in the view of mathematics
Have you ever noticed that you are more often visiting Illinois Avenue than Park Place? In long term the difference of both frequencies is 45%! But how we can determine this number? There mainly are two different possiblities, which are demonstrated using two interactive visualisations:
1. First we can take two dice and roll them very often (this way is called Monte Carlo method): Move a token like you do it during a Monopoly match and count the positions you are landing on. If the number of rolls is big enough you'll find 40 probablities, one for each of the 40 positions, as limits of the counted frequencies. If you are looking for a quicker way you can use a computer, which is rolling the dice, moving the token and counting the frequencies. Click here to start such a simulation.
2. Also you can compute the probabilities of reaching the 40 positions after the first move, then after the second move and so on. If you want to see the changing of these probabilities and their long term tendency you can start an animation here. If you aren't afraid of forumulas you can also solve a system of 121 linear equations including 120 variables. For the mathematical background have a look to books of probability theory (you'll find the details in chapters concering the so called Markov chains).
These pages are an interactive
supplement of chapter 16 ("Markov chains and the game Monopoly") of my book "Luck, Logic and White Lies: The Mathematics of Games" (preface and contens).
The results are based on the American edition. Compared to other editions (for example the German edition) there are some minor differences coming from other sets of "Chance" and "Community Chest" cards.
(C) Jörg Bewersdorff, 2002-, www.bewersdorff-online.de,