Oddly Wired
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gambler's fallacy

You think the past forces a change in probability.

A 1971 study found that people expect a coin flip to balance out after a streak of heads, as if the coin has a memory.

The human mind struggles with true randomness, preferring patterns. We view independent events as linked, believing that the universe owes us a specific outcome to maintain equilibrium.

You see fate where there is only statistical independence.

Where this comes from

Study
Tversky and Kahneman, 1971
What the check found
Tversky and Kahneman's 1971 paper is the seminal text defining this cognitive error, describing exactly the phenomenon described in the claim.
Confidence
Well replicated
gambler's fallacyprobabilitycognition

Related

One of these every day, and every one names the study it came from. When a finding is contested, it says so.