The problem you run into is that your suggested method of testing doesn't yield the result you think it does. It would have been more fun to address this in the thread you already started, but you decided to start a new one so here we are.

How close to the starting point do you think you'll end up on a globe, and how close to the starting point do you think you'll end up on a FE? Let's start there. Keep your 100km-per-leg-of-journey assumption.

For added fun, after you think about this assuming you start at a pole, think about how it might work out if you start at the Equator, or in Boulder CO, or Sydney Australia. What if you shrink the distance to 10km, or 1km, or 100m? Is it different in any of those locations/situations? Why or why not?