Russian Roulette

You are forced to play a game of Russian roulette. The gun with six chambers is initially empty, and your comrade puts two bullets in the gun in adjacent chambers. He closes the barrel, spins it, and pulls the trigger. CLICK - the chamber was empty. Now he puts the gun to your head and will pull the trigger one more time. Which do you prefer - that the barrel first be spun again or that he just pull the trigger?

Solution

Your odds are better if he pulls the trigger without spinning again.

If the barrel is respun, you have a 2/3 (4 out of 6) chance of survival. However, you know that the gun was already triggered on an empty chamber. There are 4 empty chambers, and 3 of them are followed by another empty chamber; only 1 out of 4 is followed by a bullet. So, if the trigger is pulled without respinning, you have a 3/4 chance of survival.