Here’s a little exercise with a violent setting. It might be worth remembering if you’re unfortunate enough to be in a situation like this:
A masked man puts two bullets into adjacent chambers of a six shooter revolver. The masked man aims the gun at you and pulls the trigger.
<click>…phew!
The chamber advances by one and the masked man prepares to fire once again. He offers you the opportunity to roll the barrel before firing again. Should you take the masked man up on his offer?
Assume you survive the second shot at this point.
Now suppose he is to fire two more times for a total of four shots.
Do you accept a spin of the chamber prior to third shot?
How about a spin of the chamber prior to the fourth?
What are your chances of survival after surviving the first shot?
All the probabilities for the first shot (B = bullet, X = empty):
Surviving the first shot reduces the state space to:
Best to keep the chamber where it is on the second shot. I have a 1/4 chance of being shot, compared to a 1/3 (2/6 on second shot being B) chance if I spin the barrel. As it could be any of the previous permutations.
On the third shot, it makes no difference if you spin or stay. There is always a 1/3 chance of being shot.
However, if you spin on the third AND survive, the odds on surviving the fourth shot return to 1/4.
The chances of survival after the first trigger pull would be: