Chance Has No Memory

After five heads in a row, the chance of heads on the next toss of a fair coin is still one in two. Each toss is independent: what came before does not push on what comes next.

Yet streaks feel as if they must even out. This is the gambler’s fallacy, also called the Monte Carlo fallacy, after a night in 1913 when a roulette wheel at the Monte Carlo Casino landed on black 26 times in a row.

Over many tosses, heads and tails do settle near half each. They get there because the streak is swamped by new tosses, not because the coin corrects itself. Before you call something “due,” ask whether one event can influence the next at all.

The overdue number

Lars plays the same weekly lottery. He notices that 17 has not been drawn for eight months, so he starts putting it on every ticket, sure its turn has come.

The balls are mixed and drawn fresh each week, so 17 is exactly as likely this week as any other number. The past would matter only if the draw had a memory, as a deck of cards does when dealt cards are not put back.

Try this today Next time someone says a result is “due,” ask whether the earlier events could physically change the next one.

More on this fallacy: Gambler’s fallacy →