d’Alembert

Strategy principles

The d’Alembert betting system (in reference to the French mathematician Jean le Rond d’Alembert), is another betting system with a negative progression, which implies the increase bets following losses. This is a very popular system for its simplicity and promises to reduce the risk of big losses because the increase of bets is slow.

The principle is based on the idea that a win increases the chances of losing the next bet and that inversely following a loss, you have more chances to win.

Rules of the d’Alembert method

Although it can be applied to any type of betting; sports, horse racing or even in trading, The d’Alembert betting system is popular in casinos and more particularly in roulette with simple bets (red / black, odd / even pair …).

Two simple rules :

  1. Increase the bet bey a base bet unit following each loss.
  2. After each winning bet, decrease the bet by a base unit, if we return to the starting bet and it is no longer possible to decrease, replay the basic bet unit.

Example

In this example simulated on GSimulator, played Odds are 2 (US +100), probability 50% and the bet unit is $10 :

# Cost ($) Result Win ($) Bankroll ($)
1 10 + 10 10
2 10 0 0
3 20 0 – 20
4 30 0 – 50
5 40 + 40 – 10
6 30 + 30 20
  • In this example, and following the first winning bet, it is not possible to decrease by one unit the last bet that is the starting bet, we then replay this bet of $10.
  • Following the second losing bet, we increase the bet 10 + 10 = $20 and so on as long as we lose.
  • Following the fifth winning bet, one unit is removed on the last bet. 40 – 10 = $30.

Benefits and risks

Although very promising at first glance, the d’Alembert betting system falls into the trap of the gambler’s mistake, which tends to perceive the odds in a wrong way. To think that you have a better chance of winning after a loss and vice versa does not make sense.

Mathematically, the probability of an event is independent of the event that precedes it. Draw a red ball does not increase the chances of drawing a black ball on the next stroke.

On a large number of bets, this system tends to a neutral result as the number of winning bets will be close to the number of losses.

GSimulator

GSimulator makes it possible to launch a simulation of the d’Alembert strategy under real conditions with the possibility of changing in real time several parameters such as starting bet, odds other than 2, number of repetitions or even the limit of the bankroll. The simulator also provides the tools needed to analyze results and compare cost differences with other strategies.

Start a free simulation of the d’Alembert strategy in the GSimulator or consult the documentation for more informations.

Other betting systems

Other strategies and betting systems exist and try to limit the losses, or to increase the profit, by making changes to the rules of stakes following the losses (negative progression) or following the wins (positive progression) :