The vicious wizard Neville has trapped you in the middle of a magical circle of radius $10000$, and you have to find a way out.
Every time you want to take a step (of length $1$) in a certain direction, Neville decides whether you move in that direction or the opposite one.
Of course, the wizard does his best to hinder you, not to let you escape!
This is an example:
Is there a strategy to escape? If so, how long is the path to freedom?