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How Experience Confirms the Gambler's Fallacy when Sample Size is Neglected

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  • Miller, Joshua Benjamin

    (The University of Melbourne)

  • Sanjurjo, Adam

Abstract

The Gambler's Fallacy is the mistaken belief that random sequences have a systematic tendency towards reversal, i.e. that streaks of similar outcomes are more likely to end than continue. Despite broad empirical support for gambler´s fallacy beliefs, there exists little formal explanation of why such beliefs persist. We present a simple model in which an individual formulates his beliefs about the probability of success given recent success via repeated exposure to random sequences. For each sequence he focuses on the proportion of success given recent success and then updates his beliefs, but (partially) neglects sample size. This results in probability beliefs which, in the limit, are smaller than the true (conditional) probability, i.e. gambler's fallacy beliefs. We discuss the model's novel testable predictions.

Suggested Citation

  • Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "How Experience Confirms the Gambler's Fallacy when Sample Size is Neglected," OSF Preprints m5xsk, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:m5xsk
    DOI: 10.31219/osf.io/m5xsk
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    References listed on IDEAS

    as
    1. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    2. repec:cup:judgdm:v:5:y:2010:i:2:p:124-132 is not listed on IDEAS
    3. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 775-816.
    4. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 730-778.
    5. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    6. Joshua B. Miller & Adam Sanjurjo, 2015. "Surprised by the Gambler’s and Hot Hand Fallacies? A Truth in the Law of Small Numbers," Working Papers 552, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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    Cited by:

    1. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," NBER Working Papers 25200, National Bureau of Economic Research, Inc.
    2. Salaghe, Florina & Sundali, James & Nichols, Mark W. & Guerrero, Federico, 2020. "An empirical investigation of wagering behavior in a large sample of slot machine gamblers," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 369-388.
    3. Ala Avoyan & Robizon Khubulashvili & Giorgi Mekerishvili, 2020. "Call It a Day: History Dependent Stopping Behavior," CESifo Working Paper Series 8603, CESifo.

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