Quiz

Where in the problem statement does it say that they only have one coin, and that it's crooked?

And where does it say that they have one? )

Regarding "rock-paper-scissors," it's all very simple here; it's a game of chance equivalent to flipping a coin. Whoever had the stronger option won.

Ah, so it's a trick with the conditions... Yes, I didn't even include the point that a coin must be used. Well, I'll give you credit for that.
If using a coin, here's a suggestion: flip the coin twice. Player 1 wins if it lands on heads-tails. Player 2 wins if it lands on tails-heads. In all other cases, the experiment is repeated.
Also, if there's no information about which side is more likely to appear, you can simply flip the coin in the usual way, and the randomness will be in choosing which side of the coin each player takes. That's the idea.
Neyra?