The d’Alembert Betting system is a negative progression system and it works similarly to the Martingale betting system. The system unfortunately fails to take into account statistical independence and that in almost all casino games, the outcome of a previous event, has nothing to do with the outcome of the next and is totally independent of it. D’Alembert instead puts his faith in the equilibrium of nature suggesting that if one thing happened a lot more frequently than expected then things would balance themselves out and the opposite would eventually happen. This is of course not true, for example should the ball on a roulette wheel land on a red number 10 times consecutively, there is no reason at all that it should at any time land on black, as each spin of the wheel is 100% independent of the previous.
The system is extremely easy to use, and states that if you win an even money bet you should decrease the amount of the following bet by 1 unit. If you lose a wager, then you simply increase the amount of your next bet by 1 unit. This simple system is based on the belief that a loss makes a win more likely and vice versa.
There is also the Contra D’Alembert system and this is a positive progression system, that suggests that players should increase their bets by one unit after a win, and always reduce by one unit after a loss. This is the opposite of the D’Alembert system.
The problems with both the D’Alembert and the Contra D’Alembert is that they both assume wins and losses will balance themselves out, and that by wagering higher after one or the other event, you are more likely to receive a win. While it is highly unlikely for a coin to land on heads 10 times in a row, the fact that this can in fact happen and that each flip is totally independent of the other, means that the systems are flawed. In the long run of course it is likely that 50% of the time a coin will land on heads and 50% on tails, however the outcome is not predictable.