Aatish Bhatia posted something interesting on Twitter: if you define multiplication on Rock, Paper, Scissors to be the winner of a match, the result is commutative but not associative.
Here's a neat thing about the algebra of Rock, Paper, Scissors.
If you define 'multiplication' as the game's winner, then it's commutative, i.
P x R = R x P = PS x R = R x S = RS x P = P x S = SHowever, it isn't associative!.e.
, (R x P) x S is not the same as R x (P x S)— Aatish Bhatia (@aatishb) June 3, 2019The same is true of the extension Rock, Paper, Scissors, Lizard, Spock.
Related post: Weakening the requirements of a group.