The folk belief that outcomes must even out in the short run; large samples converge, individual trials do not.
Not a law. Only the law of large numbers holds, and only in the limit — a coin that has landed heads ten times has no memory, and the folk belief is the gambler's fallacy wearing respectable clothes.
In practice
- A gambler who has lost eight hands believes a win is due, and the deck has no memory.
- A hiring manager whose last three hires failed expects the next to succeed on the same reasoning that predicted the last three would.
- Possible explanations
- The explanation for the belief is that people expect short sequences to look like the long-run average, so a run of one outcome feels overdue for correction.
- In its favour
- The underlying mathematics is real in the limit: with enough trials, proportions do converge on their expected values.
- Against it
- Independent trials have no memory, so nothing evens out in the short run. As used in everyday talk it is the gambler's fallacy under a respectable name.
- Standing
- Not a law; only the law of large numbers holds, and only in the limit.
- Further reading
- Wikipedia
- Subject
- Decision-making & Reasoning
- Essay
- Paradoxes that broke theories, and sayings that outlived them