The 3 Shooting Cowboys problem

[Britney Federline]

You're the rootin'-tootinest cowboy in your town. You think you're pretty hot stuff because you can take your daddy's lucky pistol and hit what you're shooting 1/3 of the time--much better than any of the inbred hillfolk in the rest of the town, who have trouble using a shovel due to their malformed appendages.

Anyway, riding into town one day is a bandit on the run from the law. He thinks he's hot stuff because he can hit what he's shooting 1/2 the time. And right after him is the Sheriff, who is a badass who hits what he's shooting every time.

However, the Sheriff sees the Bandit standing on your end of the street, and he thinks you two are in cahoots. He says he'll shoot either of you if you shoot at him. The Bandit doesn't care who he has to shoot to get out of there. And, with the sweat beading on your brow and the sun at high noon, you know the only way to get out of this situation is with your daddy's lucky pistol.

You decide to shoot first.

The problem: Each cowboy gets one shot per round. Everyone shoots in this order: you (with 33% chance of hitting), the bandit (50% chance of hitting), the Sheriff (with 100% chance of hitting). Once everyone has fired a round, the cycle repeats until only one person is left standing.

You are the first person to fire. Where do you shoot first?

 

[Welt]

Suicide, it's the only way out.

 

[Coey]

Shoot in the air, although because you have a 67% chance of missing the air this might actually be more dangerous than firing directly at the bandit or sheriff.

 

[Kenza]

The bandit, so you dont shoot the sherrif, "he'll shoot either of you if you shoot at him"

 

[Shadrach]

The bandit.
Its not a matemathical problem, its a moral one.

-S

 

[Skew]

The bandit, so you dont shoot the sherrif, "he'll shoot either of you if you shoot at him"

What he said!

 

[Deeival]

Shoot the bandit.

 

[fiftyone]

I shot the Sheriff !

= ?

 

[Monkwarrior]

Simple.
You try to shoot the bandit.
After your first shot the sherif will not fire his second shot at you (he has killed the bandit with his first shot), because he realises the bandit was your enemy too.

Monk.

 

[Britney Federline]

So far, you guys are totally wrong. Think probabilities.

 

[Deeival]

The problem: Each cowboy gets one shot per round.

Since I'm the only cowboy (compare to bandit and sheriff) I just shoot both of em... or neither since they do not have any ammo.

Btw:
If you consider probabilities... I might as well suicide. For all I know me and the bandit could miss the next 100 shots.

 

[Zoring]

Ze bandit will probably be shooting at the lawman, so logically i will flee as fast as i can, the sheriff will see im not here for fighting and am infact a tremendous coward not worth shooting.

 

[R1G4M0RT1Z]

But, you have a 66% chance of missing yourself if you try and suicide.

LOL!

 

[dogbadger]

Well if you have a pop at the sheriff 1st, you'l probably miss but you are banking on the bandit also having a go straight after. ( because the sheriff is the one who's a threat to him and you went for him too)

Now with you and the bandit both having a go you have a chance of killing him better than evens. So, hopefully when the sheriff is down you just holster you gun and walk away- the bandit has no reason to shoot at you now, he never did infact.

So thats what i'd do. And you don't even need to murder anyone- but if by chance you do down the sheriff, you still walk away.

 

[dogbadger]

..oh and lets say both you and the bandit miss- hopefully the sheriff will use his shot on the bandit ( who he knows as a bandit and shot at him last)
The bandit dies and looking at probability your two 33% chances and the bandit's 50% makes him a cert to drop on your second shot

 

[BuddyLee]

Shoot the Bandit, then shoot the Sheriff in the back when he is inspecting the corpse. +2 Lucky Pistol.

Or pull a Blazing Saddles and put the Gun to your head while shouting "put your guns down or the negro gets it!" then mosey your way out of town.

 

[fiftyone]

Or pull a Blazing Saddles and put the Gun to your head while shouting "put your guns down or the negro gets it!" then mosey your way out of town.

Or sit round the camp fire and fart him to death...

 

[tumbleweed]

both the bandit and the sheriff have a 33% chance to be hit if you shoot, leaving the bandit and the sheriff a 66% chance to be able to shoot back.

so the bandit has a 66% of 50% = 33% chance to hit, and the sheriff a 66% chance

if you shoot the bandit you'll have a 33% chance to get shot and the chance the sheriff will also shoot at you.

the bandit is not going to shoot the sheriff if you shoot him so he'll shoot you.

so i'dd shoot the sheriff so he get 66% chance to fire back, the bandit is thinking you are a bandit also because you shoot the sheriff, and he will shoot him to

together we have a 66% chance to kill him and he'll have to make a decision on weather to shoot you or the bandit leaving you with a 15% chance to get shot.
But he'll probably shoot at the last one that shot him giving you a second chance to shoot him =)

 

[Deeival]

What if the sheriff in reality was a PLANE ON A TREADMILL?

 

[Obr.Lt.Scheisskopf]

I shot the sheriff, but I did not shoot the deputy.
I shot the sheriff, but I did not shoot the deputy.

All around in my home town
They're trying to track me down.
They say they want to bring me in guilty
For the killing of a deputy,
For the life of a deputy.
But I say:

I shot the sheriff, but I swear it was in self-defense.
I shot the sheriff, and they say it is a capital offense.

Sheriff John Brown always hated me;
For what I don't know.
Every time that I plant a seed
He said, "Kill it before it grows."
He said, "Kill it before it grows."
I say:

I shot the sheriff, but I swear it was in self-defense.
I shot the sheriff, but I swear it was in self-defense.

Freedom came my way one day
And I started out of town.
All of a sudden I see sheriff John Brown
Aiming to shoot me down.
So I shot, I shot him down.
I say:

I shot the sheriff, but I did not shoot the deputy.
I shot the sheriff, but I did not shoot the deputy.

Reflexes got the better of me
And what is to be must be.
Every day the bucket goes to the well,
But one day the bottom will drop out,
Yes, one day the bottom will drop out.
But I say:

I shot the sheriff, but I did not shoot the deputy, oh no.
I shot the sheriff, but I did not shoot the deputy, oh no.


If you shoot the sheriff, the bandit will shoot you, because he doesn't want you to know. If you shoot the sheriff and miss, he will shoot you. If you you shoot the bandit, the sheriff will shoot you. Catch~22