Iocaine Powder Explained. How to win at Rock, Paper, Scissors. From the latter link (which has lots of great commentary):

Sure, the game has a simple optimal strategy (choose a move uniformly at random), but that has little bearing on the problem at hand. First, not all the players are optimal. This changes everything. To win a tournament where some players are known to be sub-optimal, it is absolutely essential to try to detect patterns and tendencies in the play of the opponent, and then employ an appropriate counter-strategy. A match consists of several turns, and this changes the nature of the game, as was seen in the famous Iterated Prisoner's Dilemma problem.

RoShamBo (and it's even simpler cousin, the Penny-Matching game) is an example of a pure prediction game. The difficulty lies in everything else that is associated with opponent modeling, or trying to outwit an adversary.

There is a lot of theory that can be brought to bear on the problem, including but not limited to advanced game theory (the "best-response dynamic in fictitious play"), prediction models, information theory, statistics, encryption, and even philosophical meta-theory.

(Thanks Geegaw, and subsequently David Chess.)