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The d’Alembert Roulette Betting System

 Nicholas Colon, Author

Players compete in a game of roulette

The d’Alembert roulette system, also called the montant et demontant system (a French phrase that translates to upwards and downwards) is named after the French mathematician Jean le Rond d’Alembert, and has been adapted as a way to play roulette. The system is based on a mathematical equilibrium theory devised by d’Alembert in the 18th century. The d’Alembert mathematical equilibrium theory essentially states that over the long run, each of the individually numbered slots will come up equally. This is a key part of how to play roulette.

Like the Martingale betting system, the d’Alembert roulette system works best when it is applied to the even-money bets.  That is bets that have a near 50/50 outcome. A full list of the Roulette 50/50 bets can be found on Europa Casino’s Roulette Rules article.

In roulette these bets are the red-black, even odd, 1 through 18 and 19 through 36 bets.  These bets are termed outside bets because they can be found on the perimeter of the roulette felt.

Jean le Rond d’Alembert

Both of these systems for playing roulette - the d’Alembert betting system and the Martingale roulette system has similar characteristics in that the player increases or decreases their next bet dependent on the outcome of the previous bet. The d’Alembert betting system is popular among players who want to keep the amount of their bets and subsequent losses to a minimum. The betting progression is very simple: After each loss, you add one unit to the next bet, and after each win, one unit is deducted from the next bet. Starting with an initial bet of 5 units a typical betting sequence would like the following:

  • Bet 5 and lose
  • Bet 6 and lose
  • Bet 7 and win
  • Bet 6 and lose
  • Bet 7 and win
  • Bet 6 and win
  • Bet 5 and lose
  • Bet 6 and win

The math for the previous sequence is as follows: 0 – 5 – 6 + 7 – 6 + 7 + 6 – 5 + 6 = 4. The d’Alembert roulette system is preferred over the Martingale system because while you do increase your bets after a loss, it’s at a much smaller rate than the Martingale.

Advantages and disadvantages of the d’Alembert

Like many roulette systems each have their advantages and disadvantages. Proponents of the system will accent the positives and those that oppose the system will highlight negatives. As I see them here are the best arguments for and against the d’Alembert betting roulette system. 

No roulette strategy can be described as safe. This is because they all carry an element of risk. However, this is about as safe as one can get. Secondly a relatively low bankroll is required for one to start playing.  And last the player is not in danger of brushing up against table limits, unless of course the player goes on an absolutely horrendous losing streak.

A few quick roulette tips: the potential winnings using the d’Alembert system are low.  This is to be expected from a relatively low risk system. The player is also relying on winning as many bets as you lose, this isn’t likely to happen over long term of play. The final problem I see with the d’Alembert is that the player can sometimes go on an extended losing streak where the bets increase a lot. Once this happens, you find yourself in a tremendous hole that can only be recovered by going on an equal winning run.

In the final analysis the d’Alembert system does not garnish a positive expectation for the player. The betting system relies on the gambler's fallacy—that the player is more likely to lose following a win, and more likely to win following a loss. The betting system relies on the gambler's fallacy—that the player is more likely to lose following a win, and more likely to win following a loss.

The defining weakness of the d’Alembert roulette strategy is easily identified. While it is true that the frequencies of the opposite chances even out on the long run – but that really only works on an extremely long run. Think around 100,000 trials. This is essentially the law of large numbers of mathematical probability theory.

In a single session at the casino the theory really does not help the player.  The play must be cumulative. This is essentially taking the sum of hundreds and possibly thousands of sessions.  Most all players never even approach these sessions.


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