I like the idea of there being some randomness involved. Even the most charismatic character isn't going to be perfect.
Rock Paper Scissors is MUCH better than in Fallout where it's just like "Here's your success chance." By doing Rock Paper Scissors, you actually feel like your high charisma score matters, even if you actually lose. (I've not had any major issues beating the AI at RPS. I win about as often as I should.)
But I agree that if they're going to have more than 2 people joining the minigame, then they're going to need to completely replace it. I don't think that adding Lizard Spock will be enough to fix it.