Progression d'Alembert
The progression d'Alembert is a French mathematician and philosopher le Rond d'Alembert Jean Baptiste attributed, popular game system for the game on the easy chances at roulette .
As long as the player wins, he places one unit ( piece ). After every loss he increases his stake by one unit, after every win he reduces his stake by one unit.
Since the player increases his stake with this system with the loss, it is a variant of the martingale game .
Example :
- 1st coup: bet 1 piece, lost; Balance −1
- 2nd coup: bet 2 pieces, lost; Balance −3
- 3rd coup: bet 3 pieces, lost; Balance −6
- 4th coup: bet 4 pieces, won; Balance −2
- 5th coup: bet 3 pieces, won; Balance +1
- 6th coup: bet 2 pieces, won; Balance +3
- 7. Coup: Use 1 piece: With this coup a new series of games begins.
As soon as the player has returned to a bet of one piece after an equal number of won and lost games, i.e. after six coups in the above example, this game series is over and he has won one unit for every two coups played.
This system is based on the law of equilibrium, which is misunderstood by many players .
Is allowed once the losses by the Zéro aside so one an absolute balance (so-called. Occurs with probability actually someday a zero recurrence of symmetric random walk on ) - however, it is mathematically useless to wait for the absolute balance, as the Expected value of the waiting time until the first equalization is infinitely large. This result seems downright paradoxical when you consider that an absolute equalization with probability 1/2 already occurs after two games.
In between, however, there may be deviations (in the language of the roulette game Ècarts ) of any amount; d. H. this style of play assumes that
- the player has an infinitely large playing capital,
- and the casino accepts stakes of any amount.
Both conditions are not met in reality.
These considerations apply to the game without Zéro . Because of the zero, the number of losses will surely exceed the number of wins in the long run.
With methods of the martingale theory one can prove that no system of any kind can guarantee long-term profits in roulette. That is, if a player plays according to a system and wins, it is not due to the quality of the system, but solely to chance.
Another roulette system occasionally attributed to d'Alembert is the Annulation d'Alembert .
literature
- Victor Bethell: Monte Carlo - Anecdotes and Systems of Play , London, 1910, p 69 ( Online )
- Rudolf Heinrich [d. i. Rudolf Bretschneider]: Roulette, Trente-et-Quarante, Baccara, Perlen Reihe , Volume 645, Vienna, 1954, p 32
- Alexander B. Szanto: Roulette, Trente-et-Quarante, Baccara, Black Jack . Perlen Reihe, Volume 645, Vienna, 1977 (revised edition of Heinrich's book), p 37