D’Alembert System

The d’Alembert system (also known as the pyramid system) works in a similar way to martingale. That is bets are increased after losses. Unlike martingale however, bets are not doubled, but increase by one unit with each successive loss. With a win, rather than returning to the base bet, players simply reduce by one unit.

The system was devised by French mathematician Jean d’Alembert in the 18th Century. The system relies on the law of equilibrium, that is, that in the long terms numbers of wins and losses will balance. The theory then states that after a loss you have a greater chance of a win, and vice-versa. Mathematical long term can mean infinity. The average casino player’s game-play would therefore certainly be considered short term.

As with any progressive system, d’Alembert is an extremely risky approach to use. While less risky than the Martingale system, where bets are doubled after losses rather than increasing by one unit, it still contains many inherent flaws. The risk of hitting table limits is the greatest restriction on using the d’Alembert system in a casino environment.

In spite of the risks of progressive systems, they continue to remain popular with players. The d’Alembert system has gained popularity for the simple reason of being an extremely easy strategy to understand and use. The system can also be applied to other casino games with even money bets such as player/dealer in baccarat or red/black in roulette.

As mentioned above, d’Alembert is also known as the ‘pyramid system’. The reason for this is clearly demonstrated in the table below showing a series of three losses followed by three wins. As soon as we win back our original loss, return to the base bet:

Some players also use a reverse- or contra-d’Alembert system. Using this method bets are increased by one unit after wins and decreased by one unit after losses. This system inverts to become a positive progression system.