# The Math Behind Monopoly

Math Behind Monopoly

Do you know you can dominate Monopoly using mathematics? By leveraging Markov Chains, you can calculate probability distributions to make more informed investment choices. This blog post dives into the math behind Monopoly, guiding you to become a Monopoly master.

Markov Chains are mathematical systems that undergo transitions from one state to another on a state space. In Monopoly, each space on the board represents a state. By using Markov Chains, we can predict the likelihood of landing on any given square after a certain number of moves. This insight can be crucial in making strategic decisions during the game.

## How to Calculate Probabilities

• Each space on the Monopoly board is a state. There are 40 spaces, including properties, railroads, utilities, and special spaces like “Go to Jail.”
• The transition matrix is a 40×40 grid showing the probability of moving from one space to another. For example, the probability of moving from “Go” to “Mediterranean Avenue” after rolling a two is calculated here.
• By solving the transition matrix, you obtain a steady-state distribution—essentially, the long-term probabilities of landing on each space. This tells you which properties are most frequently visited.

Based on the steady-state distribution, you should focus on acquiring properties that have higher probabilities of being landed on. Here are some key insights:

• Orange and Red Properties: These are some of the most frequently landed-on spaces due to their proximity to the jail and the high likelihood of players rolling doubles.
• Utilities: While not landed on as frequently as some properties, they offer high returns when players do land on them, especially when both are owned.

## Practical Tips for Winning

1. Prioritize High-Traffic Areas: Focus on buying properties in the orange and red color groups.