3 Man Duel (logic problem)

[Lestat]

Someone sent this to me today and I thought it was kinda fun if not a little on the easy side.

*********

You and two other men are having a duel with pistols.



You are the worst shot and hit your target only one time in three, thus you are allowed to shoot first.



Mr. Second Best hit’s his target one time in two and gets to shoot second.



Mr. Best is a crack shot and hits his target every time.



Shooters will shoot in rotation until one man is alive.



You shoot first. What is your strategy and why?

[cambraceres]

duh

[Uethym]

If I shoot at Mr. Best and hit, Mr. Second has a 50% chance of beating me on the next shot.

If I shoot at Mr. Second and hit, I lose immediately.

And if I miss, well, it didn't really matter who I shot at, did it? Either way, there can only be one opponent by the time it gets back to me (if Best doesn't die, he'll hit Second for sure), and there are no more options.

So it seems clear that I go for Mr. Best.

Edit: Unless...(white text)

<font color="white">I intentionally miss. Then either Second kills Best and it's my turn again, or Second misses, Best kills Second, and it's my turn again. Either way, I'm guaranteed the first shot once I'm down to one opponent.
</font>

Clever puzzle, I like that.

[Phil153]

[ QUOTE ]
duh

[/ QUOTE ]
So what's your answer? I agree it's easy but it's not THAT easy.

<font color="white">
Answer: abstain from shooting until one dies.

Shooting the 1/2 is certain death
Shooting the crack shot will give you 9/12 chance of dying if you hit him, 7/12 chance of dying if you miss him.

Aiming at the crack shot gives:
1/3 of the time we hit, which is followed by a 50% and a shoot-off with #2.
2/3 miss = 0 chance of dying in the first round.
In the second round:
- when crack lives (50%), he shoots the 1/2 and we have a 2/3 chance of dying.
- when crack dies (50%), the chance of dying is:
--0.5*2/3 on the first round
--0.5*2/3*2/3*0.5 on the second
--sum(0-&gt;n)[1/3^n] of dying on the nth round = 0.5 at infinity.

</font>

[J. Stew]

funny how people say to intentionally miss. it's like how if you ask a room full of people if you are a better driver than 50% of the drivers out there, more than 50% of the people will raise their hands. go ahead and aim for mr. 2, you're already a [censored] shooter.

[tolbiny]

[ QUOTE ]


You shoot first. What is your strategy and why?

[/ QUOTE ]



<font color="white"> Miss your first shot. </font>

[kidmarine]

RUN! Yer gonna die!

[Borodog]

[ QUOTE ]
RUN! I'm not an idiot.

[/ QUOTE ]

[TimWillTell]

I ran into this problem like 30 years ago, but I remember it a little different.

You would have the choice of being the best shooter, the second best or the worst.
Its not difficult, but when your young the answer can broad your horizon.

[robert jordan]

So whats the diffinitive correct answer?