# Probability of landing on each box in Monopoly game

I'm trying to understand a good way to calculate the probability of landing on each box of the Monopoly board. In Monopoly you can move both rolling dice and when extra events happen (e.g., chance/community chest cards).

Due to that heterogeneity of moving rules, I would like to simulate the game to calculate landing frequencies, but I have two issues about that:

1. if I simulate a game with only one player it's the same of a simulation with $n$ players? (e.g., the usage of chance/community chest cards could depends on the number of players)
2. Is the simulation a good way to tackle the problem? I mean: isn't there an approach better than mere computer simulation?
• – Gerry Myerson Dec 2 '16 at 11:52
• Simulation certainly seems like a natural idea...if nothing else, all the cards you might draw mess the probabilities up considerably. Not sure if one person simulation is ok...been a while since I played. Can my opponents moves alter my location? If I can't pay rent or if I draw a specific card? – lulu Dec 2 '16 at 11:57
• @lulu yes. If player $A$ picks the card "go to box $b$", player $A$ goes to box B and then the card go to the bottom of the deck of cards. Therefore next player will pick another card, but in terms of box landing frequencies, it seems the same. I'm looking for a general frequencies distribution, if any, regardless of the number of players... – floatingpurr Dec 2 '16 at 12:10
• If you can simulate for one player, you most likely can simulate for N with minor adjustments. Simulation is certainly a good idea. So go for it. An then tells us about it :-) – Rolazaro Azeveires Dec 2 '16 at 13:33
• @RolazaroAzeveires that is sure. : ) I am wondering if there are substantial differences on the calculation of landing frequency. – floatingpurr Dec 2 '16 at 13:43

Also, the likelihood of triple-doubles rolled on the dice $\frac{1}{6^3}$ lands you into Jail no matter where you are located.