Table of Contents### Gambler's Fallacy

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People see patterns in data that is random and then make predictions about the future based on those perceived patterns. These predictions appear to be affected by whether the player feels the game is fair or not. For example, gamblers know that the roulette wheel, keno, or flipping a coin is fair. Gamblers cling to the idea that if a game is fair, then all the numbers in the game should come up the same number of times, on average. This concept is true for very large trials of the game, but not for small trials. In a small number of trials, the outcome can appear very unfair.

Consider the five tosses of a fair coin: head, tail, head, head, head. A fair coin is supposed to show equal numbers of heads and tails, on average. Therefore, this outcome appears to have strayed from our notion of what we should expect. What is the probability that the next toss will result in a tail? Most gamblers behave as if they believe that some correction must occur in the sequence and that tails are more likely than heads to appear in the next several tosses. This belief that there is some self-correcting process in the other direction is known as the gambler's fallacy.^{[1]} If the coin is fair, the probability of a tails in the sixth toss is 50%, despite the outcome of the previous tosses. Yet, books are sold showing the frequency with which each number comes up in the state lottery. Why? Because people succumb to this fallacy.