Rock, paper, scissors, algebra

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.

The same is true of the extension Rock, Paper, Scissors, Lizard, Spock

Rules of rock, paper, scissors, lizard, spock.

Related post: Weakening the requirements of a group