The History of D'Alembert
One of the things you’ll quickly notice about roulette strategies is that they tend to come from the brains of mathematicians. D’Alembert was no exception, though his dabbling in physics is arguably the more well-known part of his academic life today. D’Alembert, full name Jean-Baptiste le Rond d’Alembert, lived during the 18th century and is notable for his incorrect belief that the probability of getting heads in a coin toss increases with each tail that lands. Today, we know this as the gambler’s fallacy.
So, does that schoolboy error mean that we should disregard the D’Alembert strategy? No. D’Alembert’s problem was that he invested heavily in something he termed the equilibrium of numbers, which suggests that a system that has a 50% chance of doing something will eventually result in both outcomes occurring equally. Hence, the coin toss example. However, while D’Alembert’s thinking example was flawed (the probability of landing a head never increases), there is some truth to his overall idea.
A Roulette wheel normally has a red and a black section. Over thousands and thousands of spins, there’s a good chance that these two colours will be evenly distributed in terms of where the ball lands each time. This works almost exclusively in high numbers, though, meaning that ten or twenty spins will produce variable results. To use a popular example, from Monte Carlo in 1913, the ball took 27 spins to land on red. Importantly, the chance of a red or black appearing never changed once during that remarkable spell.