18th century French mathematician proposes a less agressive betting strategy. We review how D'Alembert strategy works in roulette.

At the start of the game, we need to determine a **starting bet** as our starting point.
This starting bet will serve as a unit for us later when we increase or decrease our current bet by one unit.

The starting bet, or the size of the unit, is typically determined as a small fraction of our bankroll, **typically between 0.25% and 4%**.
The larger the proportion of the amount chosen for the starting bet, the larger the profits and losses we will incur, and the more likely it is that we will exhaust our entire budget for the game.

After determining the starting bet, we only need to follow two rules. If we lose in a round, we increase the size of our current bet by one unit. If we win in a round, we decrease the size of our current bet by one unit, but never go below one unit. Also, a third rule applies to games where a draw can occur, in which case our current bet remains unchanged.

As you can see, this method is similar to the Martingale strategy in that we increase after a loss and decrease after a win. The significant difference is that the D’Alembert method is less aggressive, so it can be applied in practice with a smaller amount of gambling money.

Now let's see an example for illustration. Suppose we are playing roulette and we continuously bet on red. We came to play with 5,000 HUF, and we determine the unit stake at 1%, which is 50 HUF.

Round | Bet* | Outcome | Balance at the end of the round |
---|---|---|---|

0 (start) | – | – | 5,000 HUF |

1 | 50 | Lose | 4,950 HUF |

2 | 100 | Lose | 4,850 HUF |

3 | 150 | Lose | 4,700 HUF |

4 | 200 | Lose | 4,500 HUF |

5 | 250 | Win | 4,750 HUF |

6 | 200 | Win | 4,950 HUF |

7 | 150 | Win | 5,100 HUF |

8 | 100 | Win | 5,200 HUF |

9 | 50 | Lose | 5,150 HUF |

10 | 100 | Lose | 5,050 HUF |

In the table above, you can see the details of 10 example rounds.
In the first round, we make a starting bet of 50 HUF, then in case of a loss, we increase the bet by 50 HUF.
If we win, we decrease our current bet by 50 HUF.
The example we used shows a particularly **unfortunate gameplay**.
Here we won four out of the ten bets and lost six.
Despite this, our profit was 50 HUF, that is, one unit.

Let's suppose we play the same rounds, but we do not use the D’Alembert method, but always bet a fixed 50 HUF. Then our balance would be negative with a loss of 100 HUF, that is, 2 units.

As the example illustrates, this method, similar to Martingale, can be useful in coming out with a positive balance from **slightly unfortunate gameplays**.
However, if we have moderately or very unfortunate gameplay, this method accelerates the depletion of our gambling money.
And as experienced players know, sooner or later everyone gets hit by an unfortunate streak.