Jean le Rond d'Alembert was an 18thh Century philosopher and intellectual who worked on solving problems and making new discoveries in mathematics, physics, and mechanics.

D'Alembert wrote about his betting system in 1754. It’s based on his calculating theory that, in simple even games of chance (e.g., side A or B), the probability of the side occurring as outcomes,

  • less frequently, is more likely to occur, 
  • more frequently in future games.

So that, if you bet on the side that is not occurring as much as the other side, you could make money. If your side begins to occur more frequently as if there’s a force trying to increase the percentage of occurrences in order to achieve an equilibrium.

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How to play the D’Alembert betting system in online casinos

A gambler plays the D’Alembert betting system by: 

  • Picking one of two betting options, e.g. Banker or Player as in the game of Baccarat or Red or Black or any other outside even money chances found in the game of Roulette.
  • In keeping with the D’Alembert theory, a bettor should select a cold occurring even-chance side.
  • The bettor then sticks to that side by placing bets,
    1. wagering smaller value unit bet sizes when your side occurs as an outcome (decreasing stakes)
    2. wagering larger value unit bet sizes after your side loses (increasing stakes). 
  • When you gain a win using the D’Alembert betting system, you reduce your bet size by 1 unit from the structure of the value unit bet size and the player continues betting, either by:
    1. Decreasing unit stakes by 1 unit following a win until you achieve a profit, or
    2. Increasing unit stakes by 1 unit following a loss in the way as follows: bet 1 lose, bet 2 lose, bet 3 lose, etc.
  1. Let’s say you bet three times and lose. Your total outlay would be -6 units. (-1, -2, -3, = -6)
  2. If you were to bet 4 units in a fourth game and win, you would then be losing -2 units
  3. Your next fifth bet would be 3 units. If you win, you would be +1 unit in profit. You could then,
  4. Stop with a +1 unit profit and start over again starting from 1 unit, or 
  5. Continue betting and reduce your stake to 2 units for the following sixth game and if you win = (+3) then reduce to 1 unit for the seventh game = (+4). If you win two more bets after gaining +1 unit profit, you would’ve increased your total profit to +4 units. 

Is the D'Alembert betting system worth trying

You might be thinking about applying the D’Alembert betting system on even money games such as, Blackjack, Roulette, or Baccarat, but don’t be too hasty. You should first weigh up the pros and cons before adopting the D’Alembert betting system.

American Roulette


Pros and cons of using the D’Alembert betting system in casino games

The thinking behind the D’Alembert betting system is regression toward the mean, also the law of averages. The D’Alembert relies on equilibrium, the process where a state of balance occurs. 

The D’Alembert’s betting system is the gambler’s fallacy on the bases that in randomness, future outcomes are independent of previous ones.

Therefore, in fair even money games such as outside chances in roulette, it can be likely that the side not occurring as much may continue in this state given that each side, e.g. red, or black, have an equal chance of occurring in future games.

On a positive note, to win using the D’Alembert betting system, you don’t need more wins over losses to realize a profit. In the above example, to gain +1 unit profit took two wins but there had already been three losses.


D’Alembert betting system versus Martingale betting system

Although negative progression, the D’Alembert betting system is less risky than the Martingale betting system.  With the Martingale betting system, a player doubles his stake after a losing bet. E.g., 1 unit is lost, so you bet 2 units on the next game. Then 4, 8, 16, etc.

  • Whereas with the D’Alembert betting system, you add 1 unit after losing so the structure of increases are 1, 2, 3, 4, 5 etc.

The D’Alembert betting system, like the Martingale betting system, is a negative progression strategy. With both, losses can go out of control and the damage caused will impact upon your bankroll. Though with the D’Alembert betting system the decline is not as aggressive.


The D’Alembert betting system and the house edge in casino games


On the outside even chances in roulette the house edge is the green zero. A solution would be to play on a single zero wheel that offers La Partage rule so that you only lose half of your wager when zero is the outcome. 


The biggest tip I can give you is to take the Player side. You would then avoid paying commission on Banker wins. 5% of the win amount is deducted and commission adds up when playing many outcomes which will reduce the value of your bankroll.



FAQ Section

  1. What is the best casino game to bet on using the D’Alembert betting system?

The best casino game to apply the D’Alembert betting system is baccarat because every shoe presents a fresh set of outcomes. 

And outcomes in baccarat shoes end at around 60 or 80 depending on the number of decks of cards in play.

To help, I have made these three interesting observations:

  1. One side will always be ahead for the entire shoe. However, a bettor has a chance to gain some wins on the weaker side due to mini winning streaks.
  2. The weaker side levels with and overtakes the other side by a few outcomes. This can occur several times. Thus, a bettor could also switch from one side to the other side when the opportunity arises. Using the D’Alembert betting system should generate a profit with this scenario. 
  3. The weaker side levels with and overtakes the other side and maintains dominance. This is an ideal opportunity to generate a profit using the D’Alembert betting system.

However, you’ve got to be good at detecting what kind of baccarat shoe is unfolding to know how to achieve the best results. 

  1. How many units should I start with when using the D’Alembert betting system?

You could start with 2 or 3 units and progress from there, however, to keep things simple it’s best to start with 1 unit when using the D’Alembert betting system.

  1. When should I stop betting when winning using the D’Alembert betting system?

You may want just +1 unit profit typically like the Martingale betting system or you may want more. 1 to 3 units is a reasonable expectation using the D’Alembert betting system, especially if you’re on a winning streak and or start playing with more units.

  1. When should I stop betting when losing using the D’Alembert betting system?

I would think about stopping if you have reached times 14 losses. At a $1 unit stake this would work out to minus $105. 14 times is long enough to have given a good go at it. In my view there’s no point continuing beyond 14 attempts. There’s always another time or different table to play on to try the D’Alembert betting system.

  1. How reliable is the D’Alembert betting system?

Regression to the mean is not something that must happen. It’s only a statistical tendency that may or may not occur in the short or long term. Like all betting systems, the D’Alembert betting system works well when outcomes are occurring more frequently when players are betting on those outcomes.


Conclusion of the D'Alembert betting system

A bettor could gain lots of frequent wins, however just like the negative progression Martingale betting system, eventually the D’Alembert betting system will encounter a progression of losses which will damage your bankroll. Therefore, it’s important to activate a stop loss. 

If you decide to play even money casino games using the D’Alembert betting system, remember that there’s no guarantee the side you’re betting on will generate enough wins to make you a profit. 

But the D’Alembert betting system is still worth trying. Moreover, if you somehow start playing an online casino game at the right time i.e., when regression to the mean is occurring or about to occur on the side you decide to bet on.

Stephen R. Tabone is an English Writer from Great Britain. He is a casino games professional pattern player and outcomes systemiser. He is the Author of Bestselling Baccarat books, ‘The Ultimate Silver Bullet Proof Baccarat Winning Strategy 2.1’ and ‘The Ultimate Golden Secret Baccarat Winning Strategy 3.0’.

In 2011, Mr. Tabone earned a Bachelor of Arts degree with Honours in Creative Writing and Philosophy from the University of Greenwich, London. And holds qualifications in Law and in Business.