> you can't get an edge against someone playing completely randomly Sure, random choice is not only a Nash equilibrium, it even has a fixed expected value with

> you can't get an edge against someone playing completely randomly Sure, random choice is not only a Nash equilibrium, it even has a fixed expected value without regard to the other player's strategy, _but_ that is only in the basic two-player game. If you have a tournament and some players use other strategies, you can get better score against them by a non-random strategy, meaning you can beat the random strategy in the global tournament. But it also means someone can defeat you! Which means RPS tournaments are interesting even if the game seemed almost trivial!