# Probability Puzzle - I disagree with their solution

**URL:** <https://boards.straightdope.com/t/probability-puzzle-i-disagree-with-their-solution/656998>\
**Category:** Factual Questions\
**Created:** [April 29, 2013, 12:02pm UTC](https://boards.straightdope.com/t/probability-puzzle-i-disagree-with-their-solution/656998 "2013-04-29T12:02:01Z")\
**Posts on this page:** 3\
**Page:** 5

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**Author:** ![SpyOne](https://avatars.discourse-cdn.com/v4/letter/s/82dd89/32.png) [@SpyOne](https://boards.straightdope.com/u/SpyOne)\
**Post date:** [January 5, 2014, 4:52pm UTC](https://boards.straightdope.com/t/probability-puzzle-i-disagree-with-their-solution/656998/81 "2014-01-05T16:52:16Z")

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> [@septimus](#):
>
> Others are interpreting **Biotop** ’s problem differently than me. Each gun is preloaded with three bullets. (Others assume a fresh bullet is provided from a probability distribution before each shot.) Assuming my interpretation is correct:
> 
> After White’s death here, Grey has two live bullets and a blank. Black has only blanks left. Unless Grey takes mercy he’s going to kill Black on his 1st or 2nd shot.

The original problem has no blanks in it, and no limit on the number of bullets. It specifically says they will keep taking turns until only one man is left.  
(Note also that it only mentions players getting shot, not actually killed. They could be using water pistols and the game remains the same: if you get hit, you’re out.)

The variable here is not whether the bullet works, but how good each player’s aim is.

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**Author:** ![SpyOne](https://avatars.discourse-cdn.com/v4/letter/s/82dd89/32.png) [@SpyOne](https://boards.straightdope.com/u/SpyOne)\
**Post date:** [January 5, 2014, 4:55pm UTC](https://boards.straightdope.com/t/probability-puzzle-i-disagree-with-their-solution/656998/82 "2014-01-05T16:55:01Z")

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OOps.  
I wasn’t solving Biotop’s version, but the original.

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**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\
**Post date:** [January 10, 2014, 7:57pm UTC](https://boards.straightdope.com/t/probability-puzzle-i-disagree-with-their-solution/656998/83 "2014-01-10T19:57:03Z")

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> [@Chronos](#):
>
> Eh, I don’t know that it is necessarily counterintuitive. That guy has the disadvantage of only having one bullet, but also the advantage of going first. A sensible person should at least recognize the possibility that one of those might outweigh the other.

Interestingly enough, a friend points out that in the “blanks/bullets” variation, Black gains NO real advantage in going first.

His odds of winning remain the same (4/9) as long as White (the guy with the three actual bullets) does not get to shoot first. Black can shoot second or \*even third \*as long as it is Grey who then shoots first and not White. Indeed, even if White shoots first, Black’s odds of winning only decrease to 1/3. Not bad for the guy with only one bullet and two blanks!

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