wins and assume you will make a profit each time.
FAQ
What is D’Alembert betting strategy?
The D’Alembert is a negative progressive betting system that requires increasing your unit bet by one with every loss. Conversely, you’ll decrease your stake by one unit each time you win!
Can you use the D’Alembert system on casino games?
You can indeed! The D’Alembert system is synonymous with roulette, which boasts a number of even money outside bets. There are similar wagers in blackjack, craps, and baccarat. D’Alembert can be used as a viable strategy in each game.
Is D’Alembert betting guaranteed to work?
Unfortunately not, but the same can be said for any betting system. You can maximize your chances of success by prioritizing even money wagers and understanding the implied probability of specific outcomes.
Is D’Alembert better than the Fibonacci system?
This depends on your outlook. Both are negative progression systems, but D’Alembert enables you to increase your bet unit more conservatively. The Fibonacci system requires you to pursue losses more aggressively over time. Bettors will need a greater bankroll and appetite for risk to be successful.
Can the D’Alembert System be used for sports betting?
Yes, it can! The D’Alembert system boasts a simple structure that’s ideally suited to sports betting as well as gaming at online casinos. It also aids responsible management of your bankroll. However, you’ll have to target close to even money wagers wherever possible.
Responsible Gambling
Betting systems can be a good way to control your betting habits and gamble responsibly. However, there’s much more to protecting yourself from any potential risks. Check out our dedicated, responsible gambling page to find out more. If you’re concerned about your betting behavior, visit one of the links below for free assistance:
The ReadWrite Editorial policy involves closely monitoring the gambling and blockchain industries for major developments, new product and brand launches, game releases and other newsworthy events. Editors assign relevant stories to in-house staff writers with expertise in each particular topic area. Before publication, articles go through a rigorous round of editing for accuracy, clarity, and to ensure adherence to ReadWrite's style guidelines.
Lewis is a seasoned sports writer and betting expert at ReadWrite. He has been written about sports, remote betting and sportsbooks for more than 10 years, with his work featuring in publications such as The Boot Room, Yahoo Sports and 90min. He writes most extensively about soccer, basketball, American football and boxing, but retains an interest in a huge range of sports.
Online casino gaming in Massachusetts is back on the agenda, as lawmakers heard pleas from the industry to protect it from the black market. The Massachusetts Legislature’s Joint Committee on...
Get the biggest iGaming headlines of the day delivered to your inbox
Gambling News
Explore the latest in online gambling with our curated updates. We cut through the noise to deliver concise, relevant insights, keeping you informed about the ever-changing world of iGaming and its most important trends.
In-Depth Strategy Guides
Elevate your game with tailored strategies for sports betting, table games, slots, and poker. Learn how to maximize bonuses, refine your tactics, and boost your chances to beat the house.
Unbiased Expert Reviews
Honest and transparent reviews of sportsbooks, casinos and poker rooms crafted through industry expertise and in-depth analysis. Delve into intricacies, get the best bonus deals, and stay ahead with our trustworthy guides.