Just like the d’Alembert’s betting system, Contra d’Alembert (in reference to the French mathematician Jean le Rond d’Alembert), is a very popular betting system, the progression here is positive, we increase bets, not when we lose, but when we win.
When in the classic d’Alembert system, the idea is that a win increases the chances of losing the next bet and that inversely following a loss, we have more chance to win. In the Contra d’Alembert, the idea is that you have more chance to win following a win. More simply, it is the idea that a win is often the beginning of a positive series, and that a loss will lead to further losses afterwards.
Rules of the Contra d’Alembert
Although it can be applied to any type of betting; sports, horse racing or even in trading, The Contra d’Alembert betting system is popular in casinos and more particularly in roulette with simple bets (red / black, odd / even pair …).
Deux règles simples :
- Increase the bet by a base bet unit after each win.
- After each loss, 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.
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||– 20||0||– 10|
|3||– 10||0||– 20|
|4||– 10||0||– 30|
|5||– 10||+ 10||– 20|
|6||– 20||+ 20||0|
|7||– 30||+ 30||30|
- In this example, and following the first winning bet, we increase the bet by a unit 10 + 10 = $20.
- Following the losses of the second, third and fourth bets, it is not possible to reduce by one unit the last bet that is the starting bet, we then replay this bet of $10.
- After winning the sixth stroke, we add a bet unit of 10 + 10 = $20. Such a seventh-round win 20 + 10 = $30.
Benefits and risks
Like the d’Alembert betting system, Contra d’Alembert falls into the trap of the gambler’s mistake, which tends to perceive probabilities in a wrong way. To think that we have a better chance of winning after a win and inversely more chances of losing after a loss makes no sense.
Mathematically, the probability of an event is independent of the event that precedes it. Drawing a red ball does not increase the chances of drawing a black ball on the next round.
GSimulator allows to launch a simulation of the Contra d’Alembert in real conditions with the possibility of changing in real time several parameters such as starting bet, the odds other than 2, the number of repetition or the limit of the bankroll. The simulator also provides the tools needed to analyze results and compare cost differences with other strategies.
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) :
- Classic Martingale
Increase stake after every loss
- Great Martingale
Increase stake + unit bet, after every loss
- Fibonacci (Whittacker)
Increase and decrease stake based on the Fibonacci sequence
- Reverse Martingale (Paroli)
Increase stake after winning until stop limit
Increase stakes after a loss, descrease after a win
Remove first and last number in the Labouchere sequence after a win, add the last bet to the sequence after a loss
- Reverse Labouchère
Remove first and last number in the Labouchere sequence after a loss, add the last bet to the sequence after a win