D’Alembert betting system

Jean-Baptiste le Rond D’Alembert was a French mathematician, mechanician, physicist, philosopher and music theorist who lived in the 18th century. 

D’Alembert stated that that a coin which has previously landed on tails is more likely to land on heads in the future. On this basis he developed the D’Alembert betting system. This argument is today known as the gambler’s fallacy, which is the mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future. Nonetheless, the D’Alembert betting system is hugely popular both within the casino and sport betting community. 

The D’Alembert betting system is another negative progression system along with the Fibonacci, Labouchere and Martingale betting systems. As a negative progression system, it involves increasing your stake when you lose a bet.

System explained

Much like other negative progression betting systems e.g. the Martingale betting system, you increase your stake after a losing bet and decrease after a winning bet. However, one of the advantages of the D’Alembert betting system is that your stakes do not increase as fast as for example the Martingale system. This means that it is less likely that the stakes get too high and that you reach your betting limit. This is good news if you do hit a long losing streak. On the other side that also makes it more difficult to win back any loses you may have suffered.

Before starting the system, you have to set your stake per unit e.g. one unit can be €5. It is up to you how much you wish to stake but it is recommended to start with a smaller stake per unit to ensure you have enough money, if you are faced with a losing streak. Setting a stake per unit at 1-2% of you bankroll is recommended.

  1. Starting the sequence: Your first bet must be a single bet with your chosen stake per unit. If, you have declared to wager €5 per unit, your first bet should be equal to €5. Continue betting with your initial stake per unit until you lose a bet.
  2. Next step after a winning bet: If your bet is won at your initial stake per unit then continue staking one unit. However, if you stake more than your initial stake per unit, you should decrease you stake by one unit after each winning bet.
  3. Next step after a losing bet: If your bet loses you increase your stake with one unit i.e. your chosen stake per unit. You continue to increase your stake with one unit until you win a bet, after which you will decrease your stake with one unit. Hence, if your stake per unit is €5, your staking sequence looks like this €5, €10, €15 etc.

Example with €5 stake per unit:

Bet Stake Outcome Loss Profit Total
1 €5 loss -€5   -€5
2 €10 loss -€10   -€15
3 €15 loss -€15   -€30
4 €20 won   €20 -€10
5 €15 won   €15 €5

Who should use this strategy

The D’Alembert betting system is considered one of the safer betting system and is therefore suitable for both new and more experienced sports bettors. Even though the system can be profitable, it is advised to set a max betting limit and start over from the beginning in case you reach that limit.

Pros and cons

Thumbs up for these Pros

  • Lower variance than other negative progression systems, which mean that the stakes don’t increase as fast
  • Frequent wins mean you can place many bets
  • Simple betting system and easy to follow

Beware of these Cons

  • The system is based on the that the frequencies of the opposite chances even out on the long run – which is only true over a very large number of bets. Hence, this theory may not apply in praxis when placing a small number of bets.
  • As you slowly increase you stake after a losing bet it can be difficult to win back any loses
  • If you hit a losing streak, your stake will still increase, although not as fast, and you may have to quit the system or start over.

Variations to the system

Contre D’Alembert

This variation of the system is a reverse of the regular D’Alembert betting system. Rather than increasing the stake after a loss, the stake is increased after a win. As such, after a winning bet you increase the stake by one unit and after a losing bet you decrease your stake by one unit. If you are already betting the initial stake per unit, you just continue betting with that amount.

The advantages of the Contre D’Alembert is that you don’t need a large bank roll to start. Also, your stake does not increase after a loss so the system is considered safer than the regular system as a losing streak will not wipe out your bank roll. This is the main advantages of the system

The example below is the same sequence as the example above with the regular system.

As shown, the initial loses were smaller than with the regular system because we did not increase the stake. However, the total outcome was €5 less than above because you need to build a winning streak to win back any loses.

Example with €5 stake per unit:

Bet Stake Outcome Loss Profit Total
1 €5 loss -€5   -€5
2 €5 loss -€5   -€10
3 €5 loss -€5   -€15
4 €5 won   €5 -€10
5 €10 won   €10 €0

Adjusting the D’Alembert system

By adjusting the stakes, you can create multiple variations to the betting system. The same can be done to any of the negative progression systems. Just bear in mind that increasing the stakes per unit, will also increase the risk of losing more if you do hit a losing streak.