Is Rock Paper Scissors Actually Random?

The payoff matrix is symmetric. That tempts people to call the game random. The matrix is not the player.

A fair random player

A program that picks each symbol with probability 1/3, independently, is random in the sense that matters. You cannot have a long-run edge against it. Duetly's computer opponent is that program.

A human player

Humans avoid 'looking random' and accidentally become patterned. They over-play rock. They under-play scissors. They react to the last round. World RPS championships exist because of this, not because someone found a fourth symbol.

So is a match random?

A single round between strangers is close to a coin toss with three faces. A best-of-5 between two people who know each other is not. If you want actual randomness, play vs computer. If you want psychology, play a friend.