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Author Topic: The Sniper and the Porta-Potty Problem  (Read 1902 times)

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Offline HybridHalfTopic starter

The Sniper and the Porta-Potty Problem
« on: June 23, 2008, 07:12:51 AM »
I dunno, I heard numerous theories and answers, so I want to know what the real answer is.

============================

Juba the sniper has been staking out an US military base, set out to kill an officer. He knows that after every daily briefing meeting, the officer will go to the portable bathrooms that are on the compound, along with any other soldier that needs to take a leak.

This is where he is going to take out the officer, and since it is a military base, he knows that he got 1 shot to do it before he needs to move.

After sitting up all night, he falls asleep right when the daily briefing at the base ends, and he does not see in what toilet the officer went to. But all toilets are occupied.

At the same extensive troop movements begin in the base and he realizes that he must take the shot now, and he can not wait for the officer to exit the toilet. He must shoot him through the door of the toilet, and he got only 1 shot. There is an officer in one of them, and soldiers in the remaining two.

He takes aim on one of the toilets. And just as he is about to squeeze the trigger, a soldier steps out from one of the other two toilets.

Question: Will it benefit Juba to switch his target to the other occupied toilet? Or should he go with the one he was aiming at at the first place?

Offline MagicalPen

Re: The Sniper and the Porta-Potty Problem
« Reply #1 on: June 23, 2008, 08:19:21 AM »
As long as he wasnt aiming at the one that the soldier came out of, there is no benefit. Its still 50/50 as to whether he will hit the officer (better then 30% chance not knowing which of the 3 the officer was in). So he should take the shot and hope its the right one.

Offline Jeramiahh

Re: The Sniper and the Porta-Potty Problem
« Reply #2 on: June 23, 2008, 01:51:54 PM »
I'm not going to spoil this for those who don't know, but I will give the correct answer. Yes, switch.

Figure out why; Silv, your math is right, your logic is wrong.

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #3 on: June 23, 2008, 02:01:09 PM »
If this is some random question where you have to know the obscure protocol regarding officers and port-a-potties, I'm going to scream... :)

My poke is this: If the sniper is aiming at the middle one and the soldier steps out of one of the other ones, best to switch to the end one. The two soldiers are probably headed off to the troop movements, while the officer is headed away from the briefing ... people traveling together tend to stay in stalls/booths right next to each other, leaving the one on the end with the officer in it.

It's kind of a lot of 'if's, though, and I've noticed these problems don't tend to involve 'if' int he solutions.

Offline MagicalPen

Re: The Sniper and the Porta-Potty Problem
« Reply #4 on: June 23, 2008, 02:10:57 PM »
It never specifies which toilet he is aiming at. I am picturing three porta-a-potties in a row.  [P][P][P]
So J is aiming at one [J] and a soldier exists the other [X]

So we have: [J][P][X]

Which means that the officer is in either [J] or [P]

I can't see the officer taking the middle stall [P] so Jabu (whatever his name is) is aiming at the correct one. [JO][PS][XS]

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #5 on: June 23, 2008, 02:13:34 PM »
Maybe that's the problem is that you're seeing them all in a row. What if it's grouped back-to-back?

[P][P]
[P]

With the top ones facing what is essentially north, and the bottom one facing south? If he'd been aiming at one of the north-facing ones ...

Offline MagicalPen

Re: The Sniper and the Porta-Potty Problem
« Reply #6 on: June 23, 2008, 02:18:08 PM »
*is confused and wants the answer, either via PM or here*

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #7 on: June 23, 2008, 02:23:08 PM »
*would like it, too, but is willing to wait until it gets puzzled out over here*

Offline Maeven

Re: The Sniper and the Porta-Potty Problem
« Reply #8 on: June 23, 2008, 06:32:03 PM »
Owww, please make it stop.  My head is about to explode here. 

The only thing I can think is this:

The soldier who leaves was probably there before the officer and the companion soldier got there-- all things considered, the toilets on the end would be more preferable, maybe less smell or something.  So the officer, who would choose a toilet first due to his status (maybe?), would take the farthest port-o-potty from the first soldier. Then the companion officer would take the middle one. 

So, if the sniper was aiming at the middle toilet then clearly it would benefit him to switch to the other end one. 

But again... like Trieste says, that's only if the first soldier leaves the end toilet and he was aiming at the middle toilet. I have no idea what happens if he's aiming at one of the ends already and the first soldier gets out of the middle toilet.  There just seems no way to explain what would make the officer choose the right toilet from the left. 

