D'Alembert Roulette strategy at Mr Green Canada

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In the game of roulette, simply place your bet, spin the wheel, and hope that the ball lands in your favor. On the surface, the unpredictable nature of the game might make it seem as though any kind of strategy is futile.

However, plenty of long-time roulette enthusiasts would disagree. Since the earliest days of the game, roulette strategy has played an important role for many players. Rather than tapping into any particular skills, the basis of all roulette strategies involves a careful understanding of odds and how you can adjust your bets to potentially increase your aggregate chances of a win.

There are countless strategies out there to try, each of which has its own merits. One of the most famous strategies in the history of roulette is the D’Alembert betting strategy, a widely tried-and-tested tactic that has its origins all the way back in the 18th century. If you’re curious about how you can utilize this strategy in your roulette game, read this official Mr Green guide to D’Alembert. 

The History of D'Alembert

Of all the roulette betting strategies in existence, D’Alembert is one of the oldest and most well-known. The basis of the strategy was developed back in the 18th century by the French mathematician and philosopher Jean le Rond d’Alembert, one of the most celebrated thinkers of his era. His statistical theory that forms the foundation of the D’Alembert betting strategy went as follows: in an equation where there is a 50:50 distribution of odds (i.e. a coin toss or red vs black), then the results will, eventually, even each other out and produce an equal distribution of results.

Let’s illustrate this with the coin toss example. According to D’Alembert, since there is always a 50% chance of landing heads or tails, statistically you will eventually get an even number of each. Therefore, every time you land on heads in a row, the odds of getting tails on the next turn will increase.

Both results will occur an even number of times in the aggregate, meaning that should you flip the coin 1000 times, you would end up with something close to 500 heads and 500 tails. It is easy to see why this appeals to roulette players, since the standard wager bets on either red or black, both of which appear on the roulette wheel in equal measure.

However, when you actually look at the roulette odds, it is clear that D’Alembert’s strategy does not hold up. After all, the inclusion of the zero pockets on the roulette wheel (“0” or “00”) means that the odds are less than 50:0. Rather, the odds are 47.37% on a European roulette wheel, with a 2.7% house edge.

Furthermore, if you land black on the roulette wheel, the odds of landing on red on your next turn does not increase at all, it remains the same. Nonetheless, D’Alembert remains an option for structuring your bets the next time you are playing Roulette. 

D'Alembert Roulette strategy

How to Play Online Roulette with the D'Alembert Strategy

Applying D’Alembert to the roulette wheel is simple. The strategy is similar to the well-known Martingale tactic, but with a slight alteration. With D’Alembert, you adjust your stake by one unit after every loss or win. When you lose a roulette bet, you increase your stake by one unit (instead of doubling it, as you would do with Martingale).

Likewise, every time you win a roulette bet, you reduce your stake in the next bet by one unit. Since this follows the D’Alembert system described above, the strategy online applies to even-money bets, such as red-black or odd-even.

Let’s walk through the strategy with an example. Let’s say you place a $1 bet on red and then you lose that bet. For your next turn, you would place a $2 bet on red. If you lost again, you would increase by one extra unit and bet $3 on red. If you won that bet, you would get your money back. After this, you would decrease your stake by one unit for your next turn and bet $2 on red. You get the picture. 

The main idea here is that you will, overall, get an even number of wins and losses and eventually make a profit by adjusting your stake accordingly. Your overall winnings amount to your stake multiplied by the number of wins. 

This table illustrates how D’Alembert compares to the Martingale strategy:

  • Red or black
  • Even or odd
  • 1-18 or 19-36

D’Alembert only applies after the first win, as you can’t reduce your bet before this point. Here’s an example run:

Bet €2. Lose. Increase bet by one unit.

Bet €4. Lose. Increase bet by one unit.

Bet €6. Win. Decrease bet by one unit.

Bet €4. Win. Decrease bet by one unit.

Bet €2. Lose. Increase bet by one unit.


So, to sum that all up, D’Alembert strategy was created to help beginner roulette players take control of their bankroll, which comes with both it’s pros and cons.

Round Mission Profit Loss Change of bet Balance
1st € 1,- X Raise € 1,-
2nd € 2,- X Raise € 3,-
3rd € 3,- X to decrease € 0,-
4th € 2,- X Raise € 2,-
5th € 3,- X To decrease € 1,-
6th € 2,- X To decrease € 3,-
7th € 1,- X Raise € 2,-
8th € 2,- X To decrease € 4,-

As seen from the table above, all in all, after the four winning and losing round, which were played with a stake of € 1, resulted in a win of € 4.

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D'Alembert Betting Strategy Pros

The D’Alembert strategy is actually based on a different system, known as the Martingale. The major difference between these two systems is that the letter requires doubling on a loss and reducing on a win by .5 of a unit. Martingale is not as risk-averse as its variant system, which means that the potential for significant losses is higher. Let’s use the Monte Carlo example, once again.

Attempting to undo fate by betting on red 26 times would have required a stake of €42 to win on the 27th spin using the D’Alembert system. However, you’ve also lost €42 to get to that point. Of course, this kind of event is so rare that the chances of it happening again are practically zero. However, it perfectly demonstrates how good D’Alembert is at maintaining a player’s bankroll.

The Pros of D’Alembert

One of the main advantages of the D’Alembert betting strategy is that it is a simple way to structure your roulette wagers. It is also much lower stakes than the Martingale strategy as it does not require you to double your bets after each turn. This can help your bankroll last a little longer.

The Cons of D’Alembert

Since D’Alembert betting is low-stakes, the maximum amount you could potentially win is lower than with higher stakes betting systems like Martingale. In addition, D’Alembert is a flawed system. The 50:50 principle upon which it is based does not take into account the house edge on the roulette wheel, or the simple fact that your outcome in one round has no impact on the outcome of the next round.