Points on RPS games.

1. Consider the frequency at which the RPS decision is made - the more frequent, the better. Being a "rock" and entering a "paper" dungeon is an un-fun experience. Taking "rocks" to a "paper" encounter isn't great either, and will shift the focus of the game to "figure out what kind of encounter it is, when possible". Making a "rock" move that loses to a "paper" move is no big deal, you can adjust your strategy next turn.
2. For RPS to work, the choices must be simultaneous. Most RPGs work sequentially.
3. You can have the basic idea of simultaneous, blind choices with different payoff matrices. That's what Burning Wheel and related games do.