Winning at Rock-Paper-Scissors
Rock, Paper, Scissors is a simple game whose winner should be determined completely by luck. Yet here is a guide to winning at the game. (HT Andrew Sullivan.)
Against a rational player you should randomize and play Rock, Paper and Scissors each with 1/3 probability. If your opponent does this you can never come up with a strategy that will give you an advantage over him. But, as the guide says, “Humans, try as they might, are terrible at trying to be random, in fact often humans in trying to approximate randomness become quite predictable.” For example, according to the guide, an inexperienced player will never play the same thing three times in a row. Taking advantage of this, you can gain an edge over your opponent.
Rock-paper-scissors is a microcosm for life.
In "You Only Live Twice" Bond plays RPS with Tiger Tanaka the head of the Japanese secret service. He contemplates trying to lose, but reflects that trying to lose is exactly as hard as trying to win (Aside: can you think of any other game where this is the case?), so in end determines that he will play randomly. Needless to say, it doesn't occur to him that this is the optimum strategy.Needless to say, he wins.