H035
After five reds in a row, is black "due" at roulette?
A long streak feels like it has to end soon, as if the wheel were keeping score. It isn't.
The wheel doesn't remember
Five reds are already spun; only the next spin is still uncertain
A streak that already happened doesn't change the odds of the next spin. Six reds in a row is unlikely from the start, about 1.3%. But once five have landed, they are no longer uncertain: the only question left is one spin, and that spin is red 48.6% of the time, the same as always. Believing black is "due" is called the gambler's fallacy.
It shows up wherever events are independent: coin flips, a newborn being a boy or a girl after three sisters, a lottery number that "hasn't come up in a while." Before expecting a run to balance out, ask whether the next event has any way of knowing what came before.
Try it somewhere else
A couple has three daughters and is expecting a fourth child.
Is a boy now more likely than usual, or is each birth its own coin flip?
When the past does matter
The fallacy is about independent events. When earlier results really change what is left, the past matters: after five red cards are dealt from a deck, the next card is a little less likely to be red, because fewer red cards remain. A roulette wheel puts every number back after each spin, so nothing is used up. On August 18, 1913, at the Monte Carlo Casino, black came up 26 times in a row, and players lost millions of francs betting that red was overdue.
Related exhibits
Sources: Single-zero (European) roulette has 18 red, 18 black, and 1 green pocket. Monte Carlo streak of August 18, 1913: Darrell Huff, How to Take a Chance (1959); Encyclopaedia Britannica, "gambler's fallacy."