A six-shooter is loaded with three cartridges in consecutive chambers, before two persons start to play "Russian Roulette" until one is dead.

If the cylinder isn't spun after each attempt, would you rather be the first shooter, or the second?

What would be your answer if there are only TWO cartridges, of course in consecutive chambers?

It is preferable to be the second shooter. There is a 1/2 chance that you will not even have to fire the gun, which is the chance the first shooter has of selecting a chamber with a bullet. Even if the first shooter selects an empty chamber, the probability that the following chamber contains a bullet is only 1/6. 1/2 (the chance an empty chamber was picked) multiplied by 1/3 (the chance that the empty chamber was the last in the sequence) gives you 1/6. The second shooter will die in the first round 1/6 times, whereas the first shooter will die 1/2 times. There are only two empty chambers in a total of six chambers which the first shooter can draw that will lead the second shooter to die (the first and last empty chambers). Therefore, the overall chance that the first shooter will die is 4/6, and that the second will die, 2/6. Consequently, it is preferable to be the second shooter.

Posted by lone on 2004-12-03 08:49:20