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I recently got a new job with another trading firm (hopefully this one doesn't blow up). I got a really wierd question in the interview, it went something like this:
Assume you are in a locked room with 9 other people (10 total). Everyone is wearing a heavy coat, and sitting in a circle of chairs facing each other, but more than arms' length away from anyone else in the room and also has their legs strapped to the chair (so you can't move).
You know:
6 people in this room have guns hidden in their coats.
3 of the guns are loaded with 1 real bullet, and 3 of the guns are loaded with 1 blank.
Everyone (including you) is a crack shot and has 100% accuracy.
Whether you have a gun or not.
In exactly 1 hour, the oxygen will run out in this room.
The door will not open to this room until three people have died.
You do not know:
Who has guns.
Whether your gun has a real bullet or not.
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What would you do if you had a gun?
What would you do if you didn't have a gun?
EDIT: Ok this question is a maximize expected gain/minimize expected loss question, so it's not about teamwork or altruism (at least that's how I approached it, since this came on the tail end of a bunch of game theory and stats questions). So just try to figure out how you would stay alive, although the altruism answers are really interesting they're probably more suited toward a nonprofit, banking, or consulting job than a trading job.
EDIT#2: On February 23 2009 14:10 Jonoman92 wrote:
How did they ask you this in an interview? Hand you a sheet of paper explaiing it and then asking what you would do? Seems kind of dumb to me.
Yea they did give me a sheet of paper to do the question. Two assumptions I made were that time was discrete and people could reacted after 1 second. My solution was
+ Show Spoiler +
assumptions: time divided in 3600 intervals. People cannot react simultaneously. Aim in interval t, shoot in interval t+1.
We are trying to preserve our own life.
How many deaths necessary? 3 deaths
How many people? 10 people: 6 gunmen and 4 innocents
How many bullets? 3 real 3 fake
axioms
1. If someone shoots, you know he can't shoot back anymore (1 bullet per gun)
2. If someone shoots, he/she does not know a priori whether he will kill for certain (real/fake)
3. Any optimal solution must include possibility of all 3 bullets hitting all 3 people
4. Any optimal solution for yourself at any time t in T will be adopted by all other gunmen at the same time t in T
5. Any optimal solution for gunman must fulfill the "suicide rule" (p(survival if you shoot yourself))
--> Then
split into gunmen and innocents
w/ gun:
take out gun. This is important so that no one shoots you because they know you could have a crucial real bullet. Do not point it at someone with a gun, because then the person with the gun will naturally point back at you, and you lower everyone's chances of survival and therefore they have incentive to shoot you. Hence every gunman will either aim at innocent or aim in the air.
If you think optimal solution is to aim at innocent, you have to assume that everyone else does so too.
Since you shoot after you aim, everyone will adjust their aim by switching targets randomly (optimal solution, proof upon request) until 2 people have 1 gun on them and 2 people have 2 guns on them, people aim by keeping aim on target if they are only one aiming at target, switching aim if target is doubled, and not switching aim to a target with only 1 aimer, and also switching aim randomly if the aiming is 3-1-1-1. After 3597 repeats of this aiming cycle, the probability of optimal aiming with 6 not being achieved with random brownian motion is less than 1 in 10 billion.
Then with 6 people shooting at 4 innocents, the chance of doubling up a real bullet is about 7/9. Hence that is not optimal because it violates suicide rule.
If you aim at no one, every person with a gun who is pointed at someone has a 1/18 chance of getting killed after everyone else has shot their bullets. If they shoot you when you have a gun pointed at no one, then they have a 1/6 chance (1/2 chance of bullet times 2/6 chance that you have one of 2 remaining bullets) of killing themselves.
ALSO
If you aim at no one, you increase your chances of survival. This is because with 6 guns aimed at 4 people, there is a chance that 2 real bullets will end up hitting the same person. If you save a bullet, you have a probability of adding to everyone's chances by potentially not wasting a bullet. So you need to add this probability to your own probability, and to the negative 1/18 that each gunman has by not shooting you for not aiming at one of the 4 innocents. This P is bigger than 1/18 (proof upon request).
