After ten heads in a row

Question

A coin is flipped and lands heads ten times in a row. 1. If the coin is known to be fair, what is the probability that the next flip is heads? Is tails "due"? 2. If you were not sure the coin was fair beforehand, should the ten heads change your estimate, and in which direction?

Accepted Answer

For a fair coin the answer is exactly 1/2; tails is not due. If the coin's fairness was uncertain, ten heads should make you expect heads more, not less. The fair coin. Each flip is independent of the past. The coin does not know it has produced ten heads and has no mechanism to compensate. The probability of heads on the eleventh flip is 1/2. Believing that tails is now more likely is the gambler's fallacy. What is true is that a long run of eleven heads is rare in advance (1 in 2,048), but ten of those flips have already happened; the rare event is mostly behind you. The uncertain coin. Sup…

After ten heads in a row

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