teknoarcanist said:
Alternative to flipping it: you could make a spinner, with each symbol designated as giving 1, 2, and 3 points depending on the placement, and then just rotate it to the next setting after each round.
I'm not sure that would actually change anything... if the order of the symbols and the order of the scores remains constant, then rotating the alignment of symbols and scores would not structurally change the game - (whateverA) would score three points still beats (whateverB) would score two points, whether (A=rock, B=scissors) or (A=scissors, B=paper). It'd be like swapping just the names of pawns and rooks in chess, but keeping all the other rules the same - the resulting game would play the same as chess, even with eight "rooks" which move one step forwards and capture one step diagonally.
With only three options for throws and only one distinct value per symbol, all possible orders of throws are rotationally symmetrical to either (3 > 2 > 1 > 3) or (1 > 2 > 3 > 1). Hence, the game and its inverse.
...unless you meant three *independent* spinners? That way, you could have a result like (Rock=3, Scissors=3, Paper=1) for a given round, which *would* be strategically distinct from (Rock=3, Scissors=2, Paper=1).
If there were *five* symbols (as in Rock-Paper-Scissors-Lizard-Spock), rather than three, then you would have 24 possible non-rotationally-symmetrical rearrangements of scoring (from among 1,2,3,4,5), instead of 2. But that's harder to fit into 20 words.
Remembering strategy, counter-strategy, and counter-counter-strategy for any of 24 possible 5x5 score matrices in use in a given round would be pretty badass.
