# Thread: simplified model of monopoly as a markov chain

1. ## simplified model of monopoly as a markov chain

Task: Synthesize a strategy and set of procedures to develop a simplified model of Monopoly as a Markov chain.

Any ideas would be greatly appreciated.

2. Originally Posted by Gul
Task: Synthesize a strategy and set of procedures to develop a simplified model of Monopoly as a Markov chain.

Any ideas would be greatly appreciated.
What do you mean by a simplified model?

3. Hi. Basically, the simplified model requires that all 40 squares of the monopoly squares be used in the model, however, rules such as double roll, go to jail etc can be disregarded so as to make the model more simple. Generally, I can simplify the 'rules' of the game, but the board must remain the same i.e. all forty squares must be used.

4. Ah right, k...

That's an interesting one.

Are you using one or two dice?

And you'll have to draw yourself up a forty by forty matrix.

It doesn't sound like a difficult task, apart from the size of the thing...

5. I am planning on using two dice for this model. Yes, the 40 x 40 matrix will be huge indeed, so a 'simpler' game of monopoly will essentially make it much easier as the 40 x 40 will take much less time to calculate.

6. So what part are you having difficulty with?

You know how to draw up the matrix, I'm guessing. And you know how probabilities work, and how to calculate them. Then you just fill in the 1600 entries...

Assuming it's just the transition matrix you're looking for and not something more?

7. I'mhaving difficulty with figuring out some reasonable 'rule simplifications', such as what cards to remove etc.

8. I am now lost.

You're leaving the cards IN???

And all the money stuff etc?

That's ridiculously complicated. Good luck with that

9. Any suggestions to make it much simpler? (please)

10. Well, you could take out the cards and money and just have yourself a giant transition matrix, describing the moves on the board only. And you could use it to guesstimate where you would land after x goes, say.

Or you could assign a positive or negative financial change to each square, and then calculate how much money you'd expect to end up with after going around the board a number of times.

Or you could work out which street is the most landed on ( up to a point x number of goes, whereafter they should all theoretically be equal )

I don't know...

11. That's excellent. Thank you very much.