Throwing for The Gold - Forbes.com

"'The mainstream view is that people ought to play the Nash Equilibrium,' says J. Doyne Farmer, McKinsey Professor at the Santa Fe Institute. Named after the protagonist of A Beautiful Mind, the Nash Equilibrium is the best possible strategy for any game where both players are completely rational. Nash proved that idealized opponents will eventually play a single best strategy in any game-it's what he won the Nobel Prize for. Pit two non-emotional, omniscient 'people' against each other to play RPS, and they will eventually converge on this best strategy. In the case of Rock, Paper, Scissors, it's simple: Choose each throw randomly, which means playing each throw exactly a third of the time, but without any pattern. In essence, for RPS, the best strategy is no strategy.

Game theorists have long assumed that the lowly human-a less than perfectly rational animal, but one capable of learning-will also settle into this best strategy after a few rounds. But the fact is that if you want to beat someone who isn't perfectly rational, then the strategy that's best against pure rationality is no longer the best strategy. In a paper he co-authored, 'Chaos in Learning a Simple Two-Person Game,' Farmer proves that, rather than lock into some perfect theoretical play, two less than perfectly rational opponents will constantly change their strategy as they begin to detect their opponent's strategy. 'It's as if each player has a biased three-sided coin, but the bias of that coin is tracking around in some slowly changing way.' People don't play RPS randomly (in fact it would be difficult to do so if you wanted to-how would you generate a random decision?), so the random play that was perfect against random play is no longer perfect, Farmer argues."

This is the best discussion of RPS strategy that I've seen yet. I'm really interested in reading this guy's paper.