Rock, Paper, Scissors

Is the rock that defeats the scissors the SAME rock that yields to paper?

Or is there an infinite hierarchy of rock, paper, scissors “within which” each game takes place?

And does this hierarchy cycle at the dictate of our neurons, which are attempting to assign randomness* so as to appear unpredictable†.

Will the same pair of scissors always yield to the same rock?

A broken pair of scissors can never cut the paper.

Therefore, the “scissors that cut” must be “remade‡” or “new”.

* I suspect humans make for unreliable RNGs
There is always “that guy” who will insidiously choose the same option over and over
Even if the scissors are remade, are they truly “the same” scissors?