That's How it Happened presents a puzzle to ponder before the weekend begins.
You're a cowboy, and get involved in a three way pistol duel with two other cowboys. You are a poor shot, with an accuracy of only 33%. The other two cowboys shoot with accuracies of 50% and 100%, respectively. The rules of the duel are one shot per cowboy per round. The shooting order is from worst shooter to best shooter, so you get to shoot first, the 50% guy goes second, and the 100% guy goes third, then repeat. If a cowboy is shot he's out for good, and his turn is skipped. Where or who should you shoot first?
(CC-licensed photo by Rick)
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It's simple. You shoot to _miss_ the 100% guy first. Then you have a 66% chance of hitting him. Even if you miss, the 50%er will probably target him too. Then you aim to miss the 50%er. ;)
It's simple. You shoot to _miss_ the 100% guy first. Then you have a 66% chance of hitting him. Even if you miss, the 50%er will probably target him too. Then you aim to miss the 50%er. ;)
Shoot yourself in the foot.
Aim for the 100% shooter. If you hit, you've got even odds of surviving the next turn. If you miss, the 50% shooter will aim for him too. If the 50% shooter misses, the 100% shooter will aim for the 50% guy who's the bigger threat. If the 50% guy hits, you get a shot at him before he gets a shot at you.
Shoot yourself in the temple and ends the misery.
This puzzle is made a lot easier by the fact that I removed the bullets from Tuco's gun last night, so I only have to worry about Angel Eyes.
There are two kinds of people in this world, Mark; the ones with loaded guns and the ones who solve logic puzzles. You solve logic puzzles.
I should shoot myself in a nonlethal place because once I'm shot I'm "out for good" and won't face being shot and killed by the better shots.
I agree that one should shoot at one's self. There is a 66% chance one will miss and then the 50% guy will...you know the rest.
What if you're so poor a shot that you only have a 33% accuracy rate for shooting yourself? Then you're screwed.
Shoot in the air. It makes you look like a badass, and it'll throw the others off their game. Of course, if you run the numbers, it's also your best chance at survival. But who wants to run the numbers? You don't go whipping out your TI-85 in the middle of a gun battle, dumbass...
Shoot into the air, intentionally missing everyone. This will maximize your chances of not being shot, assuming everyone behaves rationally.
Although, I've gotta step back and question the wisdom of getting involved in this duel in the first place, especially since your accuracy mojo is weak.
Shooting into the air isn't always the best idea. Remember what happened to Woody Allen in Love and Death?
"Does this come out through dry cleaning or is this like gravy?"
Didn't you people watch Reservoir Dogs? This isn't some game-theoretic hoo-haa, instead it is a Tarrantino plot twist. You want to be the undercover cop who shoots Nice Guy Eddy. See, technically Mr. White, Eddy and Joe are all engaged in a three-way duel. The dispute is over the assassination of Mr. Orange (Tim Roth), the undercover cop who ratted out the gang. Mr. White shoots Joe, who is in turn shot by Nice Guy Eddy. Eddy gets a cap from Orange. Be Mr. Orange.
You shoot in the air.
At any point in the shootout, the person who's shooting is probably going to shoot at the person who's the best remaining shot. If you shoot and kill the 100% marksman, then the 50% marksman is going to take a shot at you (obviously if you shoot at and kill the 50% marksman, you're dead on the next shot). If you shoot nobody, then either the 50% marksman kills the 100% marksman (half the time) or the 100% marksman kills the 50% marksman.
But you really want the first outcome, so you're going up against the 50% marksman one on one but at least you'll get the first shot. Every other outcome has you going up against someone and taking the second shot, which puts you in an awful position.
Go buy one of them there MAGIC BULLETS, like that Lee Harvey Oswald feller used, and take 'em both out with one shot! Then you can ride that Gold Plated UNICORN (that's the grand prize, right?) home on a rainbow!
