The history of Rock Paper Scissors variations is mostly a history of well-intentioned failures. Someone gets bored with the three-throw structure, invents a new gesture, declares it can beat two existing throws, and breaks the game before the first round is finished. The problem is always the same: adding a move with unequal win/loss ratios creates a dominant strategy, which means rational players all converge on the same option, which means the game stops being interesting.
The constraint for a working variant is strict: every throw must beat exactly as many options as it loses to, and the total number of throws must be odd. That's not an aesthetic preference — it's the mathematical requirement for a nontransitive cycle where no dominant strategy exists. Violate either condition and you no longer have a game in the RPS sense. You have something else, possibly fine for casual play by agreement, but structurally different.
Rock Paper Scissors Lizard Spock is the most widely played variant that actually meets this standard. Five throws, each one beats two and loses to two. The outcomes: Scissors cuts Paper, Paper covers Rock, Rock crushes Lizard, Lizard poisons Spock, Spock smashes Scissors, Scissors decapitates Lizard, Lizard eats Paper, Paper disproves Spock, Spock vaporizes Rock, Rock crushes Scissors. The Nash Equilibrium shifts from one-third each to one-fifth each, but the structure holds. It's harder to memorize but not harder to play once you've got the chart in your head.
Seven-throw variants exist and follow the same logic — each throw beats three and loses to three. They're playable but rarely worth the memorization overhead for casual use. The complexity starts working against the game's core appeal, which is speed and accessibility.
Team formats don't change the throw structure at all. They're just formats: relay play where team members rotate, tournament brackets, simultaneous multi-player (everyone reveals at once, ties replay). These work without any modification to the underlying three-throw game and are the most practical way to involve more than two people.
The WRPSA sanctions only the standard three-throw game for competition. Any variants are fine for casual play as long as everyone agrees to the rules before the first throw — the "as long as everyone agrees" part being more important than it sounds, since most variant disputes happen because the rules weren't established clearly in advance.