Chapter 11.3, Problem 10E

Monopoly is “the most played board game in the world,” according to Hasbro, its manufacturer. Players take turns moving around the board, according to a roll of a pair of dice. The board consists of $40$ squares, $28$ of which are properties such as Marvin Gardens, B&O Railroad, and Water Work. There are also three Chance squares, three Community Chest squares, Luxury Tax, Income Tax, Jail, Free Parking, Go, and Go to Jail.

This game can be analyzed by using Markov chains. There are $40$ states, one for each square on the board. Read about the game’s rules, and create a transition matrix for the game. Do not try to make a long-range prediction. Instead, discuss what information would be contained in such a prediction.

HINT: The probabilities of moving from “Go” to Mediterranean Avenue, Community Chest, Baltic Avenue, Income Tax, Reading Railroad, or Oriental Avenue are each $\frac{1}{6}$.