Notes:
1. Trying to miss the shooter won't give you a 66% chance to hit, it will give you a 0% chance. It's not how shooting works. It's like saying I have a 20% to hit a fastball so if I aim without looking I have an 80% chance.
2. Shoot in the air, and you have a 33% chance to live. Here's the math: You miss, so the next shooter will shoot at 100, since he's dead otherwise. If he hits, it's your turn again, and you have a 33% chance to survive. But it's been said before, so the only real way to survive is to:
3. Shoot yourself in the foot. Just graze your little toe and according to the rules, you will be out, and you will be skipped, leaving the other two to finish the duel themselves.
Or, preferably:
4. Call the 100% over and tell him you lied about being a 33% shot, and tell him you have 100% accuracy. Tell him that you will spare his life if he takes out the 50% shooter. When he shoots the 50% shooter, shoot the 100% cowboy in the back. It's not the noblest route, but it saves you your little toe and your life.
Sounds like an election debate strategy.
Shooting at the 50% marksman first gives you a 10/36 chance to win, shooting at the 100% marksman gives you a 13/36 chance, shooting at no one puts you at 15/36.
The goal is to act first after the first death. Once its down to heads up, that is far and away the most important thing.
You vs. 100% guy, he goes first: 0% win, 100% lose.
You vs. 50% guy, he goes first: 25% win, 75% lose.
You vs. 100% guy, you go first: 33% win, 67% lose.
You vs. 50% guy, you go first: 50% win, 50% lose.
So it's more important that the two better marksmen survive your first turn to avoid having them turn on you before you shoot again.
Ooh, interesting! Common sense says shoot Mr.100 first, but those saying intentionally missing first are correct.
If you shoot the ground on your first shot, you have over a 40% chance of winning.
(33% chance of hit from 50% chance of Mr.50 missing = 16.5%, around 24% chance from Mr.50 hitting Mr.100 and going one on one with him with you having the first turn--estimated, I didn't work out the whole regression.)
Unintuitive, but here's why: if you aim at Mr.50 and hit, you die. If you aim at him and miss, you've basically got the "miss intentionally" scenario now--66% of 40% = around 27% chance of winning.
If you aim at Mr.100 and hit, now you have 50% chance of surviving Mr.50, then 24% chance in the one-on-one battle = .24*.5*.33 = 4%
If you aim at Mr.100 and miss, now you have the "miss intentionally scenario" .66*.40 = 26.4%
Total odds of winning by aiming at Mr.50: 27%.
Total odds of winning by aiming at Mr.100: 27%
Total odds of winning by shooting the ground: 40%.
I use the "Look! The Goodyear blimp!" gambit and leg it to the nearest saloon.
Shoot the person who thinks there is a logical solution to this. 100% chance of hitting a geek.
I was told there would be no math.
didn't your mamas tell you not to grow up to be cowboys?
Deathmatchers know that you should go for Mr. Sureshot, but the lengthy discussion convinced me to think this through a bit more. As JDW said:
Although the details of JDW's explanation are incomprehensible to me, the conclusion of you having a 40% chance of winning if you intentionally miss on the first try is about right.
The reason for this is that in a duel between you and one of the others, your chances aren't too good either way, but boosted significantly if you get to go first. In that case, you have at least a 1/3 chance of deciding the fight for you. Not particularly rosy, but the absolute best you can do.
Now, no matter who you aim at on your first attempt, if you actually hit, then there's still one opponent left, and he gets to go first. OTOH, if you miss, they'll spend the rest of the first round fighting each other, and again the result is a duel between you and whoever is left over, but now you get to go first. So, you want to miss on your first attempt!
All of this involves making some assumptions, which are all reasonable, by the standards of such a contrived puzzle. A lateral thinker might discover a loophole, such as running away in a panic while the others are calmly waiting for their turn.
