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# a small twist on the loaded revolver problem

## Question

Henry has been caught stealing cattle, and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver but not in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.

Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, 'Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?'

What should Henry choose?

## 4 answers to this question

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if the decides to spin the chamber after the first shot, the chance of henry living is 4/6 to 2/6. But if he decides not to spin the chance of survival wil be 3/5 i guess... not very sure of this ... might have missed something

Edited by rookie1ja

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he should have her spin the chamber 1 in 3 chance of death vs. 1 in 2 chance if he doesn't.

the odds in favour of spinning the chamber again; 2 bullets to 6 chambers a 1 in 3 chance of death . knowing where the one blank chamber is only leaves 5 possibilities for the next chamber. so the odds of there being a bullet in the next chamber is now 2 bullets to 5 chambers. 2 to 6 is better than 2 to 5. or so it would appear. because there are only 6 possible configurations that the bullets can be alligned in once you know where that one blank chamber is( because no 2 bullets are in consecutive chambers); 3 with a bullet in the next chamber and 3 with it being blank he actually has a 50/50 chance if he has her shoot without spinning the chamber again.

Edited by tammie

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Henry does the maths correct. He figures that if the first spin landed an empty as the first shot, the probability that next one would not be empty is 50% (as Tammie reasoned). And on a fair spin the chance of getting an empty is 66.67%. So spin he should go for.

But he knows Gretchen had been itching to get back at him. All the Russian roulette stuff was designed to extend his mental torture. And in fact he was surprised that she had missed on the first spin to land a chamber with bullet under the hammer. Would he give her another chance with a spin or take his 50 odd.

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if you don't spin, you remove an empty chamber from the sample space. Spin.

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