The D’Alembert betting system, developed by Jean-Baptiste le Rond d’Alembert in the 18th century, is a simple but profoundly flawed strategy that applies to even-money propositions. Its fundamental flaw lies in its reliance on the “Gambler’s Fallacy,” assuming that the outcome of one event affects the likelihood of the next independent event.
How the D’Alembert System Works
The D’Alembert system is often illustrated using the example of a coin toss. Bettors start with a base unit (e.g., $10) and increase their bets by one unit after each loss. If they win a bet, they decrease the next bet by one unit.
For instance, if a bettor loses a $10 bet on heads, the system would recommend a $20 bet on heads for the next round. If the second bet is also a loss, the third bet should be $30, and so on. They will decrease the next bet by one unit if they win a bet.
Why the D’Alembert System Doesn’t Work
The primary reason the D’Alembert system fails is the misconception that past events influence future outcomes. Every coin toss or sports bet is an independent event with a 50/50 chance (or close to it) of success. The result of one toss or game has no bearing on the outcome of the next.
This fallacy applies not only to coin tosses but also to sports betting, especially when it comes to betting against the spread (ATS) in sports like the NFL. Assuming that a team is more likely to cover the spread after failing to do so in the previous game is an unwarranted belief, as the outcomes of different games are unrelated.
An Example of the Pitfalls
Suppose a bettor experiences a losing streak using the D’Alembert system with a starting unit of $10. After ten consecutive losses, they would have suffered a total loss of $550.
$10 + $20 + $30 + $40 + $50 + $60 + $70 + $80 + $90 + $100 = $550
If their starting unit were $20, the loss would have been $1,100. To recover from such a losing streak, the bettor must win five consecutive bets (with a mere 3.13% probability) to break even.
Is There a Context Where the D’Alembert System Could Work?
In theory, the D’Alembert system might show a positive expected value if two events were causally related and dependent on each other. For example, if data suggested that a certain team was more likely to win after a loss, betting on them might be valuable. However, such correlations are challenging to establish and are often already factored into the betting odds set by sportsbooks.
The D’Alembert betting system is fundamentally flawed due to its reliance on the Gambler’s Fallacy, which assumes that past outcomes influence future independent events. For sports bettors, it is essential to recognize that each bet is an isolated event with no causal relationship to previous ones. Relying on flawed betting strategies like the D’Alembert system can lead to substantial losses and should be avoided in favor of more sound and well-reasoned betting approaches.