This will probably be obvious in hindsight once someone gives me the answer, but I’m having trouble coming up with it on my own. The scenario is this: I have a six-shot revolver. Five chambers are loaded with regular bullets; the sixth, indistinguishable from the others, is a fake bullet that if fired will release deadly nerve gas, killing me. Each time before firing the gun I spin the cylinder so that each trigger pull will land on a random chamber. Each try I either fire a bullet (not at myself), click on a empty chamber, or hit the “joker” round. The goal is to fire all five bullets and survive; what are my odds of doing so successfully?
5/64/53/42/31/2=1/6
Another way to look at it is what’re the chances the last bullet is the hike. All are equally likely. 1/6
That might be it; what had me confused was the contribution of the empty chambers and how many times you might have to retry. But now it occurs to me that since you keep trying after each empty chamber click, effectively it’s the same as if the empty chambers vanished after their bullet is fired. Thanks.
FWIW, I wasn’t quite convinced either - your game is essentially to roll a single die until you either roll all numbers from 1 to 5 (win) , or roll a 6 (lose). I wrote a program to simulate it, and you do indeed lose 5/6 of the time.