1. Can this net be folded into an open-topped box? How do you know?

How many different nets can be folded into an open-topped box?

Extensions: What if not open-topped? How many different nets are there for other polyhedra?

2. Rock, Paper, Scissors is considered a fair 2-person game with three options: R, P, S. Why is it fair? Can you design a fair game with 4-options? 5-options?