Teaching Risk and Probability: Building the Monopoly® Board Game Into a Probability Simulator

Selection of Monopoly

Parker Brothers’ Monopoly is a board game of chance and skill played with dice in which the players attempt to buy squares representing districts. They use an initial set amount of money given them by a player holding the bank to build property on their districts and charge other players rent. The aim is to hold enough districts to form a monopoly and win by forcing other players out of the game. After evaluating a range of dice-based board games, Parker Brothers’ Monopoly was selected as it fulfilled all three of Dos Santos Ferreira et al.’s (2014) criteria for effective teaching of probability. A literature search revealed that Monopoly has been applied to teaching accounting (Bergner & Brooks, 2017; Clayton, 2003; Shanklin & Ehlen, 2007), economics (Wright-Maley, 2013), and race relations (Waren, 2011), but no use of the game in probability or risk management was found.

Learning Objectives

The game is typically played as a “beat-the-tutor” challenge, where students who engage in the activity will be able to:

Preparing the Class

Classroom and Board Preparation

Prior to students arriving, the classroom needs to be set up in a seminar format with a table for each group where discussion will take place. The tutor has a separate table for the Monopoly board. The board needs to be prepared prior to commencement. Only two sides of the board are used as the active area, from the “Just Visiting/In Jail” square to the “Go to Jail” square, with the “Free Parking” square in-between being the other corner used. Two of the property groups, orange and yellow, belong to the tutor and are populated with property. The number of houses placed on each property can be varied to adjust the level of challenge, with three houses on each giving an easier game and four houses being more challenging and more likely to result in bankruptcy (see Table 1). All other spaces on the board are inert. The other property groups can be assumed to belong to the students, but they do not affect play as the tutor does not take a turn. Students land on any squares not owned by the tutor with impunity. “Community Chest” and “Chance” cards are not needed.

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Table 1.

U.K. and U.S. Monopoly® Districts Showing Cost and Rent.

U.K. district	Cost	Rent payable for U.K. district (3 houses)	U.S. properties	Cost	Rent payable for U.S. properties (3 houses)
Bow Street	£180	£550	St. James Avenue	$180	$550
Marlborough Street	£180	£550	Tennessee Avenues	$180	$550
Vine Street	£200	£600	New York Avenue	$200	$600
Leicester Square	£260	£800	Atlantic Avenue	$260	$800
Coventry Street	£260	£800	Ventnor Avenue	$260	$800
Piccadilly	£280	£850	Marvin Gardens	$280	$850

The amounts are the same in both U.S. dollars and £ sterling on the respective U.S./U.K. versions.

Preparation of Students

Students are introduced to permutations, combinations, and dice probability theory before the game is “revealed.” Keep the Monopoly board hidden until the students have worked out the probability of throwing a 2, 3, 7, and so on, with two dice. Once this basic concept is understood, a Dice Probability Template (see Figure 1) with missing figures can be given out. This template must be completed by the students to show probabilities for each outcome. If this template is on cardboard, more aware students will realize it can be folded and made to stand next to the board. A simple exposition will show them how many of the 36 different outcomes from the throw of two dice result in each throw probability.

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Figure 1.

Dice Probability Template.

Running the Class

Game Briefing

The tutor organizes the students into groups, introduces the game, and gives each group £1,500 of game currency, suggesting that the completed Dice Probability Template will help to reduce risk if used properly. Each student group chooses a playing piece (or counter), which starts the game in the “Just Visiting” space. Finally, the tutor introduces a special rule concerning the option of purchasing insurance in advance of a risky throw. Landing on one of the tutor-owned squares can be very costly (at least £550 in our simulation), and the groups may insure any one throw for £330, guaranteeing no rent is payable. It can be useful to perform a single “dry run” to explain this principle to students. Some students may realize placing the Dice Probability Template at the edge of the Monopoly board, as shown in Figure 2, gives them the ability to use the risk calculations.

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Figure 2.

Probability distributions when making a move in a game of Monopoly®.

Timing the Session

Timings will vary with size of group and teams involved, but Table 2 will give a generally accurate time for the activity for a group of 20 with four teams.

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Table 2.

Session Timings.

