Chance of Landing on a Spot in Monopoly

2013-02-02

It makes an intuitive kind of sense that my chances of landing on a specific square in monopoly are different depending on where I start. As a simple example, if I am at a distance of one to the target (ie. rolling a one will cause me to land on the target), then my chances of landing on the target are simply 1/6 (16.67%). If I am at a distance of two, I have the same chance of landing directly on the target. However, I also have a chance of landing at a distance of one to the target, from which I can roll again, increasing the changes of landing on the target to: 1/6 + (1/6 * 1/6) = 7/36 (19.44%)

What are the chances for distances up to 20?

Hint:

distance(7): 25.36%
distance(19): 28.47%