Three gunslingers duel at once. The worst shot should have the best odds — why?
A, B and C fight a three-way duel, firing in turn. A hits 1 in 3 shots, B hits 2 in 3, and C never misses. Each may aim at anyone. A goes first. Counter-intuitively, mathematicians who analysed the game found A's best move isn't to aim at either rival at all. What should A do, and why does the worst shot end up favoured?
Reveal the answer
A should deliberately fire into the air. If A hits B, C (a perfect shot) kills A next; if A hits C, B likely kills A soon after. By missing on purpose, A lets B and C fight each other first, then gets a shot at whoever survives, badly weakened. Game theorists call this a 'truel', a term coined by Martin Shubik in 1964 to show how being the weakest player can be a strategic advantage.
— Martin Shubik, Game Theory and Related Approaches to Social Behavior — 1964