Contra d’Alembert System

A description of the Contra d’Alembert Betting System, with examples of basic play and how to apply it in various situations that come up at the table.

Contra d’Alembert Betting System

Before learning how to apply the Contra d’Alembert Betting System, it is useful to first become familiar with the traditional d’Alembert system of betting, as detailed in a separate section on this web site. The French mathematician whose name is associated with both approaches to wagering was Jean-Baptiste le Rond d’Alembert (1717~1783). He subscribed to a theory of wins and losses balancing each other, known as the “Law of Equilibrium.”

Although d’Alembert’s belief in “equal outcomes” as it pertains to games of chance has long been disproved, the betting systems to which his thinking gave rise are still viable for even-money wagering. The advantage of the contra version of d’Alembert wagering is that is based upon positive expectation, rather than negative, which minimizes the portion of the player’s bankroll put at risk on any given hand.

Basic Play

As the name implies, the Contra d’Alembert Betting System is the opposite of the d’Alembert system. Instead of requiring a player to wager more after a loss and less after a win, the bet is increased by one unit following a win and it decreases by one unit after a loss.

Unlike the usual d’Alembert progression, the contra version depends on streaks. It focuses on gaining as much profit as possible during winning steaks, while limiting losses on losing ones. It is up to the player to determine at what point a series of wins can be counted as sufficient to restart the progression as a winner.

For example, a player who sets a goal of winning six units at $5 per unit would begin by betting a single unit of $5. Upon winning, the bet would be increased by one unit to $10. Upon winning again, the wager goes up by another unit to $15. At this point, all of the money being wagered has come from winnings. The original $5 would be secured, taken out of play, and a third win in a row would result in a profit of six units, ending the progression as a winner.

Realistically, some intervening losses can be expected, of course. Each time one occurs, the amount to be wagered becomes one unit less than what the previously bet was. If the very first bet loses, or if any subsequent loss would cause the next bet to be zero, the progression ends as a loser. The object, then, is to get at least one progression ending in a win before the number of progressions terminating in a loss equal six or whatever number of units has been set as the goal.

Applying the System

Like the d’Alembert Betting System itself, the contra version requires development of a special strategy for dealing with non-even-money situations. Those include splitting, doubling down, insurance, and higher odds paid for a natural 21.

Again, just as with the original d’Alembert wagering, any extra money won for a successful split, double down, or 3-to-2 payout for a natural blackjack can be treated as “bonus” cash to cover the costs of additional losses on unsuccessful splits and double downs. Insurance is best ignored entirely or else funded out of the bonus pool.

The main difficulty that one encounters during normal play is a lack of winning streaks. Without the occasional winning “hat trick” (three wins in a row), the progression becomes stuck and the attrition caused by losing progressions can gradually whittle a bankroll down to nothing. Such a situation may warrant switching over to a traditional d’Alembert approach or moving to another, more “contra” friendly table.


  • Trevor Hallsey

    Passionate webmaster, devoted card game enthusiast, and proud son of the Great White North. With over a decade of iGaming experience, Trevor has launched numerous web portals to share his passion for game theory and all things Canadian gaming. With this site, he acts as a fact checker and mostly writes at the intersection of gaming and finance. He aims to offer statistical insights and unique information that you might see lacking in similar sites.

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