Same goes for the 2nd gunman to point his gun in the air. His P(benefit by reducing wasted shot) is greater than the P(chance he might backstab defenseless gunman in t+1).
Hence you won't be killed for aiming gun in the air, and you will increase your own chances of survival.
So therefore 2 people will try to aim their guns in the air, but because you guys will make this decision simultaneously, then everyone will aim guns in the air.
Then everyone will swing guns down to 4 people. Then everyone will swing guns down in next cycle t. However, since this is repeated game, then people will realize this is retarded and leads to death, hence they will adopt a cycle of random movement with 1/3rd chance of pointing in air and 2/3rd chance of pointing at a random target.
Optimal is 4/2 wave, eg 4 shots in 1st wave to 4 targets and 2 in second wave to second 2. The chances that this solution will not happen when everyone is picking randomly is less than 1 in 40 billion across 3597 trials.
Once you get 4/2 wave it is easy... just shoot if you are in 4 wave and shoot one of the survivors if you are in 2 wave. The 4 gunmen are not going to care about the chance that you might cap them because there is still a higher chance they would have died from 2 bullets striking the same person.
Everyone with guns will do this (remember you assume everyone is rational and play GTO (game theory optimal)).
w/out gun:
You will be fired upon at least once and have a small chance of fired upon twice. However, since you do not have any weapons, you have no choices to make and you are effectively a null economic actor, hence any actions you make are irrelevant and will not affect GTO solution. So if I were you, I'd go down having some fun, maybe by singing Strangers in the Night or something.
 
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LOL sweet queestion. this is sorta like the prisoners dilemma, funny they would ask you in a job interview though 
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Easy, pull out the gun and have everybody else with a gun pull them out. 3 of the people who can't produce a gun (4 people), are then killed by the people with guns.
If you don't have a gun, wait for death as the other people do what I just said.
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Interesting. I'm curious as to how you answered it~
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Wow that's pretty morbid for a job interview...sounds like something out of Saw...
I'd watch out if I were you =P
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oh man that would be awkward. how did you answer it?
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On February 23 2009 11:24 ZoW wrote:
Wow that's pretty morbid for a job interview...sounds like something out of Saw...
I'd watch out if I were you =P
haha exactly what I was thinking..
Why would they ask this question? Whatever answer you give would make you look bad unless you kill yourself if you had a gun. How did you answer it btw?
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I'd probably ask everyone there age and whether or not they support a family, youngest live as well as mothers/bread winners if I did not have a gun. If I had a gun I'd probably do myself in, sounds like the ideal hero situation, no complexities, pure sacrifice for noble cause
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iNfeRnaL
Germany1908 Posts
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On February 23 2009 11:40 n.DieJokes wrote:
I'd probably ask everyone there age and whether or not they support a family, youngest live as well as mothers/bread winners if I did not have a gun. If I had a gun I'd probably do myself in, sounds like the ideal hero situation, no complexities, pure sacrifice for noble cause
The people could just lie though.
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this sounds like a pretty difficult question... how much time did you have to answer this question?
oh, and how was this relevant to the job? reasoning? decision making?
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Say you'd shoot yourself if you had a gun, and hold your breathe until you died if you didn't.
Then look him dead in the eye and say: "Sir, I am a team player"
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this is a VEEERRY interesting question.
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Osaka27128 Posts
The people without guns are the lucky ones. Everyone with guns has to shoot themselves. Three people are out of luck.
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Well this is a trading firm, so I think they would want you to be analytic, and they would want you to be excited to solve a new problem analytically.
On February 23 2009 11:22 Azrael1111 wrote:
Easy, pull out the gun and have everybody else with a gun pull them out. 3 of the people who can't produce a gun (4 people), are then killed by the people with guns.
