There is, but you are not taking advantage of it as long as you choose randomly.
Imagine the other tries to exploit your imagined human non-randomness and plays rock all the time. You play totally random, so on the long term you win/lose/tie roughly same number of times.
You would be taking advantage if you played paper all the time.
> There is, but you are not taking advantage of it as long as you choose randomly.
You're right. I was just thinking that 1/3, 1/3, 1/3 was the Nash equilibrium and not really thinking the whole thing through. Once I gave it a little more thought, I came up with the same rock example you gave.
In most toy games you would be right; playing the GTO/nash equil. solution would naturally benefit from an imbalanced/exploitive style on an opponent. It's only in games like rock-papers-scissors where this isn't the game.
Imagine the other tries to exploit your imagined human non-randomness and plays rock all the time. You play totally random, so on the long term you win/lose/tie roughly same number of times.
You would be taking advantage if you played paper all the time.