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The Magic Cafe Forum Index » » Puzzle me this... » » 3 way duel (0 Likes) Printer Friendly Version

kmpx18
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You are one of three people in a duel to the death. You are standing at 12 o'clock in a giant circle. Duelist B stands at 4 o'clock and Duelist C stands at 8 o'clock. Each of you have pistols with unlimited ammo. You will be the first to fire a single shot. Then firing will continue one shot at a time in a clockwise fashion until there is only one person standing.

You are a horrible marksman with the probability of inflicting a fatal shot in 1 of 5 attempts. Duelist B is an average marksman with the probability of inflicting a fatal shot in 1 of 3 attempts. Duelist C is an excellent marksman with the probability of inflicting a fatal shot in 1 of 1 attempts.

You are not allowed to communicate with the other duelists.

Its your turn. Who do you fire at?
kmpx18
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Any takers???
Jonathan Townsend
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? A shoots at C (no hit?)
? B shoots at C (no hit?)
? C shoots at B (no hit?)
? A shoots at C ->

that about right?

Gives A the best odds of making it to second round in my model.

Next model: A and B point their guns at C and tell him to shoot himself.
Then, A takes that moment to shot B a few times.
...to all the coins I've dropped here
tjw
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Shoot the ground and hope that B and C will do the same.
kmpx18
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Haha uhm actually I don't know the answer
captainsmiffy
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You fire at C (the expert) as you have a 1 in 5 chance, so you might get lucky! B will definitely fire at C or he will be dead at the next shot since C will take out the greatest threat to himself, this being B, first. So B will either kill C or be killed himself at the third shot. (C, everybodies greatest threat, has to thus endure 2 shots before he gets a go). Either way, you get one more shot! Use it wisely....Your greatest hope lies in either your shot, or Bs shot, taking out C. After this, well I wouldn't want to be in your shoes....
Have you tried 'Up The Ante' yet?? The ultimate gambling demo....a self-working wonder! See the reviews here on the cafe.
tjw
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If both B,C are vulcans, and you fire at C and C dead, then you are 5/7 dead.
If you fire at C and miss, then 1/3 of the time, C is killed by B and your chance of surviving is 3/7. 2/3 of the time, C kills B and your chance of surviving is 1/5.
1/7+2/15 makes your chance of surviving 29/105, slightly less than 2/7=1/105.
not sure the calculation is correct, but if it is right,
the best strategy is 0.2% better than shooting the ground.
I will shoot the ground to make vulcans confusing.
Scott Cram
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Let's look at the possibilities:

1. I shoot B and kill him. This means C has the next shot, and I'm dead.

2. I shoot B, but don't kill him. B is probably surprised that I would go after him, but is probably still more worried about A's superior marksmanship. B is next, and probably shoots A instead of me.

3. I shoot C and kill him. This means B has the next shot, and I could wind up dead very easily.

4. I shoot C and leave him alive. Just as with B, he's probably surprised that I would go after him, but is more worried about C's superior marksmanship, so he goes after B (especially since B's turn is next, and B has probably used his turn to shoot at superior marksman C instead of me).

Two things come to mind here:

• If I kill either B or C, I wind up in a 2-person duel with the remaining one having the first shot. This isn't good!

• B and C, both being better marksman than me, are probably more worried about each other than about me. They're more likely to go after each other.

Let's see if I can take advantage of this:

If B kills C, I go next, and I have the first shot at B.

If C kills B, I got next, and I have the first shot at C.

It seems I wind up with an answer very similar to tjw's (above), althought not exactly.

Shooting the ground, or 6 o'clock, or some other variation of shooting to miss, is my best option.

Let B and C kill each other, and they'll not only leave me alive for a 2-person duel, but give me the first shot (and my best hope for survival) for the next round of firing.

Better strategy: The Clint Eastwood approach
Dave V
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I think you might have your ACB's mixed up.

In (2) you talk about "A" as other than yourself.
In (4) you talk about "C" being worried about "C's" superior marksmanship.

I like your thinking, but it's kind of hard to follow as written.
No trees were killed in the making of this message, but a large number of electrons were terribly inconvenienced.
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