Rock Paper Scissors psychology
Rock, Paper, Scissors is making the blog rounds with an excellent strategy guide from the World RPS Society and a fun mental floss article too. (Though the First International RoShamBo programming contest should be noted.) Having played far too much RPS last year, I can say these tips look pretty decent for the most part. I will say I am a huge fan of the elegant move Running With Scissors -- scissors three times in a row. "You think I'm crazy enough to play that AGAIN?" Un-frickin-stoppable.
Everyone thinks, "but wait, RPS is a lame game. Playing randomly is the best strategy!" This is not true. Playing randomly is the best defensive strategy, since your opponent can never do better than 50% against it. However, it is not the best offensive strategy if you can infer what your opponent will play. For example, if you are confident that your opponent is too scared to play scissors for a third time in a row, exploit that and play paper (the only move vulnerable to scissors, which you believe will not be played). You don't have to exactly predict your opponent's next move, but rather, you merely need to believe a non-uniform distribution over their next move. That is, if you can use any information or heuristics to make decent guesses, you can exploit that.
The game only works because of information imbalances in each player's beliefs about the other's psychological state. The problem of other minds, baby! And even more satisfyingly, the ONLY world state on which players want to make inferences is psychological state. RPS is shorn of silly artifices like a board with pieces or cards on the table. It is simply your mind versus your opponent's.
Incessant trash talking makes the game even more fun.
And don't forget 25-RPS or 4-RPS!