I'm sure this is way off... but I've spent entirely too much time tonight thinking about soldiers in port-o-pottys.  *ponder* 


Offline HybridHalfTopic starter

Re: The Sniper and the Porta-Potty Problem
« Reply #9 on: June 24, 2008, 01:07:15 AM »
This was the common answer, which caused a shitstorm:

http://en.wikipedia.org/wiki/Monty_Hall_problem

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #10 on: June 24, 2008, 01:20:11 AM »
Ahhhh... I think it might have been a bit better in the 'door' format rather than the officer and his port-a-potty.

With the 'door' problem, the host pretty much HAS to narrow your choices down by showing you where one goat is. The only disadvantagous position is if you choose the car in the first place. But your chances of doing that are 1/3... so you've most likely chosen a goat... in which case it's probable you should switch.

*click* I got it now. :)

Offline HybridHalfTopic starter

Re: The Sniper and the Porta-Potty Problem
« Reply #11 on: June 24, 2008, 03:49:16 AM »
Ahhhh... I think it might have been a bit better in the 'door' format rather than the officer and his port-a-potty.

The argument was it was a cleverly worded Monty hall problem!!

Offline Kalen

Re: The Sniper and the Porta-Potty Problem
« Reply #12 on: June 24, 2008, 06:03:29 AM »
I think that it really, truly depends on the portapotties themselves.  Maybe if they are truly, utterly stank... one bullet will make them explode, creating a shitstorm that will make it a truly crappy day for each of the men inside.

OR

Shoot the toilet paper.  The men, if they're into being clean, will kill each other for that last square... mission accomplished.

Offline Xillen

Re: The Sniper and the Porta-Potty Problem
« Reply #13 on: June 24, 2008, 09:08:08 AM »
Even after reading HybridHalf's link, my answer is still: Doesn't matter, it's 50/50 (unless of course he's aiming at the door that just was opened).

Because, you see, the Soldier/Officer dilemma is NOT the same as the Goat/Car dilemma.

In the Goat/Car dilemma, the door that is opened by the Game Host is in a reaction to the choice made by the show candidate. The extra factor is that the door chosen by the game candidate is not opened.

In the Soldier/Officer dilemma, this extra factor is non-existing. It might very well be that the door that the sniper was aiming at got opened.

Therefor, don't bother switching doors. The chance remains 50%.

Offline MagicalPen

Re: The Sniper and the Porta-Potty Problem
« Reply #14 on: June 24, 2008, 09:19:35 AM »
What Xillen said....it can only be 50/50 because there are only 2 targets to chose from, one containing the office, one containing the soldier. If the 3rd Potty was still an option, then it would change.

Put it this way: There are two doors, A and B. Behind one door is a Car. You win the Car if you pick the right door. What are your chances? 50/50!!!!

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #15 on: June 24, 2008, 09:29:31 AM »
He takes aim on one of the toilets. And just as he is about to squeeze the trigger, a soldier steps out from one of the other two toilets.

Added the bold.

So it still reveals what's behind one of the doors as bad.

So your initial chance is 2/3 that you chose the wrong one. Then your remaining chance is 50/50 of 2/3. You can't ignore the initial probability.

So your chance of having chosen the wrong one becomes 1/2 of 2/3... which means it's likely you chose the wrong one to begin with, and it's in your advantage to switch. It's not perfect; you may be wrong. But the numbers say you should probably switch. Makes sense to me...

I personally prefer Kalen's answer.  ;D

Offline Kalen

Re: The Sniper and the Porta-Potty Problem
« Reply #16 on: June 24, 2008, 10:08:58 AM »
I do so enjoy thinking outside of the box!

Offline MagicalPen

Re: The Sniper and the Porta-Potty Problem
« Reply #17 on: June 24, 2008, 10:12:17 AM »
Well, if i was shooting Porta-Potties, i'd just use an RPG. Pretty effective that way - even if i aim at the wrong one - and I won't have to worry about brining the launcher back with me (as opposed to a sniper rifle, which i would)....

Offline Xillen

Re: The Sniper and the Porta-Potty Problem
« Reply #18 on: June 24, 2008, 10:14:45 AM »
I disagree.

If you look at the Goat/Car dilemma, the Game Host purposely opens a door that A. is not the door the candidate is choosing and B. is not the door the car is behind. Because it's purposely, the candidate can rationalize it.

In this case, the soldier opens the door by mere chance. Yes, it's A. not the door the sniper is aiming at and B. not the door the officer is behind. However, this is completely random. It could've been the officer that was done peeing first, or the soldier that's behind the door the sniper is aiming at. They're not sitting there with earsets while someone else is watching the sniper, telling them: "Ok guys, he's aiming for Carl at cabin A, so John at cabin C, you should leave your cabin now." Therefor, the sniper can make no more assumptions than that the officer is behind one of the remaining doors and has a 50/50 chance of getting the right one.

