The d'Alembert System is a progression system which tries to win back your losses in small steps instead of all at once like the Martingale. It was designed for use on the even chance bets on a roulette table but can be used on any even chance bet.
The d'Alembert System works under the assumption that over a period of time there will be an equal number of `reds' and `blacks'. We start the session by placing one unit ($1, $5 or any other value) on one of the even chance bets (e.g. `red'), after a losing spin we increase the next bet by one unit and after a winning bet we decrease the next bet by one unit. So if we were betting oin `red' and the spins were - black, black, black, red, black, red, red, black, red, red, red - then the bets placed would be as follows (the numbers in brackets show the level of your bankroll after the spin):
1 (-1), 2 (-3), 3 (-6), 4 (-2), 3 (-5), 4 (-1), 3 (+2), 2 (+0), 3 (+3), 2 (+5), 1 (+6)
This sequence would end with a win of $6. As you can see, as soon as the number of `reds' is equal to the number of `blacks' plus one then the sequence ends with a win. You may also notice that after the 7th, 9th and 10th spins we were also showing a profit, this is because the bets placed on winning spins are one unit greater than the previous losing spin. Having the possibility of a positive bankroll before the sequence is complete allows us to choose to cut the session short and take a smaller win rather than risking the chance of the session ending badly.