A randomised Monty Hall experiment: The positive effect of conditional frequency feedback

Abstract

The Monty Hall dilemma (MHD) is a notorious probability problem with a counterintuitive solution. There is a strong tendency to stay with the initial choice, despite the fact that switching doubles the probability of winning. The current randomised experiment investigates whether feedback in a series of trials improves behavioural performance on the MHD and increases the level of understanding of the problem. Feedback was either conditional or non-conditional, and was given either in frequency format or in percentage format. Results show that people learn to switch most when receiving conditional feedback in frequency format. However, problem understanding does not improve as a consequence of receiving feedback. Our study confirms the dissociation between behavioural performance on the MHD, on one hand, and actual understanding of the MHD, on the other. We discuss how this dissociation can be understood.

Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review

“…In addition, in the study of Herbranson and Wang (2014) and in one experimental condition (with the classical MHD) of the study of Mazur and Kalhbaugh (2012), participants showed no significant increase in switching rates over trials. These participants, however, already showed a high switching rate in the first block of trials as compared to other studies (Franco-Watkins et al, 2003; Klein et al, 2013; Petrocelli, 2013; Petrocelli & Harris, 2011; Saenen et al, 2015b; Slembeck & Tyran, 2004). An important question that arises with the evidence of increased switching behaviour across successive trials is whether participants gain understanding of the problem as well.…”

“…The results of most of these studies provide strong evidence for learning from experience: Increased switching rates over trials were observed (Franco-Watkins et al, 2003; Herbranson & Schroeder, 2010; Hirao et al, 2017, Klein et al, 2013; Mazur & Kahlbaugh, 2012; Petrocelli, 2013; Petrocelli & Harris, 2011; Saenen et al, 2015b; Slembeck & Tyran, 2004; Tubau & Alonso, 2003). However, in none of these studies the repeated experience led to participants consistently switching on all trials.…”

“…All included studies of this systematic review in which participants received feedback, either conditional or non-conditional, show that participants fail to fully understand the advantage of switching because 100% switching behaviour was never observed (DiBattista, 2011; Herbranson & Schroeder, 2010; Hirao et al, 2016, 2017; Klein, Evans, Schultz, & Beran, 2013; Mazur & Kahlbaugh, 2012; Saenen, Van Dooren, & Onghena, 2015b; Slembeck & Tyran, 2004). …”

“…First, in several studies, participants were given multiple trials of the MHD which allowed the researchers to investigate whether repeated experience and feedback with the problem would improve performances (Efendic & Drace, 2015; Franco-Watkins et al, 2003; Herbranson & Schroeder, 2010; Herbranson & Wang, 2014; Hirao et al, 2016, 2017; Klein et al, 2013; Mazur & Kahlbaugh, 2012; Petrocelli, 2013; Petrocelli & Harris, 2011; Saenen et al, 2015b; Slembeck & Tyran, 2004; Tubau & Alsonso, 2003). The results of most of these studies provide strong evidence for learning from experience: Increased switching rates over trials were observed (Franco-Watkins et al, 2003; Herbranson & Schroeder, 2010; Hirao et al, 2017, Klein et al, 2013; Mazur & Kahlbaugh, 2012; Petrocelli, 2013; Petrocelli & Harris, 2011; Saenen et al, 2015b; Slembeck & Tyran, 2004; Tubau & Alonso, 2003).…”

The Monty Hall Problem as a Bayesian Game

“…The typical justification put forward by the subjects is that the likelihood of success if they were to switch curtains is the same as if they were to stay with their original choice of curtain. This mistake is often cited as an example of the equiprobability bias heuristic ( [14], [15], [19], [9]) as described in Lecoutre (1992) [7]. [6].…”