Abstract

http://ssrn.com/abstract=2627354
 
 

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Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers


Joshua Benjamin Miller


Bocconi University - Department of Decision Sciences; IGIER - Innocenzo Gasparini Institute for Economic Research

Adam Sanjurjo


Universidad de Alicante - Departamento de Fundamentos del Análisis Económico

September 30, 2016

IGIER Working Paper No. 552

Abstract:     
We find a subtle but substantial bias in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The mechanism is a form of selection bias, which leads the empirical probability of a given outcome (i.e. proportion) to underestimate its true probability, when conditioning on prior outcomes of the same kind. The bias has important implications for the literature that investigates incorrect beliefs in sequential decision making --- most notably the Hot Hand Fallacy and the Gambler's Fallacy. When the bias is corrected for, the conclusions of prominent studies in the hot hand fallacy literature are reversed. The bias also provides a structural explanation for how belief in the law of small numbers can persist, even in the face of abundant experience.

Number of Pages in PDF File: 75

Keywords: Law of Small Numbers, Alternation Bias, Negative Recency Bias, Gambler's Fallacy, Hot Hand Fallacy, Hot Hand Effect, Sequential Decision Making, Sequential Data, Selection Bias, Finite Sample Bias, Small Sample Bias

JEL Classification: C12, C14, C18,C19, C91, D03, G02


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Date posted: July 7, 2015 ; Last revised: September 30, 2016

Suggested Citation

Miller, Joshua Benjamin and Sanjurjo, Adam, Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers (September 30, 2016). IGIER Working Paper No. 552. Available at SSRN: http://ssrn.com/abstract=2627354 or http://dx.doi.org/10.2139/ssrn.2627354

Contact Information

Joshua Benjarmin Miller (Contact Author)
Bocconi University - Department of Decision Sciences ( email )
Via Roentgen 1
Milan, 20136
Italy
HOME PAGE: http://didattica.unibocconi.eu/mypage/index.php?IdUte=111643&lingua=eng
IGIER - Innocenzo Gasparini Institute for Economic Research ( email )
Via Roentgen 1
Milan, 20136
Italy
HOME PAGE: http://didattica.unibocconi.eu/myigier/index.php?IdUte=111643
Adam Sanjurjo
Universidad de Alicante - Departamento de Fundamentos del Análisis Económico ( email )
Campus de San Vicente
Alicante, 03690
Spain
HOME PAGE: http://sites.google.com/site/adamangelsanjurjo/
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