D’Alembert Law of Equilibruim Strategy

Among the various progressive betting systems used for casino table games today, more than a few were developed by some of the greatest scientific minds of the 18th century. Of special note, French mathematicians often took the lead in analyzing games of chance. They were fascinated with statistics and probability, particularly in connection with tossing coins and dice.

One of those fascinated French academics was Jean-Baptiste le Rond d’Alembert (1717~1783), whose credentials included honors in physics, philosophy and music theory as well as maths. One of his rather odd (an incorrect) theories was that the probability of a tossed coin landing “tails” would increase for every time that it came up “heads.” He referred to this as the “Law of Equilibrium.”

The mistake d’Alembert made was basing his theory solely upon observation rather than calculations. He had witnessed that whenever two events are equally likely, such as coin flips resulting in heads or tails, that they really do appear to occur in equal number over the long term. Streaks losses seem to be counterbalanced by streaks of wins.

In truth, of course, all coin flips are independent outcomes, unaffected by past results. Nevertheless, based upon his faulty logic, d’Alembert’s system of betting promoted a process of decreasing one’s bet when winning and increasing it when losing, confident that wins and losses would eventually become equal for wagers with odds of 1:1.

The d’Alembert Betting System is therefore most commonly used for “even money” bets, such as Red or Black wagers at the Roulette table, Pass or Don’t Pass wagers at the Craps table and Banker or Player wagers at the Baccarat table. With modification, the system can also be used for Blackjack as well as for sports betting where vigorous must be accounted for.

The objective of the d’Alembert Betting System is to win a single unit in profit, so the player begins by wagering one unit at Evens. Each time a bet succeeds, one unit will be subtracted from the total just wagered and the remainder will be the amount of the next bet. Whenever a bet loses, one unit is added to the total wagered for the next bet. The progression continues until the amount of the next wager becomes zero.

As an example, if £1 is the basic unit and the first bet succeeds, subtracting one unit results in a next wager of zero, so the progression ends with a profit of £1. On the other hand, if the bet loses, the wager is increased by one unit to £2. If it wins, reduce the wager by one unit back to £1. If it loses, increase it one unit to £3. Continue playing in this fashion until the required wager is zero, resulting in a single unit (£1) in profit. Then, the progression begins anew.

One aspect of the d’Alembert Betting System that sets it apart from Martingale is that it does not require risking huge amounts at unfavorable odds in an attempt to recover previously lost wagers. Also, it differs from Labouchere because strings of losses never increase the wager by more than a single unit for the next bet. The d’Alembert Betting System is thus a very slow and methodical approach to wagering, making it a less risky progression than its cousins.

Where the system fails, however, is in its basic premise of Equilibrium. An initial loss might easily be followed by series of wins and losses in equal number, never quite recovering the original wager. Indeed, the progression might never end at all.

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