So hopefully you actually read and thought about the 3 Card Mindgame: https://willowrants.wordpress.com/2006/08/31/3-card-mindgame/
Ok, I promised there would be an awesome conclusion. (If you didn’t go through the 3 Card Mindgame thought exercise, this will be less awesome. Go do that right now.
Ok, we know from our analysis of the 3 (or more) card Mindgames that it’s essentially a pointless game: there’s no strategy, and you’re no more likely to win than you are with RPS.
Why is that? Here’s the rub: each card play is meaningless. There’s no context; each one is just worth “a point.”
When you put this in an RPG context, and make each play is own self-contained stake, it becomes meaningful. Suddenly its not just “do I get a point?” its “do I rescue the princess?” The game now becomes something of “how much do I care about this?” and is suddendly interesting and relevant again.