A Microsoft Interview Question (aka basic Bayes' Theorem)

[Dan Mezick]

Guys, at the time the first player pulls the trigger, there are SIX possible states for 2 bullets in the 6-gun:

2 Bullets adjacent in 6 possible chambers:

1&2
2&3
3&4
4&5
5&6
6&1 (whoops)

OK, six.

Let's assume chamber #1 was the chamber that clicked for player #1.... with no bullet inside.

That eliminates the first possible state (1&2) and the last possible state (6&1) from consideration, leaving 4 possible states (of initially 6 possible) remaining for the 2nd player to deal with.

Only one of them can kill you now (2&3) so you are looking at 1 chance out of 4 that you are going to die if you do not spin.

If you choose to instead spin the 2 bullets in the 6 chambers, there is a 2/6 = 1 out of 3 chance you will get a headache.

Don't spin and you have a 1 in 4 chance of a bullet.

Spin and you have a 1 in 3 chance of a bullet.

Don't spin.