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

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.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)