The constraint for a working Rock Paper Scissors variant is strict: the total number of throws must be odd, and every throw must beat exactly as many others as it loses to. Violate either condition and you no longer have a nontransitive game with a Nash Equilibrium at equal probability across all throws. You have something else — possibly a fine house-rule game by agreement, but structurally different from the original.
Most invented variants fail this test immediately. Someone adds Dynamite with the rule that it beats Rock and Scissors but not Paper. Now you have a four-throw game, which makes equal distribution impossible, and Dynamite is strictly better than Rock in most situations, which means competitive players all converge on throwing it against the Rock half of an opponent's range. The dominant strategy exists. The game loses its balance. This is why the WRPSA doesn't recognize Dynamite or similar unbalanced additions in sanctioned play.
Rock Paper Scissors Lizard Spock is the extension that works. Created by Sam Kass and Karen Bryla and popularized by The Big Bang Theory, it adds two throws to create a five-option game where every throw beats exactly two others and loses to exactly two others. The Nash Equilibrium shifts from one-third each to one-fifth each, but the structural integrity is maintained. Rock crushes Scissors and Lizard. Paper covers Rock and disproves Spock. Scissors cuts Paper and decapitates Lizard. Lizard poisons Spock and eats Paper. Spock smashes Scissors and vaporizes Rock. It's harder to memorize but not harder to play competitively once you have the chart in your head.
Seven-throw variants follow the same logic — odd total, each throw beats three and loses to three. They're theoretically sound but rarely worth the memorization overhead for casual play. The complexity starts exceeding the game's core advantage, which is that it takes under ten seconds and requires no equipment.
Cultural variants from around the world — the Japanese Mushi-Ken using Frog, Slug, and Snake; the Malaysian Bird-Water-Stone; the Singaporean Ji Gu Pa — follow the three-throw triangle structure with different symbols. The game is the same. The gestures are local. The math is universal.
What all of these share with the original is the underlying design insight: a cyclic dominance relationship with no hierarchy, where the theoretically optimal play is complete randomization. That insight doesn't become less elegant at five throws. It just becomes more complicated to execute.