If you don't have a gun, wait for death as the other people do what I just said.
That's a pretty cool solution. If you have a gun and you describe this strategy, then survival is guaranteed. If I was in the situation without a gun, then I would say this strategy, and then say that "I should the one, out of the four w/o a gun, to live because I described this strategy."
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Canada7170 Posts
If you don't have a gun, tell the 6 guys with guns that you know how to keep them all alive if they listen to you and keep you alive in return. Then shoot the other 3 guys.
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If everyone with guns were to shoot, there are those with guns that would be shot. Not wanting to be shot, those with guns would agree not to shoot their own gun.
Reasoning that 3 people will inevitably die first when the oxygen runs out, everyone would decide to wait for the hour, including me.
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On February 23 2009 11:47 Manifesto7 wrote:
The people without guns are the lucky ones. Everyone with guns has to shoot themselves. Three people are out of luck.
Or just wait until people start dying from lack of oxygen.
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1 guy shoots the lock, 2 guys shoot leg straps of one of the guys. that guy goes and gets help
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On February 23 2009 11:22 Azrael1111 wrote:
Easy, pull out the gun and have everybody else with a gun pull them out. 3 of the people who can't produce a gun (4 people), are then killed by the people with guns.
If you don't have a gun, wait for death as the other people do what I just said.
The problem with this solution is that there are only three bullets in the room. If all 6 people divided their aim toward 4 different people, there is a chance that fewer than three people would die by getting shot.
But my solution is guilt free 
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An important clue is missing: do other people know what i know?
The point of the game is not to shoot people who has real bullet and has not shot yet; otherwise less than 3 people are killed and no one can escape the room.
If i have the gun, i'll explain to other people the problem and ask all people who have the gun to reveal themselves so that people without guns can be killed.
If i don't have the gun, then i only have 25% chance of surviving. Unless other people don't know what i know, in which i'll let the first person shoot (30% chance of shooting the person without a real bullet) then trick other people to shot that person (since he's safe to be killed now) and trick the last one with real bullet to kill the person who killed the first person.
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On February 23 2009 11:52 dasanivan wrote:Show nested quote +On February 23 2009 11:22 Azrael1111 wrote:
Easy, pull out the gun and have everybody else with a gun pull them out. 3 of the people who can't produce a gun (4 people), are then killed by the people with guns.
If you don't have a gun, wait for death as the other people do what I just said. The problem with this solution is that there are only three bullets in the room. If all 6 people divided their aim toward 4 different people, there is a chance that fewer than three people would die by getting shot. But my solution is guilt free
They don't all have to shoot simultaneously.
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Then again firms have a tendency to cut the weak ones from their own group...
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On February 23 2009 11:47 mikeymoo wrote:
If you don't have a gun, tell the 6 guys with guns that you know how to keep them all alive if they listen to you and keep you alive in return. Then shoot the other 3 guys.
lol? you only have one bullet at max.
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I'd push for not doing anything until the hour is up and the oxygen runs out. Then this becomes a less question of morals and more of a question of which 3 have the smallest lungs. Once 3 people suffocate to death, door opens, oxygen returns, 7 live with their conscience intact... some of whom are armed and loaded, ready to take down the buster who set this entire thing up in the first place.
BTW, at the 59 minute and 59 second mark, i'd tell a funny joke, so everyone else would be laughing and wasting precious air ... Either that or fart. XD
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On February 23 2009 11:51 travis wrote:
1 guy shoots the lock, 2 guys shoot leg straps of one of the guys. that guy goes and gets help
"The door will not open to this room until three people have died."
=D I wouldn't know how to respond to a question like that.
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On February 23 2009 11:54 Abydos1 wrote:Show nested quote +On February 23 2009 11:52 dasanivan wrote:On February 23 2009 11:22 Azrael1111 wrote:
Easy, pull out the gun and have everybody else with a gun pull them out. 3 of the people who can't produce a gun (4 people), are then killed by the people with guns.
