Poll

6 votes (50%)
4 votes (33.33%)
2 votes (16.66%)

12 members have voted

TheNightfly
TheNightfly
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September 28th, 2010 at 3:20:03 PM permalink
Idea taken from all of those great spaghetti westerns.

Three gunfighters. They all have their hands on their guns and are ready to draw. All three know that gunfighter A is the fastest draw but the least accurate shot. All three know that gunfighter B is the slowest draw but the most accurate shot. All three know that gunfighter C has an average draw (slower than A but faster than B) and an average shot (more accurate than A but less accurate than B).

One bullet in the chamber, one shot only.

Who would you rather be in this scenario? Who would you gun for? Who do you thinks wins most often in a million run simulation and who aims for whom?

***EDIT***

Ok, we've got a lot of splitting hairs going on here. So, to make things very clear:

A, B and C all draw in less than one second. There is no way for anoyone to have a clear advantage beyond a fraction of a second - not nearly enough time for either of the other two gunslingers to make a decision AFTER anyone else has moved. Gunfighter A is MARGINALLY faster than the other two and is MARGINALLY less accurate than the other two.

The 3 gunslingers are standing in an open field with an unobstructed view in any direction (other than the two opponents). Each one is standing precisely 20 feet from either of the other two, creating positions equivalent to the three corners of an equilateral triangle. Each one draws with his left hand. The sky is perfectly clear and the sun is directly overhead. Each one has exactly 20/20 vision. They have all had a hearty breakfast and brushed their teeth.
Happiness is underrated
mkl654321
mkl654321
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September 28th, 2010 at 4:14:21 PM permalink
A should fire his gun into the air!

Seeing that, C will consider B to be the sole remaining threat, and aim at B. B, seeing that, will aim at C in turn. Neither would have any reason to aim at A.

The question as you've put it, though, needs clarification. What is each gunfighter's relative chance of hitting his opponent? Who "wins" if there are two survivors? Three? Is it more important for gunfighter X to survive, or to kill his opponents?
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
TheNightfly
TheNightfly
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September 28th, 2010 at 4:26:34 PM permalink
Quote: mkl654321

A should fire his gun into the air!

Seeing that, C will consider B to be the sole remaining threat, and aim at B. B, seeing that, will aim at C in turn. Neither would have any reason to aim at A.

The question as you've put it, though, needs clarification. What is each gunfighter's relative chance of hitting his opponent? Who "wins" if there are two survivors? Three? Is it more important for gunfighter X to survive, or to kill his opponents?



The question is as clear as it can be. You have a moment to decide what to do. By the time "A" fires his gun into the air he might also have a bullet in his heart. I'm asking YOU to determine the relative chance of any possible outcomes and figure it out yourself. You have 3 seconds and the other two guys are about to draw...
Happiness is underrated
Wizard
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Wizard 
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September 28th, 2010 at 4:52:13 PM permalink
Good puzzle, and I think mkl's answer is right. I'm pretty sure I've heard it told that way before, which seems sufficient to me. It ruins a puzzle to add too much detail.

Speaking of puzzles, I encourage you to keep them coming.
It's not whether you win or lose; it's whether or not you had a good bet.
chook
chook
Joined: Jul 5, 2010
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September 28th, 2010 at 4:57:46 PM permalink
Quote: TheNightfly

Idea taken from all of those great spaghetti westerns.

Three gunfighters. They all have their hands on their guns and are ready to draw. All three know that gunfighter A is the fastest draw but the least accurate shot. All three know that gunfighter B is the slowest draw but the most accurate shot. All three know that gunfighter C has an average draw (slower than A but faster than B) and an average shot (more accurate than A but less accurate than B).

One bullet in the chamber, one shot only.

Who would you rather be in this scenario? Who would you gun for? Who do you thinks wins most often in a million run simulation and who aims for whom?



You need to provide a diagram as to who is standing where.
You can't trust a dog to mind your food.
Wizard
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Wizard 
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September 28th, 2010 at 5:03:13 PM permalink
Quote: chook

You need to provide a diagram as to who is standing where.



I assumed it was a triangle. That is all I think that needs to be said.
It's not whether you win or lose; it's whether or not you had a good bet.
FleaStiff
FleaStiff
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September 28th, 2010 at 5:08:17 PM permalink
The only winners are the guy who wrote the script and the guy who drives the Honey Bucket truck during its filming.

Actually, the wise gunman will prepare himself to possibly take a slug but will make his first (and in this case only) shot count: his greatest threat must be taken out. An average draw can still be nervous at that fight, so the greater threat is the one who is a better shot. Its the bullet that does the damage, not the sight of someone standing their with smoke coming out of his gun. Everyone there knows he may have to take a slug and it won't be fun. Chances are A, B and C have all been in gunfights before. So whoever marks a target knows its one slug. Shoot at the most dangerous shooter and throw your empty pistol at the one still standing while you try to step into the sun.

Which would I prefer to be? The set's armorer. He gets well paid to make sure those are blanks.

A will probably shoot at which ever he thinks is the calmest and smartest because that is his threat.

B will shoot at C because he will think A will shoot at B. If A's shot goes wide of the mark, A is not a threat but there is no time to then aim at C. So B will start off aiming at C. B may or may not live to see how his shot goes.

C wants to kill B. If A aims at C and his shot does not miss, well C will have a slug in him and probably not do well with his shot at A so he might as well go for the surer kill, B.
chook
chook
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September 28th, 2010 at 5:12:07 PM permalink
I think B & C will try to take each other out.
You can't trust a dog to mind your food.
MathExtremist
MathExtremist
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September 28th, 2010 at 6:03:10 PM permalink
Quote: TheNightfly

The question is as clear as it can be. You have a moment to decide what to do. By the time "A" fires his gun into the air he might also have a bullet in his heart.



Well, no, if A is the quickest to shoot, he's going to get his shot off before the others draw. The answer to the question really does depend on whether the players can alter their choices after seeing A's action (and C's action) in turn. If A shoots into the ground/air and C *sees this and alters his decision* then C shoots at B before B shoots at C. If C's decision is set in stone before A acts, it's an entirely different problem.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Wizard
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September 28th, 2010 at 6:28:06 PM permalink
If I were to ask the question, I would say that three gunmen are all quick-thinking perfect logicians. Would that satisfy you?
It's not whether you win or lose; it's whether or not you had a good bet.

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