Journal article

A Bridge from Monty Hall to the Hot Hand: The Principle of Restricted Choice

Joshua B Miller, Adam Sanjurjo

Journal of Economic Perspectives | American Economic Association | Published : 2019


We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the recently discovered hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes's rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

University of Melbourne Researchers


Awarded by Spanish Ministry of Economics and Competitiveness

Awarded by Generalitat Valenciana

Funding Acknowledgements

Financial support from Bocconi University, Bocconi Experimental Laboratory for the Social Sciences (BELSS), and the Spanish Ministry of Economics and Competitiveness (Project ECO2015-65820-P) is gratefully acknowledged. We also gratefully acknowledge Generalitat Valenciana (Research Projects Grupos 3/086 and PROMETEO/2013/037). This draft has benefitted from conversations with Maya Bar-Hillel, Ben Cohen, Lola Collado, Vincent Crawford, Carlos Cueva, Martin Dufwenberg, Jordan Ellenberg, Maria Glymour, Inigo Iturbe, Steve Kass, Mike Lipkin, Massimo Marinacci, Judea Pearl, Lones Smith, and Dan Stone, as well as seminar participants at University of Alicante, Radboud University Nijmegen, Nova School of Business and Economics, Technical University of Dortmund, the 2016 International Meeting on Experimental and Behavioral Social Sciences (IMEBESS), and the 2017 Research Unit on Complexity and Economics (UECE) Lisbon Meetings in Game Theory and Applications.