If you don't have a gun, wait for death as the other people do what I just said. The problem with this solution is that there are only three bullets in the room. If all 6 people divided their aim toward 4 different people, there is a chance that fewer than three people would die by getting shot. But my solution is guilt free They don't all have to shoot simultaneously.
good point, but how terrible it would be at the receiving end in that case.
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Ok this question is a maximize expected gain/minimize expected loss question, so it's not about teamwork or altruism.
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ok the 3 guys with bullets hand their bullets to the guy with the strongest hands
he opens up 2 of the bullets creating a trail of gun powder, and then shoots it
the powder burns through the coat/chair. he then stands up and pulls out his cell phone, calls his mom.
turns out his entire family (mom, dad, sister) just died in a car accident. door opens, everyone is saved.
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On February 23 2009 11:45 29 fps wrote:
this sounds like a pretty difficult question... how much time did you have to answer this question?
oh, and how was this relevant to the job? reasoning? decision making?
Maximize expected value given incomplete market information. (Kinda like poker)
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On February 23 2009 12:03 t_co wrote:Show nested quote +On February 23 2009 11:45 29 fps wrote:
this sounds like a pretty difficult question... how much time did you have to answer this question?
oh, and how was this relevant to the job? reasoning? decision making? Maximize expected value given incomplete market information. (Kinda like poker)
business is a cold world :[
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On February 23 2009 12:03 travis wrote:
ok the 3 guys with bullets hand their bullets to the guy with the strongest hands
he opens up 2 of the bullets creating a trail of gun powder, and then shoots it
the powder burns through the coat/chair. he then stands up and pulls out his cell phone, calls his mom.
turns out his entire family (mom, dad, sister) just died in a car accident. door opens, everyone is saved.
what if there was poor reception in the room?
LOL GG
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On February 23 2009 12:03 travis wrote:
ok the 3 guys with bullets hand their bullets to the guy with the strongest hands
he opens up 2 of the bullets creating a trail of gun powder, and then shoots it
the powder burns through the coat/chair. he then stands up and pulls out his cell phone, calls his mom.
turns out his entire family (mom, dad, sister) just died in a car accident. door opens, everyone is saved.
i think this would work very well!
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What if one of the people who had a gun+bullet wasn't able to kill a person, so there would be no bullets left and only 2 people dead.
Then the rest of the 7 are gg?
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I look at my arms, and say "It's impossible that i don't have a gun"
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On February 23 2009 12:10 ilovejonn wrote:Show nested quote +On February 23 2009 12:03 travis wrote:
ok the 3 guys with bullets hand their bullets to the guy with the strongest hands
he opens up 2 of the bullets creating a trail of gun powder, and then shoots it
the powder burns through the coat/chair. he then stands up and pulls out his cell phone, calls his mom.
turns out his entire family (mom, dad, sister) just died in a car accident. door opens, everyone is saved. what if there was poor reception in the room? LOL GG
verizon wireless ftw
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the only thing you need to concern yourself with (apart from the general fucked-up-ness(?) of the situation) is making sure that everyone with a gun and a real bullet kills someone.
In both cases you have to concern yourselves with the decisions others make. I'm going to assume they're rational creatures that are just as smart as you and are in the room for the same reason (to live).
if you have a gun, you guarantee survival just like it's been said previously (shoot non-gun people). This assumes other gun people agree with this logic, and since they want to live, they will.
if you don't have a gun, it's tricky because you have to rely on the decisions made by other people. However, given the smart and rational assumption, they would would implement the same strategy even without your help (because that guarantees the gun people 100% of survival, and the non-gun people don't have a say in the matter.)
So, if you have a gun you have 100% chance of survival, and if you don't, you have a 25% chance. I don't see how you could alter this if my smart and rational assumption is reasonable.
