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Perceptions of randomness in binary sequences: Normative, heuristic, or both?

Stian Reimers1, Chris Donkin2, Mike E Le Pelley3

  • 1City, University of London, UK; University College London, London, UK.

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Summary
This summary is machine-generated.

People often misjudge the probability of random sequences, favoring less structured ones like HTTHT over more ordered ones like HHHHH. This study reveals these judgments rely on representativeness heuristics, not objective probabilities.

Keywords:
BiasesGambler’s fallacyHeuristicsProbabilityRandomness

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Area of Science:

  • Cognitive Psychology
  • Probability Judgment
  • Heuristics and Biases

Background:

  • People exhibit biases when estimating probabilities of random sequences.
  • The local representativeness heuristic suggests people expect short sequences to mirror long-term statistical properties.

Purpose of the Study:

  • To test whether people's probability judgments for random binary sequences are based on objective probabilities or representativeness heuristics.
  • To investigate the factors influencing these judgments, such as sequence structure and complexity.

Main Methods:

  • Participants rated the likelihood of occurrence for all possible binary sequences of lengths 4, 5, and 6.
  • Incentivized binary choice procedures were used in subsequent experiments.

Main Results:

  • Judgments were better explained by representativeness heuristics (alternation rate, proportion of heads/tails, complexity) than by objective probabilities.
  • Participants were insensitive to variations in the objective probabilities of sub-sequences.

Conclusions:

  • People's estimations of random sequence probabilities are driven by representativeness heuristics, not accurate calculations of objective probability.
  • This suggests cognitive heuristics play a significant role in how individuals perceive and evaluate random events.