Perceptions and Probabilities: Influence of Increased Options on Performance Generalization Across Two Variations of the Monty Hall Dilemma

Abstract

The Monty Hall dilemma (MHD) is a probability puzzle in which humans consistently fail to adopt the optimal winning strategy. The participant chooses between three identical doors, behind one of which is a valuable prize. After the participant makes their initial decision, the host reveals that there is nothing behind one of the two remaining doors, then asks the participant if they would like to stay with their originally selected door or switch to the remaining unopened door. The optimal choice is to switch to the previously unchosen door, which increases the probability of winning from 33% to 67%. Despite this basic solution, humans repeatedly perform suboptimally. Previous attempts to improve performance by increasing the number of available doors have been successful (Burns & Weith, 2004; Franko-Watkins et al., 2003; Saenen et al., 2015; Stibel et al., 2009; Watzek et al., 2018). However, prior studies that examined whether this improved performance could generalize to different contexts have been inconclusive (Franko-Watkins et al., 2003; Watzek et al., 2018). To examine whether human performance can generalize across two computerized variations of the MHD, the present study explored how previous experience involving trials presented with eight options affects switching percentages in subsequent trials with three options. The results replicated findings from previous studies, which demonstrated that switching rates increased as a function of more available options. The findings also revealed participants can successfully generalize their behavior when returning to three-option trials. Further exploration of the MHD is needed to determine why performance generalization occurs in certain contexts, but not others.