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This is most interesting if you don't have a gun, assuming that all you care about is maximizing your own survival and the situation is set up so there's no easy way out.
Here's two possibilities:
1. Quickly speak up and tell the gunholders the strategy of taking turns shooting 3 of the defenseless people. Plead with them that since you just worked together with them - have them kill the other 3 defenseless people.
2. Quickly start with "OK EVERYONE CALM THE FUCK DOWN. If anybody here pulls out a gun before we agree on a strategy, the rest of us are going to shoot you." (The goal of this is to try to prevent the gunholders from identifying each other and executing 3 defenseless people.) Then try to get people to agree on the strategy of first identifying one person without a gun, have the person to his/her left shoot at him or reveal that they don't have a gun, and continue on clockwise. Then everyone has exactly a 30% chance of dying, depending on whether or not the guy to their left has a loaded gun. You can even be the one to reveal that you don't have a gun first (it doesn't actually hurt your chances, except that you might piss people off), or wait until it's closer to the hour for someone else to.
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not a solution, but could be a potential problem
after one shoots a defenseless person, whether it's a blank or real, the shooter also becomes defenseless, since there's only one bullet......
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How did they ask you this in an interview? Hand you a sheet of paper explaiing it and then asking what you would do? Seems kind of dumb to me.
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On February 23 2009 11:56 Makiva wrote:
7 live with their conscience intact...
You'd probably have permanent brain damage if you went without oxygen long enough for other people to die.
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You have ten people.
First look for volunteers whom feel that either they have lived long enough, are sick of the world, etc. etc. etc. And I mean actual volunteers. If we get volunteers, each person with a gun shoots them, one at a time.
To Maximize my personal gain I need to live.
Without a gun: I do not have the benefit of force for me. However, this makes persons with a gun more likely to listen to me. If we try to force people to kill someone with a gun, they will likely try and take somebody down, most likely the most vocal of the group. Therefore, one must guide the guns against those without a weapon: thus, one unarmed man will be sacrificed, probably chosen by false representation (i.e. child molesters). Randomly assign persons to shoot that guy, one at a time, until he is shot.
Now, the person with a gun who killed him is guilty of murder. Murder is punishable by death. The killer of this man will be protected as an executioner: thus, they will kill the 2nd guy.
Then, we will kill one of the guys who fired a blank: either because they attempted murder or because they tried to spare a murderer. Both are bad people. The people whom have already fired/fired a blank have no methods of force against the rest of us. Thus 3 people will die and we will be freed.
If I had a gun:
I have an instrument of force: thus I would tell all of the fellow gunmen to kill one of the unarmed persons: since they have no recourse against us, we can kill 3 of them (probably not the youngest/family/w/e) and be freed thusly. Those with the guns have all the power, regardless of whether or not there were blanks or real bullets.
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On February 23 2009 14:10 Jonoman92 wrote:
How did they ask you this in an interview? Hand you a sheet of paper explaiing it and then asking what you would do? Seems kind of dumb to me.
Yea they did give me a sheet of paper to do the question. Two assumptions I made wer that time was discrete and people could reacted after 1 second. My solution was
+ Show Spoiler +
assumptions: time divided in 3600 intervals. People cannot react simultaneously. Aim in interval t, shoot in interval t+1.
We are trying to preserve our own life.
How many deaths necessary? 3 deaths
How many people? 10 people: 6 gunmen and 4 innocents
How many bullets? 3 real 3 fake
axioms
1. If someone shoots, you know he can't shoot back anymore (1 bullet per gun)
2. If someone shoots, he/she does not know a priori whether he will kill for certain (real/fake)
3. Any optimal solution must include possibility of all 3 bullets hitting all 3 people
4. Any optimal solution for yourself at any time t in T will be adopted by all other gunmen at the same time t in T
5. Any optimal solution for gunman must fulfill the "suicide rule" (p(survival if you shoot yourself))
--> Then
split into gunmen and innocents
w/ gun:
take out gun. This is important so that no one shoots you because they know you could have a crucial real bullet. Do not point it at someone with a gun, because then the person with the gun will naturally point back at you, and you lower everyone's chances of survival and therefore they have incentive to shoot you. Hence every gunman will either aim at innocent or aim in the air.
