What is Gambler's fallacy?
The gambler's fallacy is the mistaken belief that past results of independent random events change the odds of future ones, such as thinking red is 'due' after a run of black.
In roulette, each spin is independent. After ten blacks in a row, the chance of red on the next spin of a European wheel is still 18 in 37. The same applies to slots driven by an RNG and to dice in craps. Machines and wheels have no memory.
The fallacy is sometimes called the Monte Carlo fallacy after a famous evening at the Monte Carlo Casino in 1913 when black came up 26 times in a row, and many players lost heavily betting that red must follow.
The idea underpins many betting systems that raise stakes after losses. These systems cannot overcome the house edge and can increase losses quickly. Understanding the fallacy is a core part of responsible gambling information.