Five heads in a row: is tails due next?

Before you start, the odds of calling five heads in a row are low, 1 in 32. That is why the streak feels as if something must even out soon. But once five heads have already happened, the only question left is the sixth toss, and that single toss is still fifty-fifty. Believing past results change the next one is called the gambler's fallacy. A well-known story says that in 1913 a roulette ball at the Monte Carlo casino landed on black 26 times in a row, and people who kept raising bets on red lost a fortune.

A common mix-up is thinking, "If you toss enough, it ends up half and half, so the missing tails have to catch up." It is true that the share of heads drifts toward one half as you toss more. But that is not because tails comes up extra often. The early five-toss gap simply gets diluted among thousands of later tosses. Toss 1,000 more times and a gap of five barely shows in the overall share.

When people are asked to invent the results of 100 coin tosses, they tend to switch between heads and tails too often. In real runs of 100 tosses, a stretch of five or six of the same side is normal. Mathematician Mark Schilling's work shows the longest streak in 100 tosses is usually around six or seven. Five in a row is less a sign of a strange coin than proof that randomness is naturally lumpy.

Real coins do have one tiny habit. In a 2023 study, researchers tossed coins more than 350,000 times and found the side facing up before the toss came up again about 50.8% of the time. That comes from the coin wobbling as it spins in a hand toss, and it has nothing to do with earlier results. The effect also varied between people and shrank with practice. When you hear "that number hasn't come up lately" or "it's my turn now," remember this. For events that do not affect each other, past results cannot change the odds of the next one.