If you think optimal solution is to aim at innocent, you have to assume that everyone else does so too.
Since you shoot after you aim, everyone will adjust their aim by switching targets randomly (optimal solution, proof upon request) until 2 people have 1 gun on them and 2 people have 2 guns on them, people aim by keeping aim on target if they are only one aiming at target, switching aim if target is doubled, and not switching aim to a target with only 1 aimer, and also switching aim randomly if the aiming is 3-1-1-1. After 3597 repeats of this aiming cycle, the probability of optimal aiming with 6 not being achieved with random brownian motion is less than 1 in 10 billion.
Then with 6 people shooting at 4 innocents, the chance of doubling up a real bullet is about 7/9. Hence that is not optimal because it violates suicide rule.
If you aim at no one, every person with a gun who is pointed at someone has a 1/18 chance of getting killed after everyone else has shot their bullets. If they shoot you when you have a gun pointed at no one, then they have a 1/6 chance (1/2 chance of bullet times 2/6 chance that you have one of 2 remaining bullets) of killing themselves.
ALSO
If you aim at no one, you increase your chances of survival. This is because with 6 guns aimed at 4 people, there is a chance that 2 real bullets will end up hitting the same person. If you save a bullet, you have a probability of adding to everyone's chances by potentially not wasting a bullet. So you need to add this probability to your own probability, and to the negative 1/18 that each gunman has by not shooting you for not aiming at one of the 4 innocents. This P is bigger than 1/18 (proof upon request).
Same goes for the 2nd gunman to point his gun in the air. His P(benefit by reducing wasted shot) is greater than the P(chance he might backstab defenseless gunman in t+1).
Hence you won't be killed for aiming gun in the air, and you will increase your own chances of survival.
So therefore 2 people will try to aim their guns in the air, but because you guys will make this decision simultaneously, then everyone will aim guns in the air.
Then everyone will swing guns down to 4 people. Then everyone will swing guns down in next cycle t. However, since this is repeated game, then people will realize this is retarded and leads to death, hence they will adopt a cycle of random movement with 1/3rd chance of pointing in air and 2/3rd chance of pointing at a random target.
Optimal is 4/2 wave, eg 4 shots in 1st wave to 4 targets and 2 in second wave to second 2. The chances that this solution will not happen when everyone is picking randomly is less than 1 in 40 billion across 3597 trials.
Once you get 4/2 wave it is easy... just shoot if you are in 4 wave and shoot one of the survivors if you are in 2 wave. The 4 gunmen are not going to care about the chance that you might cap them because there is still a higher chance they would have died from 2 bullets striking the same person.
Everyone with guns will do this (remember you assume everyone is rational and play GTO (game theory optimal)).
w/out gun:
You will be fired upon at least once and have a small chance of fired upon twice. However, since you do not have any weapons, you have no choices to make and you are effectively a null economic actor, hence any actions you make are irrelevant and will not affect GTO solution. So if I were you, I'd go down having some fun, maybe by singing Strangers in the Night or something.
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Valhalla18444 Posts
guys with guns can't shoot other guys with guns
there must be an action before there is a reaction, shooting someone before they pull the trigger potentially fucks everyone if that person had a loaded gun - the bullet in that gun kills no one
shoot at the people without guns, one shot at a time until three of them are dead
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If people are going to be suspicious at being targeted by others with guns, you could just fire into a random wall to remove yourself as a potential threat and leave them paying attention to each other.