Time (minutes)	Keyword	Tutor activity	Student activity	Resources
15 (Preclass)	Preclass setup	Set up board at front of class with two sides populated with houses as per Table 1; set seminar group tables if required; upload slide presentation; count out cash	Not present	Monopoly board, Slides, projector, computer
5	Introduction	Introduction to session	Listen, make notes	Slides Computer
30	Dice probability theory	Outline of dice probability theory and workings	Complete simple workings	Slides Probability Graph
15	Game briefing	Monopoly® simulation student briefing	Make notes, plan	Slides, Monopoly board
45	Simulation gameplay	Facilitate Gameplay Board; Teams take turns to run the 2 set up sides to beat the tutor by having cash left at end (observe who used Probability Graph)	Planning discussion	Monopoly board
20	Debrief	Use slides to consider chance and randomness, probability risk, mean cost, risk vs. time, alternative strategies	Feedback answer questions	Slides
5	Summary	Revisit learning outcomes and close	Questions	Slides

Debrief

The session debrief discusses the game and the probability aspects and summarizes by reviewing the learning objectives.

Debriefing the Probability Aspects

Students will benefit from a formal debrief on the measurement of risk. A good way to enhance this discussion is with a worksheet showing a decision tree. This worksheet can be worked through on a whiteboard with weaker groups or done as a facilitated session. Figure 3 illustrates this principle, whereby the known cost of buying insurance is £330 while the mean cost of taking the risk is £298.38. It is therefore cheaper to take the risk, yet groups who consistently embrace risk seldom survive to beat the tutor.

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Figure 3.

Monopoly® insurance decision tree.

Sensitivity

Adjustment in sensitivity is achieved by increasing or decreasing the number of houses on the tutor’s two property sets. Different permutations have been tried, but the game works best with three or four houses on each tutor-owned property. With a good student group, even four houses on each will see more groups survive than go bankrupt.

Variations

McMahon (2018) discusses giving token prizes for successful teams, and we have tried this. We found it did not appear to make any difference to motivation and distracted from the purpose of using the game as a learning tool, so we would argue prizes are not important for this simulator.

We have run the simulator as a group competition where students with the most cash left won. This variation did create more excitement, but it tended to take the focus away from the probability aspects as more competitive members of groups focused just on winning, so we discarded this approach.

The exercise can also be extended to explore the opportunity cost of not insuring and the concept of compound probabilities and to apply probability simulations to real-life situations. These themes are developed in the appendix.

Concluding Remarks

Games of chance are exciting, especially when played competitively in groups. We found the beat-the-tutor-scenario kept the students focused and helped the tutor maintain the learning outcomes. We have had no instances of students being unwilling to participate in the game. This may be because of limited student expectations of modules perceived to involve mathematics (Warwick, 2010); when they are then presented with an unexpected alternative, they perceive it to be more fun.

We found student engagement and motivation in the early classes of the risk and decision-making module significantly improved over previous sessions, and this continued through the program with constant references by the students to the Monopoly exercise. Students continued to work with problems of randomness and probability in a more collaborative manner, forming groups and discussing problems rather than asking for help from the tutor; we found we needed far fewer interventions to help students out. We also changed the teaching approach from an instructional facilitated style to a more problem-based learning approach as the module progressed.

The simulation also helped to improve students’ understanding of the concept of randomness and their ability to describe and apply it to risk situations. Batanero et al. (2016) argue that students often struggle with notions of randomness when studying probability. This was evident in our earlier teaching on the module when students found randomness as a concept difficult to comprehend and explain in relation to mathematical or abstract problems. We found comprehension improved after the Monopoly simulation as it introduced students to the randomness at the beginning of the module in a practical manner where the focus is not on the students or their work but on the game board. Later in the module when students needed to discuss and explain elements of randomness and examine risk situations where randomness was present, comprehension was much improved.

This simulation brings together the three areas of good practice for teaching probability: “the perception of chance, the idea of randomness and the interpretation of probability” (Dos Santos Ferreira et al., 2014, p. 132). It is simple to set up and play, and generates more excitement than other random probability simulators we have used. We found the game fostered excellent group motivation, facilitated collaborative learning processes, and encouraged good decision making.