One day Mr. Black, Mr. Gray, and Mr. white decide to resolve a conflict by trueling with pistols until only one of them survives. Mr. Black is the worst shot, hitting his target on average only one time in three. Mr. Gray is a better shot, hitting his target two times out of three. Mr. White is the best shot, hitting his target every time. To make the truel fairer Mr. Black is allowed to shoot first, followed by Mr. Gray (if he is still alive), followed by Mr. White (if he is still alive), and around again until only one of them is alive.

Where should Mr. Black aim his first shot in order to have the best chance of survival.

Mr. Black could aim at Mr. Gray. If he is successful then the next shot will be taken by Mr. White. Mr. White has only one opponent left, Mr. Black, and as Mr. White is a perfect shot then Mr. Black is a dead man.

A better option is to aim at Mr. White. If he is successful then the next shot will be taken by Mr. Gray. Mr. Gray hits his target only two times out of three and so there is a chance that Mr. Black will survive to fire back at Mr. Gray and possibly win the truel.

The second option appears to be the strategy Mr. Black should adopt. However, Mr. Black could aim into the air. Mr. Gray has the next shot and he will aim at Mr. White, because he is the more dangerous opponent. By aiming into the air, Mr. Black is allowing Mr. Gray to eliminate Mr. White and vice versa. Eventually Mr. Gray or Mr. White will die and then Mr. Black will aim at whoever survives. Mr. Black has manipulated the situation so that, instead of having the first shot in a truel, he has the first shot in a duel.