The D’Alembert System
The D’Alembert system is one of the simpler betting systems. In terms of its popularity it’s probably second only to the Martingale system. It actually shares some characteristics with the Martingale, as they are both negative progressions that involve increasing stake sizes after a losing bet and decreasing them after a winning bet.
Stakes are increased more slowly with this system than with the Martingale though, making it less likely for the stakes to get ridiculously high. This is an advantage to some extent, however the flipside to this is that losses are recovered more slowly. So the chances of making some kind of loss are actually greater, but the size of any losses are generally less catastrophic when hitting a streak of bad luck.
We explain the D’Alembert system in detail on this page. We tell you how to use it, and then explore whether or not it can work.
How the D’Alembert System is Used
This system was named after the French mathematician Jean-Baptiste le Rond d’Alembert. He, like many gamblers before and after him, made the mistake of falling for the gambler’s fallacy. It’s not known how much this cost him, but others who have made the same mistake have lost their entire bankrolls.
What is the gambler’s fallacy?
The gambler’s fallacy, or the Monte Carlo fallacy, is essentially the mistaken belief that the probability of an outcome has changed when it’s actually remained the same. D’Alembert fell for it, as he argued that the probability of a coin landing on heads increased the more often it landed on tails. This is false, as the chances remain exactly the same regardless of what’s happened previously.
The D’Alembert system is commonly applied when making even money bets at the roulette table, but it can be used for pretty much any even money wager. It’s based on the theory that there should be some equilibrium with even money bets. The idea is that you should always win roughly the same number of even money bets as you lose. To put it another way, it works on the basis that red would come up approximately the same number of times as black during a session of playing roulette.
It’s a very straightforward system to learn, which perhaps explains its popularity to some degree. Here’s a quick guide to putting it into practice.
- RULE 1 – Decide Your Base Unit
- Before you start you must decide what your base staking unit is going to be. This can be whatever you want, but we’d advise making it no more than 5% of your total bankroll. 2% is best in our opinion.
- RULE 2 – Begin With One Unit
- You must stake exactly one base staking unit on the first wager of any cycle when using the D’Alembert system.
- RULE 3 – Increase Stakes After a Loss
- After every losing wager, the stake for the following wager must increase by one base staking unit. If you started with $5, for example, then you would increase the stake to $10 if you lost. If you then lost again, you’d increase the stake to $15.
- RULE 4 – Decrease Stakes After a Win
- After every winning wager, the stake for the following wager should decrease by one base staking unit. If a wager is won at a stake of only one unit, then it remains the same for the following wager.
As you can see, this system is certainly simple enough to implement. And, if you do win roughly the same number of bets as you lose, then you should come out ahead. This is because your winning bets will have been at higher stakes than your losing bets. Sounds great in theory but the key question, of course, is does it work in practice?
Does the D’Alembert Work?
There is no doubt that the D’Alembert can help you to win money in the short term. You can make a profit even when losing more bets than you win. You need the right sequence of results for this to happen though, and this is where the system is fundamentally flawed. Any sequence is possible, and some sequences can be very costly when using the D’Alembert.
It’s quite possible to get a streak of several losing bets in a row. Let’s take a look at the results if that happened. We’ll assume you started with a base unit of $5, and were betting on black at the roulette table.
- Stake $5, lose. $5 down.
- Stake $10, lose. $15 down.
- Stake $15, lose. $30 down.
- Stake $20, lose. $50 down.
- Stake $25, lose. $75 down.
- Stake $30, lose. $105 down.
At this point you’re 21 betting units down, and a streak of six losses is not at all uncommon at the roulette table. It could go on to get a lot worse, and there is absolutely no guarantee that you will then go on enough of a winning streak to recover all those losses. There is also always the risk that you go on a losing streak long enough to decimate your entire bankroll. Even if you have plenty of money to gamble with, you might reach the stage where the required stake is above the table limit.
This system does absolutely nothing to protect you from losing several bets in a row. In fact, you’ll actually end up losing substantial sums if you do. And losing streaks happen to everyone on occasion. Therefore, while it can be profitable in the short term, it will probably cost you money in the long run.
Adjusting the D’Alembert
There are a couple of modifications you can make to this system to make it potentially more appealing. For example, you can adjust the stakes by two (or more) units after each bet to help increase your chances of turning a profit when results are alternating reasonably frequently between wins and losses. Of course, the flip side to this is you will lose more if you go on a losing streak.
You can also choose to set a stake level at which you stop increasing the stakes and go back to your base stake and start again. For example, you could decide to never go higher than five times your base stake. This would minimize your losses if you went on a lengthy losing streak, but would also reduce your chances of recovering your losses.
The D’Alembert can help you win money in the right set of circumstances, but it can also cost you a lot of money in the wrong set of circumstances. Ultimately the exact same is true if you just bet level stakes. As such, we don’t really recommend this system, as it effectively serves very little purpose.
It is somewhat less risky than the Martingale, as the rate at which you increase your stakes is much slower, but it doesn’t offer the same potential benefit of being able to recover all your losses with one winning bet. We wouldn’t go as far as to say you absolutely shouldn’t use it, but if you’re set on using a betting system then there are better options in our opinion.