After ten blacks in a row at roulette, red feels overdue. It is not: the wheel has no memory, each spin is an independent draw, and red's probability on the eleventh spin is exactly what it was on the first. Long streaks feel meaningful because they are rare, but a rare past does not bend a future probability.
The fallacy has a mirror image: believing a result is hot and will continue. Both readings extract a signal from noise, and both lead to the same behaviour, raising stakes on the strength of information that does not exist. Games are engineered so that history carries no information, and the certified RNG behind an online game guarantees exactly that.
Why it matters
It is the most expensive belief in gambling, because it justifies chasing losses: the sense that a losing streak must end soon is precisely what escalates a bad session into a ruinous one.
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