There are simulators for "deterministic" games like chess and Go that will estimate each player's win probabilities (probably using Monte Carlo simulation), and also combat resolution simulators for wargames such as Axis and Allies. I was wondering if there are simulators that will estimate your "win chances" in Monopoly, based on the positions that occur after a given trade.

Example: I won a game after giving an opponent the green monopoly in exchange for the maroons. I won the game because I had $1200 cash (and quickly built three houses on each) while my opponent had only $200 cash. (Consider the remaining properties to be "evenly" distributed, including two railroads and one utility for each person.) I would guess that the outcome might very well have been different if my opponent had the $1200, and I the $200.

This isn't a simulator, but it is a calculator that calculates the theoretical value of properties given various "states" of building development. The main thing that is missing is the role of players' cash positions in win chances, because more cash means that you can develop faster than your opponents.

Is there a simulator that can estimate my win chances given starting monopolies and starting cash, (and assuming that the other properties were evenly divided)?

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    To close voters. This is not a question about "game "recommendations." I have already chosen the game (Monopoly). This a question about game 'tools" Does such and such a tool exist (that meets certain objective specifications), and does certain calculations.(I have edited the title to make this clear.) – Tom Au Dec 24 '20 at 21:13
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    If it is closed, we vote for reopen. ;-). There are three Leave Open verdicts in the review queue. – Toon Krijthe Dec 25 '20 at 14:42

Using the calculator linked in the question, you can do your own rough simulators. The calculator already calculates the theoretical value of each roll in your making money from each configuration. The condition that "other properties are evenly divided" equates to "outside of the properties in question, the net gain or loss between the players equals zero.

The thing that is missing from the calculator is the cash levels. To make matters simple, you could invest $900 of cash in three houses each on the maroons (which is what I did), as still have $300 left for emergencies. Your opponent probably needed to retain all of his $200 cash for "emergencies." He could not buy as much as one house each for his greens (unless he mortgaged some properties, and he didn't do that in the actual game).

Let's examine the states, $300 for you, three houses on each of the maroons; $200 for him, no houses. According to the calculator, each of his rolls is worth $35 to you. It takes about 5.85 rolls (averaging seven on a 40 square board) each time around, which is about $205 dollars. That is (slightly) greater than his $200 salary, which means he is on the verge of defeat. Add more houses or build hotels, and he should be sunk.

With the money reversed, the story is different. You opponent could build two houses on each of the greens, deplete his cash, and rely on mortgaging property for his turn to turn needs. You could build one house each on the maroons only by mortgaging for $100 above your cash. Each of your rolls is worth $32 each to him (average expectation for the two houses on each of the greens) and each of his rolls is worth $4 to you (one house on each of the maroons). With a net difference of $28, each time around the board, you are on the verge of defeat, and will be sunk when he adds third houses to each green.

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