You decide to play Russian Roulette. You put one bullet into a 6 cylinder revolver...

You decide to play Russian Roulette. You put one bullet into a 6 cylinder revolver. You put the revolver into a bag containing 5 other revolvers, all empty. You shake the bag, pull out one revolver and shoot at your head. If it doesn't go off you put it back. You do this a total of six times.

Assuming the pistol is well oiled, a successful shot will kill you, and no other silliness applies what are your odds of dying?

100%. I'd pull the triggers 30 times.

1 in 6

1/24

1/30

Every time you pull the trigger on the one with a round, it becomes more likely to go off the next time.

But how many times do you pick that gun? In which chamber was the round to start with?

you have a 1 in 6 chance to pick that gun each time. It's odds of going off are (I think) 1 in six the first time, 1 in 5 the second time, and so forth.

Depends on whether you spin the cylinder before firing as per roulette etiquette.

You have a 99% chance.

No cylinder spinning after the first one

1/6 is the chance of pulling the right revolver
1/6 is chance of firing the right chamber if you spin the after every every shot. In that case you have 1/36 chance of killing yourself, so doing this 6 times gives 1-(35/36)^6 = 0.1555

If however you don't spin you can view the situation as if you have 36 separate chamber in the bag, each time you pick one but you don't put it back if it was empty. In that case the chance of picking the right one once is 1-(35*34*33*32*31*30)/(36^6) = 0.4631.

Note: This solution only works if you do it fewer times than number of chambers per revolver, because it wouldn't account for fact that a chamber could be picked multiple times.
Have fun dying

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Your chance of dying can significantly approach 0% if you shake the revolvers. Done the right way, the bullets may very well empty out into the bag.


It was literally you who suggested shaking a bag full of revolvers.

On the first shot there is a 1 in 11 chance that the pistol will go off. If you pick the pistol with the bullet in it the chances of dying on the next shot will increase to 1 in 10, so even if you pull the loaded gun's trigger five times there's still a 1 in 6 chance on the last shot.

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100%
not losing in russian roulette does not make you immortal

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1/6

There is 6 cylinders in each gun and there are 6 guns. So, there is a 1/36 chance of dying the first time you shoot. Since you spent one of the cylinders, there is 1/5 chance of dying if you fire that gun again. So, there is now a 1/35 chance of dying the next time you shoot a random gun. For 6 shots, the math goes :

1/36 + 1/35 + 1/34 + 1/33 + 1/32 + 1/31 = 0.179572065874248, which is a bit more than 1/6. Math is fun.

Except not, since regardless of any of it there is only a 1/6 chance of you dying. You've used all the guns, there's only one gun that is loaded with a single bullet. There are five guns that are completely safe. There is one gun that has a 1/6 chance of you dying. The guns with no bullets are zero, this means they don't exist.

ONE DAY - YOU WILL DIEā€¦ SO IT IS 100%

Faggots

If only you knew.

But you don't account for the fact that if you fire this unsafe gun, the probabilities of shooting yourself goes up. Let's forget about the other guns and focus only and loaded one. If there are 6 chambers and you fire it one time, you have 1/6 chances of dying. But if you fire it again, there are only 5 safe chambers left, so the probabilities of dying are then 1/5. Then it goes down to 1/4, 1/3, 1/2 and finally 1/1.

However, you then need to account for the 5 other guns. Each of them can be fired instead, which lowers the probabilities of killing yourself. So, the first time you fire it, you have 1/36 chances of killing yourself. Every time after that, the chances lowers by 1 because you've "spent" one of the chambers. In the end, the probabilities of dying are close to 1/6, but it's a little higher.

Then it would be a 1/30 chance of killing yourself.

I think you meant 1/31 and no, that only the last time you fire. You have to add all those probabilities together to get result.

1 in 12

13/30

gg

I can feel the weight difference, I cannot lose.