Help Guy Pefect (the Sentinel/Sentinel+ Guy)

[Mister Bison]

Let me do a double post here because the concept is pretty different, and I wish to split the threadjack.

You can solve the problem with a "quantic" approach. Let's say you get 3 selves, each one selects a door, so you have 1 that is right, and two that are wrong.

Now, the one you that is right gets one of the wrong door opened (wether by random, or by choice, what matters is the result that one wrong door is opened, which is always possible. You don't need to measure the gain of changing your mind if your door was opened, right ?). He has another choice to change his door to open, so he splits again, the staying right and the changing right. Only one of them wins.

Now remember the two you that were wrong? Now the remaining wrong door gets opened (Again, doesn't matter if it was random or not, you wouldn't be asking this question if they opened the good door, you would know). They have a choice, again, so they split, too. the staying wrongs, and the changing wrongs.

The problem is, those are three you. So either you are staying, or you changing. So, where are there more "you" winning ? When you stay, or when you change ?

Again, what matter is how many "you" were here at the first choice, and how your second choice will affect all of them.

[Codewalker]

But statistically speaking, it doesn't matter.  Since the the wind doesn't know which door is the bathroom, the 1/3 probability of it being the door it opens is shifted equally to the other doors, which now makes it 50/50.  That's why in the Monty Hall problem, it's critically important that you make it crystal clear that Monty knows which door has the prize behind it, and he deliberately opens a door that has a goat.

Actually, the wind does know which door the bathroom is. Arcana stated the problem as such:

So here's the real test of probability mastery.  You're looking for the bathroom, but you've forgotten which door leads to the bathroom.  You really, really need to use the bathroom and you can't wait long enough to open all three doors.  You mentally pick the door you guess is the right door, but as you run up to that door the wind blows open one of the other two doors, showing its the washing machine.  Should you switch doors?

Emphasis mine. The way the problem is stated rules out any possibility that the wind can blow open the bathroom door, so it's effectively the Monty Hall problem in disguise. The given information completely excludes 1/3 possible sets of circumstances right off the bat, just like Monty opening a door he knows is wrong excludes them.

[Mister Bison]

Actually, the wind does know which door the bathroom is. Arcana stated the problem as such:

Emphasis mine. The way the problem is stated rules out any possibility that the wind can blow open the bathroom door, so it's effectively the Monty Hall problem in disguise. The given information completely excludes 1/3 possible sets of circumstances right off the bat, just like Monty opening a door he knows is wrong excludes them.

Well, the wind did not know, but now you do know which door the wind opened.

That's what problematic in probabilities, it's knowing how to interpret the problem, and this can make a whole world's worth of difference.

[Arcana]

The way the problem is stated rules out any possibility that the wind can blow open the bathroom door, so it's effectively the Monty Hall problem in disguise. The given information completely excludes 1/3 possible sets of circumstances right off the bat, just like Monty opening a door he knows is wrong excludes them.

Actually, the problem as stated eliminates 2/3rds of all possibilities.  Since the wind is presumed to open a door at random (the wind didn't and can't explicitly select the wash room) it isn't the same problem.

The easiest way to look at this is that initially there are six possibilities.  There are three possibilities for my choice: washing room, bathroom, bedroom.  And for each of those possibilities, there are two possibilities for the other two doors: the wind opens one of them or the other.  These six possibilities look like this:

My Choice, Wind, Other
wash, bed, bath
wash, bath, bed
bed, wash, bath
bed, bath, wash
bath, wash, bed
bath, bed, wash

That's all six possibilities, all equally likely, the instant prior to the wind opening a door.  When the wind blows open the wash room, *four* possibilities are eliminated: 1, 2, 4, and 6.  Notice that two of the options that are eliminated are the ones where I picked the wash room.  That's impossible if the door that blows open leads to the wash room.  That leaves 3 and 5.  In one my choice is right and the remaining door is wrong, and in the other my choice is wrong and the remaining door is right.  Therefore, its now 50/50 and it doesn't matter if I keep or switch.

Why is this different from Monty?  Because with Monty, there are only three possibilities:

My Choice, Box 2, Box 3
Prize, Empty, Empty
Empty, Prize, Empty
Empty, Empty, Prize

When Monty opens one empty box, he doesn't actually eliminate any of those possibilities.  All three are still possible (and equally likely), because in all three cases he can open an empty box, and its presumed in the Monty version that Monty knows where the prize is so its always *guaranteed* he opens an empty box.  So his action adds no information, or alternatively you can say it eliminates no possibilities.

