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The gambler's fallacy is a thought process that has a person believing probabilities of unique occurrences will change because of previous results. It is also called the maturity of chances. In other words, it is the belief that an event with a fixed probability, such as a coin toss or dice roll, is somehow affected by previous examples.
A famous example of this occurred at a Monte Carlo casino in 1913 where a roulette wheel repeatedly came up black. After each successive spin, more and more individuals would bet on red, assuming that red was "due" to be hit. The odds never changed, however. No matter what happened previously the chances of red coming up were still just below 50 percent. Because of this specific example the gambler's fallacy is sometimes referred to as the Monte Carlo Fallacy.
This illusion of control is seen frequently by gamblers who have developed a betting system that they believe maximizes their chances of winning. They assume that by observing their surroundings they can increase their odds. They can do this by picking slot machines that they think are ready to pay out after seeing others repeatedly lose at them, engage in the previously cited example at a roulette wheel, or bet on a certain sequence of numbers in the lottery because they believe they haven't been picked in a while.
This is what psychologists call a cognitive bias, which is when people draw false conclusions not on the hard evidence, but instead on their own thoughts and beliefs, which have no factual basis. Many who fall into the gambler's fallacy cite the law of averages as a fact to support their claims. They believe that any "run" on a machine or game, such as a streak of black or red on the roulette table, will be corrected on the next spin. Actual laws of probability state that anomalies even out over a long period of time, not the next spin of the wheel.
Gambler's conceit plays heavily into the the idea of the gambler's fallacy. Gambler's conceit is the frequently mistaken belief that a person can walk away from a game during a winning streak, commonly referred to as quitting while they're ahead. Yet gamblers rarely quit before losing. This is because they are falling into the gambler's fallacy. They believe that previous results will dictate future winnings, even though those previous events have no bearing as to what will happen in the future.
This behavior can often lead to gambler's ruin, which is when a gambler fails to walk away after earning a large amount of winnings, and instead slowly gambles it all away. Casinos bank on this, letting the odds of the games balance, which is when the house wins.
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