Gambler's fallacy vs Hot hand: two myths in opposite directions | Ludwig Explains

Two famous "we're bad at randomness" fallacies — that point in OPPOSITE directions.

**Gambler's fallacy.** A roulette wheel comes up red 8 times in a row. Is black "due"? No. The wheel has no memory. Each spin is independent. P(red) is 18/38 ≈ 47.4% every single time, regardless of streak length. Streaks don't "use up" the chance of an outcome.

**Hot hand "fallacy"… that turned out to be partly real.** In 1985, Gilovich, Vallone & Tversky published a famous paper showing basketball "hot hands" were a perceptual illusion — streaks in shooting were no more frequent than random. That finding stood for 30 years.

Then in 2018, economists Joshua Miller and Adam Sanjurjo found a subtle statistical bug in the original method: when you sample streaks the way Gilovich did, you systematically underestimate the conditional probability of a hit after a hit. Correct for that, and the hot hand IS real — just smaller than fans claim (~2-4 percentage points). Detectable, modest, real.

The two fallacies push opposite ways:
- **Gambler's:** "streaks reverse." Wrong, for independent events.
- **Hot hand:** "streaks persist." Right (with a small effect), for skill events.

The deep idea: independent events have no memory. Skill events do. The trick is knowing which is which.

Topics:
- Gambler's fallacy on truly independent events (roulette)
- The 1985 hot-hand paper (Gilovich, Vallone, Tversky)
- The 2018 Miller-Sanjurjo correction
- Why two opposite biases reflect the same cognitive blind spot

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