However, this isn't a real possibility. According to the original puzzle, the duelists (trielists?) are cyborgs, programmed to, err, get with the program. So, yes, there is math, no, it doesn't matter what their mamas told them, and if Sureshot goes for someone who doesn't think there's a logical solution, there's a 100% chance of hitting an idiot.
I like your style, Nex.
http://boards.ign.com/teh_vestibule/b5296/150925734/p1
crushed. there's math there and everything
Can't we just talk this out??!
This is why I don't like these kinds of math puzzles.
Here the player is being asked to make a decision completely rationally, but can he expect machine-like rationality from the other participants, or is the player supposed to expect the participant he shoots first to shoot back? The answer to that question determines my response.
Oddly, the original source of the puzzle made the participants not cowboys but cyborgs, which not only makes the percentages a little more reasonable but also implies that the opponents will act rationally.
Run away!!!!
#28 is correct.
What if the reason for the duel involves you sleeping with the other two cowboys' wives? At that point, your odds of survival is 0%.
Shoot yourself in the foot? WTH? No way, man. The answer is simplicity itself. You're the first shooter. By the rules, they can't shoot 'till you have. So go have a beer and forget about the whold damn duel, buddy. Until you shoot at them (which you never will), you're totally safe!
You don't need to use probability.
You don't need to think through several rounds.
If you kill the 50% shooter, he's dead, so the next shot comes from the 100% shooter, and there's only one person to aim for: you. So you're dead.
So you don't want to kill the 50% shooter.
So you aim for the 100% shooter and hope for the best.
Simple.
CS
To those who claim that intentionally missing somehow increases your chances are insane.Dean is right. You shoot yourself in the foot or some other less vital place.
When dealing with the possibility of death, pay attention to the worst case scenario. The worst case is that you, the 33% accurate shooter, miss your first two shots...It goes like this... On your first turn you whmoever you pick; then the 50% accurate shooter misses his target, and the 100% shooter will plug either you or the 50% shooter. On your second turn, if you are still alive, your only target is the 100% shooter, but you'll miss him again becuase you're only 33% accurate and in the worst case scenario, you'll miss your second shot. Then the 100% shooter shoots you and unless its a Tarantino movie and he shoots himself he walks away.
Ghanburighan is clearly right, and furthermore provides an explanation for why you, brilliant logician but mediocre marksman, would have entered into such a duel in the first place. You've just tricked the two meanest hombres in town (one of whom never misses, remember) into a position where they can't shoot at you. (They are men of honor, right? I mean, they wouldn't decide to just drill you anyways, seein' as yer yeller?)
#31
Put down the gun and walk away
Live to think another day
There are many imaginative solutions here; but to a true logician, imagination is not in "the spirit of the question".
You know what? FUCK true logicians.
This sounds oddly like the "Dinning Philosophers" problem.
Plainly what you need to do is start saying a wisecrack, but stop in mid-syllable like on directions.ytmnd.com . Hold still like you crashed and just keep singing that last phoneme.
The REAL answer.
You should shoot nothing and then hope the 50% kills the 100% then you will have a 39.2% chance of not pushing up daisies.
These are possibly win scenario percentages
Shoot 50% and hit = 0% chance of winning
shoot 100% and hit = 19% - 20% chance of winning
shoot nothing or miss and then 50% dude misses then dies = 33% chance of winning.
Shoot nothing or miss and then 50% kills 100% then the exchanging shootout gives you 39.2% (goes into decimals) chance of winning.
Whenever I have dinner with philosophers, I always bring an extra fork.
If you're allowed to shoot first, and they won't shoot until you've taken your turn, you walk over to the 100% guy and shoot him point blank. Or, if you can, put them in a line so the second dude gets the exiting bullet also. You don't need to aim for point blank.
The question is clearly too fuzzy. "Where or who should you shoot first?" - to what? Not get killed? Not get shot?
And what does accuracy mean anyway, 100% accuracy = certain death?
This is no puzzle, this is some kind of discussion starter.