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There was a computer simulation run a few years ago for Monopoly which calculated the most likely properties and squares to land on and some other data. Does anyone have or know the stats of the simulation?

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Here is a link to some books with such stats: amazon.com/The-Monopoly-Book-Strategy-Tactics/dp/0679202927 –  Tom Au Oct 16 '13 at 23:08
    
Your title doesn't match your question very well - winning and being likely to land on certain squares are very different things. –  Jefromi Oct 16 '13 at 23:11

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I know the results. Red and Orange properties are places where players most often lands on. Most often visited places are the Jail and the 3rd red property ("Illinois Avenue" in the American version and "Avenue Henri-Martin" in the French version).

I found a table here (fr). The table contains the French names so I join a french Monopoly board to this answer in order to help people who do not know French names.

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Here are the (quite extensive!) results: http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml

The first part of that page is the long-term probabilities for ending up on a particular square. The last column tells you the ranking: you will end up in Jail most often, Illinois second-most-often, then Go, then the B&O Railroad, etc. This is neat, but you'll need to figure out whether those most-frequently-hit squares are profitable in the short and long term; the next part is about the expected income per roll, and after that is how long it will take you to recoup the cost of things. (Fun fact: buying the third house is the fastest thing to recoup. That doesn't mean you should buy straight to three houses, or that you should stop there; it just means that you'll earn the money-for-the-third-house back fastest.)

The problem with that page is that it doesn't point you to The Best Strategy. Do you want to earn back your initial money fast? Do you want to earn the most money overall, even if you'll have less money in the early game? Do you just take a hedonistic joy in getting people to hand you money, and want that to happen as often as possible? You'll go far by picking up the properties that recoup your costs quickly, but those properties are the light blue and orange properties - they're nicely profitable and quick to set up, but they don't rake in the gobs of money you'll want in the end-game.

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I am not sure which particular site you are referencing, but How to Win at Monopoly calculated the Return On Investment (ROI) of all the properties based on the liklihood of landing on them. They concluded that Railroads (especially 4) had the fastest most consistent ROI, followed by a Monopoly with 3 Houses, utilities were the worst ROI.

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I highly recommend Winning Monopoly if you are interested in such analysis. As other answers point out, payback period (combining rent amount and frequecy) is key for making winning decisions. One of the point from this book that I haven't seen else where is determining what version of Monopoly you are playing. Are you really playing until all others are bankrupt, or is there some (probably unstated) time limit for the game. Knowing how much longer the game will last is key to putting payback period statistics to use.

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