I was playing a game of monopoly the other day, and in the course of strategizing I came up with the idea that how 'safe' you were in the game was a matter of what your expected income/outcome was as you went around the board. I figured it would be a fun project to make a helper program that would compute these values based on a given board configuration, but I found that the statistics got too complicated for me.
At first I was going to just sum up the amount of potential costs you could have on each tile (excluding Chance and Community Chest cards for simplicity), and dividing by 40, the number of tiles on the board, to get the expected value. But I realized that's not actually the expected value because you're not going to land on every tile, and you definitely won't land on 40 tiles in the course of traversing the board. At this point, I figure, there are several assumptions I could make - average die roll is 7, 40 tiles divided by seven steps is ~5.7 turns, so I could divide the total costs by that for an expected value, but that seems like an overly broad assumption in this case - there could be too much variance in the number of turns to get an accurate projection, I think.
I was wondering if anybody more skilled with statistics could give me a hand with this - what is the expected value of your costs in traversing the monopoly board? I intended on ignoring chance and community chest and being sent to jail, as those seemed to overcomplicate the model, but if somebody can incorporate those effects I'd be interested in seeing them.