# Mathematics Research

Markov Chain Models of Board Games:

Recently, a math professor grew tired of his son’s requests to play Chutes and Ladders every day. This situation stimulated the math professor to think about how to shorten the length of the game. He decided to focus on the spinner that controls the number of spaces that a player moves on each turn. It turns out that Chutes and Ladders can be modeled using a probability model called a Markov chain. After the math professor applied this model to Chutes and Ladders, he determined that the expected length of the game is shortest when the spinner has 15 sectors. Students in this research project will attempt to answer similar questions. For example, we may change the spinner so that a player is more likely to spin 1 than to spin the other numbers. How does this new spinner affect the expected length of a game? We may also apply the Markov chain model to other board games, e.g. Hi-Ho! Cherry-O.

Read MoreRecently, a math professor grew tired of his son’s requests to play Chutes and Ladders every day. This situation stimulated the math professor to think about how to shorten the length of the game. He decided to focus on the spinner that controls the number of spaces that a player moves on each turn. It turns out that Chutes and Ladders can be modeled using a probability model called a Markov chain. After the math professor applied this model to Chutes and Ladders, he determined that the expected length of the game is shortest when the spinner has 15 sectors. Students in this research project will attempt to answer similar questions. For example, we may change the spinner so that a player is more likely to spin 1 than to spin the other numbers. How does this new spinner affect the expected length of a game? We may also apply the Markov chain model to other board games, e.g. Hi-Ho! Cherry-O.