The outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is 1 / 2 (one in two). The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. Examples Coin toss Over time, the proportion of red/blue coin tosses approaches 50-50, but the difference decreases to zero non-systematically. The term 'Monte Carlo fallacy' originates from the best known example of the phenomenon, which occurred in the Monte Carlo Casino in 1913.
The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes. The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if an event (whose occurrences are independent and identically distributed) has occurred more frequently than expected, it is less likely to happen again in the future (or vice versa).
Mistaken belief that more frequent chance events will lead to less frequent chance events
