What’s fun about this problem is that it’s an example of a random walk: a stochastic process made up of a sequence of random steps (in this case, left or right). What makes this a fun variation is that it’s a random walk in a circle- passing 5 to the left is the same as passing 15 to the right. I wasn’t previously familiar with a random walk in a circle, so I approached it through simulation to learn about its properties.
Click through for a simulation. Or 50,000 of them.