Testing the limits of optimality: the effect of base rates in the Monty Hall dilemma

Abstract

The Monty Hall dilemma is a probability puzzle in which a player tries to guess which of three doors conceals a desirable prize. After an initial selection, one of the nonchosen doors is opened, revealing that it is not a winner, and the player is given the choice of staying with the initial selection or switching to the other remaining door. Pigeons and humans were tested on two variants of the Monty Hall dilemma, in which one of the three doors had either a higher or a lower chance of containing the prize than did the other two options. The optimal strategy in both cases was to initially choose the lowest-probability door available and then switch away from it. Whereas pigeons learned to approximate the optimal strategy, humans failed to do so on both accounts: They did not show a preference for low-probability options, and they did not consistently switch. An analysis of performance over the course of training indicated that pigeons learned to perform a sequence of responses on each trial, and that sequence was one that yielded the highest possible rate of reinforcement. Humans, in contrast, continued to vary their responses throughout the experiment, possibly in search of a more complex strategy that would exceed the maximum possible win rate.