The Math Behind Monopoly

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.
  • Railroads: Owning multiple railroads increases your chances of earning steady income, as they are frequented by players moving across the board.
  • 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.
  2. Monopolize Railroads: Owning all four railroads can significantly boost your income.
  3. Balanced Investment: Don’t overspend on low-impact properties; instead, save your money for strategic buys.
  4. Build Wisely: Invest in houses and hotels on your high-traffic properties first to maximize your rental income.

For those keen to explore this topic further, read Walter Hickey’s article, How to Use Math to Dominate at Monopoly. He provides an in-depth analysis and practical tips for using math to gain an advantage in the game.

Understanding the math behind Monopoly can transform the way you play. By using Markov Chains and probability distributions, you can make informed decisions that increase your chances of winning. Next time you play, remember to apply these mathematical strategies and watch as you dominate the board.

Ready to become a Monopoly master? Grab your game board, crunch the numbers, and start making strategic investments today!

Ali Kaya


Ali Kaya

This is Ali. Bespectacled and mustachioed father, math blogger, and soccer player. I also do consult for global math and science startups.