Imagine a 2-player board game consisting of a board with four squares and one 4-sided die.

Rules of the game. The game is fairly simple: both players start on square 1 and take turns rolling the die to advance their positions on the board (after square 4, players will continue back to square 1). For example, if a player starts on square 2 and rolls a 3, they will advance back to square 1. However, if a roll results in a player stopping on square 3; they will automatically be transported back to square 1. So, if a player starts on square 2 and rolls a 1, they will end up back on square 1. If they instead roll a 2, they will move past square 3 and end up on square 4. In addition, squares 2 and 4 are "for sale and can be purchased by the players on a first-come first-served basis (each player may only own one square). As in Monopoly, if you land on the square owned by the other player, you must pay that player "rent".

In addition, squares 2 and 4 are "for sale" and can be purchased by the players on a first-come first-served basis (each player may only own one square). As in Monopoly, if you land on the square owned by the other player, you must pay that player "rent". The first player to run out of money loses the game. The goal of this question is to see how we can encode aspects of the game using the language of linear algebra. Later we will see how this will help us determine which of the two squares is more likely to be landed on and help us determine a winning strategy for the game. (a) Because the 4-sided die was constructed poorly, it is not a fair die (i.e. the probability that you roll a l may not be the same as the probability that you roll a 2). The probability of rolling each number using the game board's die is shown below: