Nice post. Much to say about Monopoly.
I studied this over a decade ago, and it is a little foggy. I made a transition matrix and made precise calculations as a Markov chain (as you mentioned). Precise calculations of the expected payoffs behind building on Connecticut, etc.. I will try to find it. Of course that code is very out of date. Your visualizations are great. (Note that Mod[n,40,1] will give you a number between 1 and 40)
Perhaps one of the surprising things, but not really so surprising, is the dependence of all this analysis on strategy. Early in the game, everyone pays to get out of jail because it is so important to land on unbought properties, and late in the game you sit it out in jail. This has a noticeable effect on the likelihoods. (Not to mention the complexity of developing or mortgaging properties and the dynamic feature of going out of the game which also has a big effect.)
One question that arises is how to explain the practical importance of the orange and red monopolies. It could just be a feature of the cash on hand. For instance, with extremely large cash reserves you expect more out of the greens than the oranges. Or it could be for the practical reason that it is easier to recover from a catastrophe , but if I remember right, there isn't a really satisfactory explanation for why the oranges and the reds are so good.
Many people think that Monopoly is a simple game. Say I land on the first railroad, Reading Railroad, buy it, and then ask "who wants to buy it? Make an offer." Not so obvious.
