# Choosing Your Monopoly® Investment Wisely

The popular board game, Monopoly, offers an opportunity for a whimsical lesson in selecting investments based on forecasted performance. The objective of the game is to accumulate as much money as possible by buying real estate and charging opponents “rent” when they land on your property. Much of the game is determined by chance, but key decisions involve selecting which properties to purchase and improve by building houses and hotels. As in real life, players make their investment decisions based on expectations of future returns. One common metric used for comparing investment opportunities is a ratio called “return on assets” (ROA) which is calculated as net income divided by the total assets required to generate that income. I take this approach towards the game of Monopoly, offering recommendations for which properties are the “best” investment.

The ROA calculation involves a numerator (income) and a denominator (total assets). The denominator is the easier of the two numbers to calculate and simply involves adding together the cost of the property and various “improvements” (i.e. houses, adjacent properties, and hotels). The income is more challenging to calculate because a property’s income is affected by the probability that a player lands on that property, and that probability isn’t easily calculated. I rely upon the excellent work of Truman Collins, who models the probabilities of landing on a particular square in any given roll using a computer simulation that “rolls the dice” 32 billion times. Based on Collins’s work, the following investments produce the five greatest incomes per roll:

 Investment Income per Opponent Roll Boardwalk with Hotel (=5 Houses) \$52.52 Boardwalk with 4 Houses 44.64 Boardwalk with 3 Houses 36.76 Illinois Ave. with Hotel 35.04 Pennsylvania Ave. with Hotel 35.01

Notice that the most expensive investments (Boardwalk with a hotel being the highest) generally produce more income per roll. At the same time, we should appreciate that a more expensive property doesn’t always produce greater income. Illinois Ave. with a hotel, for example, is cheaper than several other investments, but it still makes more income per roll.

Investment decisions should be based not only on the amount of income they produce, but also on how much capital is required to generate that income. For example, even though Boardwalk Ave. produces greater income, it is also the case that this investment requires more assets. Since players have finite assets, the critical question is which properties generate the greatest income relative to the required assets. The ROA ratio described above indicates which investments make the best use of capital. The top five investments according to this metric are:

 Investment Return on Assets Per Opponent Roll New York Ave. with 4 Houses 0.035 Boardwalk with 4 Houses 0.032 Tennessee Ave. with 4 Houses 0.032 St. James Place with 4 Houses 0.030 Connecticut Ave. with 4 Houses 0.030

This analysis of monopoly, however playful, illustrates at least two important steps in selecting investment options. First, predict future income from each investment, and second, normalize these returns based on the assets required. If nothing else, we’ve learned that next time we play Monopoly, we should buy New York Ave. if given the chance.