A game-theoretical analysis of RPS inevitably breaks down, as there is no optimal strategy. Any strategy other than uniform random choice (i.e., 1/3 chance of each throw) has a counter-strategy, and can therefore not be optimal. However, uniform random choice isn’t optimal, either. If your opponent is using uniform random choice, then it doesn’t matter what strategy you use: All of your possible strategies are exactly equivalent. And if your opponent is using anything other than uniform random choice, then there are strategies better than URC for you to use.
And Aro:
That’s not cheating; that is the game. Saying that pattern-analysis is cheating in RPS is like saying that passing the ball and running are cheating in football.