d’Alembert Betting System

Many of the famous betting systems that are still being discussed today were originally devised over 300 years ago by some of the sharpest mathematical minds of the time. Scientists, statisticians and mathematics in Europe and beyond learned a great deal from analysing games of chance such as dice throwing and coin tossing. In particular, the French scholars were pioneers in this field.

On such academic thinker was Jean-Baptiste le Rond d’Alembert who held honours in physics, philosophy, music and maths. Despite his obvious talents, his mathematical calculations were not always correct. In fact, on the subject of coin tossing, he once proclaimed that the chance of tossing a heads increased every time you tossed a tails. This flawed theory was named the “Law of Equilibrium” and was later proved to be false.

His assumptions were based on the fact that such events were likely to balance themselves out over the long term. While this appears to be true to an observer, the law ignores the mathematical fact that every coin toss is an independent event that is in no way related to past or futures results.

So while, over a long period of time, there does appear to be a balancing of results, the probability on each toss always remains the same. However, it was on the basis of this flawed theory, that d’Alembert devised his betting system.

The system he promoted was based on the idea that by decreasing the size of a bet after a win and by increasing it following a loss, the results would eventually even themselves out.

As a result, the d’Alembert betting system is most commonly applied to bets that have odds of evens or 50/50 such as choosing red or black in Roulette, picking pass or don’t pass in Craps or backing banker or player in Baccarat. The system can also be modified and used for other types of bet that are close to evens or contain a bookies commission.

The aim of the system is to win a single unit in profit. To begin, the player must wager a single unit at a price of Evens. If the bet wins they must subtract one unit from the total wagered, if the bet loses they must add one unit to the total wagered. When the total is zero, the sequence ends and a profit of one unit is made.

So if the first bet wins, one unit is subtracted, the total is zero and the sequence ends immediately with a profit. If the first bet loses, then the next bet is increased to 2 units and so on until it wins at which point one unit is subtracted. This continues until the total is reduced to zero. This is where the Law of Equilibrium should come into play.

However, once a few losses have occurred and the bet has been increased, there is no guarantee that the total will ever revert to zero, even after thousands of plays. As a result, the player could spend hours trying to recover the original wager yet never quite achieve it. The system differs from similar systems such as the Martingale or Labouchere in that the stake is only increased by a single unit each time. In that respect it appears less risky - however, while other systems may need just a single win to put you back in profit, the d’Alembert betting system can put you in a scenario where you need a massive winning run to balance out a losing streak and recover your initial wager.