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The cross-sectional “Gambler's Fallacy”: Set representativeness in lottery number choices

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  • Lien, Jaimie W.
  • Yuan, Jia

Abstract

Traditionally, the Gambler's Fallacy is described as the belief that a sequence of independent outcomes over time should exhibit short-run reversals. The underlying psychological bias thought to drive this fallacy is Representativeness Bias: the idea that even a small sample of outcomes should closely reflect the theoretical probability distribution (Tversky and Kahneman, 1971). Yet representativeness also has less commonly explored consequences in the cross-sectional dimension. We find strong evidence for this in lottery play where probabilities are well-defined and transparent, using a dataset of over 1.6 million lottery tickets purchased by over 28,000 players. Specifically, individuals prefer number combinations that are cross-sectionally representative of the uniform distribution from which they are drawn. We test two possible approaches to implementing representativeness; a heuristic 3-bin approach which is promoted in some gambling advice literature, and a direct optimization approach in which gamblers try to spread the numbers in the chosen set as evenly as possible across the lottery number range. By both measures, gamblers over-gravitated to highly representative lottery number sets and over-avoided less representative sets, compared to the proportions that the true lottery odds would suggest. In this pari-mutuel lottery setting, a cost is incurred by gamblers with this type of bias, by reducing their expected winnings.

Suggested Citation

  • Lien, Jaimie W. & Yuan, Jia, 2015. "The cross-sectional “Gambler's Fallacy”: Set representativeness in lottery number choices," Journal of Economic Behavior & Organization, Elsevier, vol. 109(C), pages 163-172.
    • Handle: RePEc:eee:jeborg:v:109:y:2015:i:c:p:163-172
    DOI: 10.1016/j.jebo.2014.10.011
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    References listed on IDEAS

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    1. Richard H. Thaler & Shlomo Benartzi, 2001. "Naive Diversification Strategies in Defined Contribution Saving Plans," American Economic Review, American Economic Association, vol. 91(1), pages 79-98, March.
    2. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-317, May.
    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.
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    Citations

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    1. Michał Wiktor Krawczyk & Joanna Rachubik, 2019. "The representativeness heuristic and the choice of lottery tickets: A field experiment," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 14(1), pages 51-57, January.
    2. Tong V. Wang & Rogier J. D. Potter van Loon & Martijn J. van den Assem & Dennie van Dolder, 2016. "Number preferences in lotteries," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(3), pages 243-259, May.
    3. Brian Dillon & Travis J. Lybbert, 2024. "The gambler’s fallacy prevails in lottery play," Journal of Risk and Uncertainty, Springer, vol. 69(1), pages 33-56, August.
    4. Brian A. Polin & Eyal Ben Isaac & Itzhak Aharon, 2021. "Patterns in manually selected numbers in the Israeli lottery," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(4), pages 1039-1059, July.
    5. Michal Krawczyk & Joanna Rachubik, 2018. "Verifying the representativeness heuristic: A field experiment with real-life lottery tickets," Natural Field Experiments 00699, The Field Experiments Website.
    6. Oluwaseun A. Otekunrin & Adesola G. Folorunso & Kehinde O. Alawode, 2021. "Number preferences in selected Nigerian lottery games," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(4), pages 1060-1071, July.

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    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • L86 - Industrial Organization - - Industry Studies: Services - - - Information and Internet Services; Computer Software

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