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 a particular event occurs more frequently than normal during the past, it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. 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 usual number of sixes.
Perhaps the most famous example of the gambler's fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in a row is (18/37)26-1 or around 1 in 66.6 million, assuming the mechanism is unbiased. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red.
Perhaps the most famous example of the gambler's fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in a row is (18/37)26-1 or around 1 in 66.6 million, assuming the mechanism is unbiased. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red.
