It’s simple. To keep it balanced, for any one item there have to be the same number of items for winning or losing, so the total always has to be 2x+1.
“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, and as it always has, rock crushes scissors.”
I’ve been on the receiving side of the theater thing. Not fun.