Earlier quoted context omitted.
Do you mean to say that 100% random RPSAIs have a lower winrate vs humans than RPSAIs that learn and exploit human patterns? Surely a 100% random RPSAI doesn't have a poor win rate against any other RPSAI?
A 100% random RPS AI doesn't have a poor 1-on-1 win rate against any other RPS AI, but it absolutely can have a poor rate of winning tournaments , if "poor" is defined broadly enough. For a tournament that pays cash to the top 10%, most human players would consider anything in the bottom 90% to be poor, which would include a 50% win rate from a random AI. This happens because some entrants aren't 100% random, and the…
The 33%-each Nash Equilibrium is the mixed strategy Nash Equilibrium of the micro game (i.e. a single round of RPS, averaged over all possible randomizations).
This is in no way the Nash strategy of the tournament game, which is "win the tournament given a pool of unknown participants and a set of rules for whom you face when". You have to add additional assumptions (e.g. that everyone else is going to play the uniform random strategy) in order for uniform random to be the Nash strategy for the tournament game.
If the pool includes players who deviate from the single-round nash equilibrium strategy, there is opportunity to exploit them (and in doing so, open yourself to possible exploitation). This is why pure random play can often perform very poorly at the tournament game.