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On February 23 2009 21:28 FakeSteve[TPR] wrote:
guys with guns can't shoot other guys with guns
there must be an action before there is a reaction, shooting someone before they pull the trigger potentially fucks everyone if that person had a loaded gun - the bullet in that gun kills no one
shoot at the people without guns, one shot at a time until three of them are dead
That's what most people are suggesting, but there's also a problem. What if someone shoots a blank? Then they would become a target. So no one would want to fire first. The OP addresses this issue by introducing some randomness to who shoots as part of an optimal strategy.
edit: In fact even if they shoot and kill someone, they still become a target. Possibly an even larger target because they've just become a murderer.
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whats wrong with people these days
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On February 23 2009 11:51 travis wrote:
1 guy shoots the lock, 2 guys shoot leg straps of one of the guys. that guy goes and gets help
so you thought, later bitches!
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On February 23 2009 12:33 Not_Computer wrote:
What if one of the people who had a gun+bullet wasn't able to kill a person, so there would be no bullets left and only 2 people dead.
Then the rest of the 7 are gg?
how can he not hit someone.... people with guns fire one at a time at first innocent person until he dies... then remaining guns fire at 2nd innocent person....then the 3rd....
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If i have a gun - three gunless people die as the gunholders have all the power. I discourage the idea of 'duels' by stating the obvious - one cheater on countdown and we risk 100% casualties due to a lost live round.
If i don't have a gun - i device the plan "no killer walks out of here". All gunholders take turns shooting at one unarmed (decided by some random game giving me 25% chance of certain death - it's quite likely that the game will only determine order of aim though, if the first shot fired is a blank, it will probably be generally accepted as divine intervention and the person who finished second in the random game will be the next target) until a real bullet has killed unarmed #1. Once unarmed #1 is dead, the next target becomes the unlucky gunholder who turned out to have a real bullet which is now used. His bullet has already been put to use - others will have an easier time aiming at him, he will have an easier time accepting death. Once he is dead, one real bullet and 0-3 blanks remain.
If 0 blanks remain, the decision falls on the last gunholder to either kill someone else or commit suicide.
If 1 blank remains - the two gunholders will either agree to a shootoff (probable) or fire at someone randomly (unlikely) - this is best case scenario for me.
If 2 blanks remain, the three gunholders will fire at the three remaining unarmed - giving me a 1/3 chance of survival (worst case scenario for me).
If 3 blanks remain i will try to propose a 4-way shoot-off giving all remaining gunholders a 25% chance of survival. Reaction time doesn't matter as only one bullet is lethal at this point. Hopefully they'll agree.
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United States47024 Posts
It depends whether you assume everyone else in the room has an "maximize gain" mindset going into the room, and if they're all assumed to be as intelligent as you are.
If you're a gunman, it doesn't matter. The optimal solution is always to shoot 3 people that are unarmed at the start.
If you're unarmed, the solution differs. For example, pitting the gunmen against each other (e.g. saying the first gunman to kill an unarmed is a murderer) won't work, because you can't assume that anyone else will be concerned with anything other than survival (since thats the only thing you're concerned about). Since backstabbing each other reduces their chance of survival, you can't assume a gunman would ever shoot another gunman, whether or not they've fired their shot or not. Similarly, if you assume everyone is going to employ an optimal strategy, saying you deserve to live because you gave the the gunmen the idea that lets them all live won't work because all unarmeds will offer that idea simultaneously.
If you're unarmed, the only way you can make your odds of survival better than 25% is on the assumption that everyone else in the room is either less concerned with staying alive than you, or less intelligent than you.
t_co: you also seem to make the assumption that no one talks to each other, and that people can't sequentially shoot someone, because otherwise, all the gunmen would come to a consensus that no gunman would ever shoot another gunman, and that no two people should ever fire at the same person at the same time. If two people both aim at someone, they'd mutually agree who fires first, and neither of them would be endangered, since backstabbing the person who shot first reduces their own chance of survival. There's no need for randomness at all.
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EPT
