While browsing through YouTube, I came across this video discussing how Monopoly doesn’t have each position at the same probability and some are more likely than others. I decided to take this as a task for myself and make a naive simulation of the game. What followed was a couple of hours of coding, plotting and preparing this text, all while having my Monopoly board open on the side to ensure accurate information in the code. The code for this fun mini-project can be found here
A Broad Overview
I considered organizing the board into a single-dimensional array and assigning to each position a unique index with which they could be referred by. Simulating multi-player dynamics turned out to be an extremely computationally intensive task depending upon a whole lot of luck in the choices made. In order to be computationally feasible while maintaining a modicum of accuracy, I ran a million simulations of a 100-turn single player game. It must be noted that turn here includes multiple movements caused by repeated die rolls as part of the original turn and not as a unique turn. This classification helps make the arbitrary choice of the number of turns not as crazy as it might seem on the face of it. All mechanics of the game, including special cards, were simulated exactly as one would expect in a real game of Monopoly. None of this is ground-breaking, of course, so let us go for the more interesting part of this article.
Analysis
My approach was to model a formula for the “value” of various investments possessed by a user in order to quantify their net worth. The reasoning takes into account the following – The costlier the property, the higher the rent. Adopting a linear dependence of the value of properties upon their rent thus seems to be a fair starting point. The costlier the property, the tougher it is to acquire the property group and provide construction. Because of this, we end up facing what is essentially a negative feedback effect which must be accounted for.
An assumption made in this analysis is that players will try to complete their property groups with a higher priority than what they would assign to acquiring individual properties belonging to distinct property groups. This assumption might seem to be the craziest of them all, but it works out in this simulation since this is a single player simulation and the dynamics of a multi-player game which includes fun stuff such as trades and auctions do not apply. There is no simple way of simulating this behavior as far as I can tell and probably needs to be looked at as a research problem.
So, what do I buy?
That is the million-dollar question behind doing all of this hard work after all! By and large, my simulation yielded results which agreed broadly with what I had observed in all the times I had played Monopoly with my friends. Namely,
There is a tremendous value in acquiring the costliest property group owing in part to its ease of completion and its high rent Railways come second in terms of pure value and this makes total sense considering their low investment cost and higher chances of landing on a railway location The cheapest property group comes as a close third in terms of pure value and this too makes the most amount of sense since they are very easy to complete and have a good return on investment once properties are constructed Lastly, of all the property groups to be surveyed, it was the orange property group (the one terminating in free parking) that had the worst value, followed by the group immediately following it (the red group) All in all, this was a fun experiment to do. I welcome all suggestions and contributions to improve the results obtained here.