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #19 on: June 24, 2008, 12:32:08 PM »
Even though it's not on purpose, it's the same concept, and the numbers are the same. Yes, it happens to be chance on this particular problem, but 'chance' is all that probabilities add up to. The nearest comparison I can come up with is, say, the chances of a woman getting pregnant (biogeek, here). Whether it's on purpose or by accident, there are still only a few days a month (roughly 3/30ths - or 1/10) that it can happen. The intent doesn't change the probability - you're still working with (or against) the numbers.

So you still have to take the original probability into account... majority chance of being wrong, then even shot at being right.

Offline Xillen

Re: The Sniper and the Porta-Potty Problem
« Reply #20 on: June 24, 2008, 07:05:34 PM »
So you still have to take the original probability into account... majority chance of being wrong, then even shot at being right.

You can't take the original probability into account, since the quiz candidate can assume something that the sniper can't.

Let's say the left and right door are wrong. The middle door is right. Both the candidate and the sniper pick the left door.

For the candidate: The host can't open the left door, because it's the door the candidate is picking. The host can't open the middle door, since it shows the car. The host has to open the right door.

For the sniper: The left soldier can be done first, the officer can be done first, the right soldier can be done first. Even if the right soldier is done first, there's nothing that the sniper can dictate from that, since there's no hidden rule behind it that he could backtrack on.

The difference is the capability to rationalize on the idea.

Offline Trieste

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Re: The Sniper and the Porta-Potty Problem
« Reply #21 on: June 24, 2008, 07:16:44 PM »
I'm going to agree to disagree, here, because I don't think I'm going to convince you that the intent of the revelation doesn't matter, and I don't think you're going to convince me that it does.

*bows and scampers off* :)

Offline Vekseid

Re: The Sniper and the Porta-Potty Problem
« Reply #22 on: June 25, 2008, 12:03:59 AM »
This is exactly a ... creative rendition of the Monty Hall problem. You are confusing the host's active choice with another random chance that is taken as a given by the problem - there is only a 2/3rd chance that one of the other portapotty doors would open, and of that 2/3rd chance, either a 1/2 chance that it would not be the officer or a 100% chance, depending on the initial choice. These random factors must normally be accounted for by the host, of course, but they are taken as a given by the problem.

A person makes a completely random initial choice between one of three objects, only one of which is the object of their desire. The format, or method, does not matter - they have a 1/3 probability to choose the correct object, and a 2/3 probability to choose the wrong one.

If one of the two choices not chosen is revealed to be incorrect, no matter the means, then the original probability of being correct does not change. It's not 50/50. It's 1/3rd, thus, the wise choice is to switch.

Another example is to use a thousand, and 998 non-officers step out. You can also map out the states to prove it.

Offline Apple of Eris

Re: The Sniper and the Porta-Potty Problem
« Reply #23 on: June 25, 2008, 12:34:05 AM »
Well, he way this question was asked, it's no the monty hall problem. The monty hall has a host who actively opens a door that is NOT the car (officer) here you have a host who forgets which door the officer is behind making it complete chance whether a soldier or officer is revealed. So you would have to reference this section of the Wikipedia summary of this problem:

"The most commonly voiced objection to the solution is that the past can be ignored when assessing the probability—that it is irrelevant which doors the player initially picks and the host opens. However, in the problem as originally presented, the player's initial choice does influence the host's available choices subsequently.

This difference can be demonstrated by contrasting the original problem with a variation that appeared in vos Savant's column in November 2006. In this version, Monty Hall forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch" (vos Savant, 2006)."


You see in this case, at least as I interpret the way it is written the 'host' is clueless, so it's fifty fifty.

If say the Enemy knows your sniper is there and PURPOSELY sends a soldier out first, THEN YOU SWITCH, because switching wins with a 66% probability.

So, depending on how you interpret this problem, everyone here was basically right.

Offline Vekseid

Re: The Sniper and the Porta-Potty Problem
« Reply #24 on: June 25, 2008, 01:45:54 AM »
Err.

Okay, you have a set of random possibilities for the host to make. If the host picked a door completely at random, then you would have the distribution as I gave above. But, he doesn't, he puts constraints on it.

Likewise, the description of the problem makes these exact same constraints. For your purposes, the text of the problem itself acts as the 'sentient host' - the same criteria are followed.

Imagine it like this. Monty Hall decides to be a jerk, and he does not reveal a door. But instead, one of the goats - which just happens to be in a door that the contestant does not pick (note that the described situation here stands in for the conscious decision of the host), goes nutso and kicks its door open.