# 7 Days of Christmas: Day 3

Day 3: Not all Monopoly spaces are equally likely!

The odds of landing on a space can be explored using ‘Markov Chains’. These are a way to map out the end of complex probability systems, like the Monopoly board.

We can make a chart and find the probability that you move you another state in the Monopoly boards with these Markov Chains. For example, someone who rolls the dice on ‘Go’ has the following probabilities for what space they go to next:

• If you roll a 2 – 2.7% chance – Community Chest
• If you roll a 3 – 5.5% chance – Baltic Avenue
• If you roll a 4 – 8.3% chance – Income
• If you roll a 5 – 11.1% chance – Reading Railroad
• If you roll a 6 – 13.9% chance – Oriental Avenue
• If you roll a 7 – 16.7% chance – Chance
• If you roll a 8 – 13.9% chance – Vermont Avenue
• If you roll a 9 – 11.1% chance – Connecticut Avenue
• If you roll a 10 – 8.3% chance – Just Visiting Jail
• If you roll an 11 – 5.5% chance – St. Charles Place
• If you roll a 12 – 2.7% chance – Electric Company
• If you roll a 13+ – 0% chance – Rest of Board

Each space on the board has probabilities like this for where the next roll can take you, which is then further complicated by the ‘Chance’ card and the ‘Go To Jail’ space. By building a large Markov chain model, the probabilities of landing on each space of the Monopoly board can be found:

The most likely is the Jail space; maybe that’s why I always lose!