d'Alembert Roulette System

This system was invented by a French mathematician, based on the assumption of equilibrium in gaming contests. Jean Le Rond d'Alembert reasoned that since winning and losing bets must eventually equal one another, a system of adding one chip after each losing bet and subtracting a chip after a winning bet would ultimately result in a win as winning wagers would always be greater than losing ones.

It is not unusual to win only ten of the first thirty wagers in an even-money betting contest. With d'Alembert's system, the player will wager higher and higher amounts until he eventually runs into our old nemesis, the house limit.

d'Alembert betting system

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d'Alembert betting system

The d'Alembert betting system can be fairly successful if it is modified to include no more than nine or ten bets in a series of wagers so that potential losses are limited. An additional modification to improve the system is to space the bets so that the win of two consecutive wagers will offset prior losses. A series which accomplishes this is 1 2 3 4 7 11 18. With this series, a player would drop back to the lowest bet after winning two consecutive wagers, such as 7 and 4. This system can be fairly successful if used by two partners betting the opposite in roulette, craps or baccarat.

The betting system incorporated for even-money wagers in the Roulette Strategy uses a highly modified type of d'Alembert. As you will see, in a modified form, coupled with a special bet selection strategy, the system can become a very stable and predictable performer.


Like Reverse Labouchere, the idea behind Contra-d'Alembert is to reduce the amount risked while allowing profitable runs to rise to great heights. With this strategy, we will increase our wager one level after a win and reduce it one level following a loss.

The only positive aspect to the strategy is that when you hit a prolonged losing streak the size of your wagers is quickly reduced. In this respect, this system can help protect your bankroll.

However, the upside of using any system requiring increasing your wager following wins is limited. Trends of long, uninterrupted winning streaks are fairly rare in gaming and a system relying on piling up a win after consecutive win is not going to win very often.

Here's an example. Your first bet is for one unit. You win and move up to betting two units. With another win, you wager three units and have a loss. You have won two out of three bets and have absolutely nothing to show for it. All of your profit evaporated with that single loss.

If you could always pick your spots, this system would have merit. Of course, if pigs could fly . . . well, you get the idea. It is just about impossible to know in advance when a three-wager consecutive win might occur so that you could jump in with a Contra-d'Alembert. Like so many systems, this one sounds good on paper but is difficult to squeeze profits out of in real-world gaming.

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