MobLab
Guides
Aa

# Monty Hall

## Game Description

We put a spin on this classic decision theory problem. Students are space explorers attempting to purchase a teleporter to return home (if you want the classic version that is an option in the Basic Panel). Dave is an eccentric teleporter salesman that loves games. Dave hides one working teleporter amid (2 or 19) broken teleporters and tells the space explorer to make a choice. After the explorer makes a choice Dave reveals all but one of the broken teleporters, leaving the explorer with one working teleporter and one broken teleporter. Then Dave asks the intrepid space explorer if they would like to stay with their initial choice or switch.

### Learning Objective: Bayes' Rule

Through repeated trials and adding more teleporters (i.e. doors), and changing student perspectives to be in the role of Dave (i.e. the host) this game seeks to build intuition about Bayes’ Rule.

## Brief Instructions

In the default setting students act in the role of space explorers (contestants) choosing among a set of teleporters (doors). All but one teleporter is broken (as all but one door is empty). After the explorer makes an initial choice, the salesman (the host) reveals all but one of the broken teleporters, leaving the explorer with one working teleporter and one broken teleporter. Should the explorer switch their initial choice?

## Key Treatment Variations

#### Repeated Trials

Bayesian thinking is not natural for students (or for many of us!) therefore repeated trials are recommended to show there is an empirical basis for this rule.

#### Initial Set of Choices

Alter the initial number of teleporters to be either three (the classic problem) or twenty. An increase in the number of doors should help build intuition as student's realize their initial choice was not likely.

## Results

There are two multiround summary graphs. Figure 1 averages across rounds to show the fraction of students who choose “No Switch” versus “Switch”. Figure 2 presents information on the average fraction of individuals switching each round.

Figure 3 presents the multi-round summary table that contains basic information on the number of individuals, number of initial choices (3 or 20), fraction of individuals switching, average win rate (switch), average win rate (no switch).