It matters that Monty knows where the prize is.  Suppose in Monty that a random audience member is chosen, and they are asked to open one of the boxes you didn't pick, and its empty.  You might think that increases the likelihood that the remaining box you didn't pick now has a 2/3rds chance of having the prize, same as if Monty opened a box.  But that's wrong, and to see why lets look at the degenerate case again.  Suppose its a million boxes, and you pick one.  At the moment you believe you have a one in a million shot, and there is a 999,999 chance out of a million (almost a certainty) that the prize is in one of the other 999,999 boxes.  But suppose we randomly pick an audience member, and ask them to open one of those boxes, and its empty.  Then another.  And another.  They are asked to open 999,998 of them, and they are all empty.

Question: if the prize *was* in one of those boxes, what are the odds that a random audience member could manage to avoid opening the prize box 999,998 times in a row?  Ah, that's the rub.  If boxes are opened randomly, there's a chance the box that is opened is the prize box itself.  The fact that it does not happen is itself information if the boxes are opened randomly.  But if Monty does it, the odds of the prize box being opened is zero.  And that's what causes the odds of the prize being in the box Monty doesn't open to rise with each box he opens.  He's telling us something we already know - that some boxes are empty - while providing no additional information about whether the remaining box is or is not the prize box.

[GuyPerfect]

The doors in the picture are actually living, wash, bath.

[Risha]

Couldn't manage much, but done.

[Arcana]

The doors in the picture are actually living, wash, bath.

That's a lot of edits.  Could you move your bed into the living room instead?

[Mister Bison]

<clever word reading skills>

You're twisting the words. Actually, a door, can't be a washing machine. And no probability mastery can make that so.

So here's the real test of probability mastery.  You're looking for the bathroom, but you've forgotten which door leads to the bathroom.  You really, really need to use the bathroom and you can't wait long enough to open all three doors.  You mentally pick the door you guess is the right door, but as you run up to that door the wind blows open one of the other two doors, showing its the washing machine.  Should you switch doors?

Note that it does not say "Showing the washing machine was behind it/the door".

[GuyPerfect]

Great, you've done it this time. Now we need to invent a door that is also a washing machine.

[Triplash]

Great, you've done it this time. Now we need to invent a door that is also a washing machine.

Well, I don't have any that are doors... but there's one you could hang on a door, and even one you can carry around with you.

And just think, guys. With a washing machine that small there could be one behind all three doors. Problem solved! :D

[SerialBeggar]

Well, I don't have any that are doors... but there's one you could hang on a door, and even one you can carry around with you.

And just think, guys. With a washing machine that small there could be one behind all three doors. Problem solved! :D

How is the plumbing handled with those portable washers?

[Triplash]

How is the plumbing handled with those portable washers?

From the way I read the article, the idea is that the water and electricity hookups would be built into communal locations, and each person brings their own container with their items in it. Like plug 'n play. It's quite an efficient idea actually, with just two drawbacks: (1) remodeling existing buildings to accomodate it, and (2) remodeling existing people to actually use it. That's probably why it's still a lab prototype and not in the market yet.

[Arcana]

Note that it does not say "Showing the washing machine was behind it/the door".

Well, I suppose technically speaking switching the doors won't change what's behind them either.  And ironically, based on the picture the only two doors you can easily switch from the only room that views all three doors before actually opening them are the two doors that don't lead to the bathroom.

Which makes for an interesting mnemonic: the bathroom is behind the only door you can't switch, if you're asked to pick a door and then given the option to switch the door.

I suppose its also the only door that opens into its room, but that's not nearly as interesting a mnemonic.

[Megajoule]

And here I figured, seeing three doors all lined up like that, that they were Male, Female, and Huge.

[Mister Bison]

Well, I suppose technically speaking switching the doors won't change what's behind them either.  And ironically, based on the picture the only two doors you can easily switch from the only room that views all three doors before actually opening them are the two doors that don't lead to the bathroom.

Which makes for an interesting mnemonic: the bathroom is behind the only door you can't switch, if you're asked to pick a door and then given the option to switch the door.

I suppose its also the only door that opens into its room, but that's not nearly as interesting a mnemonic.

Seems to me you can switch all of them, they all revolve the same way (counterclockwise, if you could Hover over them). I guess the right one appearing too small is because it's aligned to the other side of the 20 or so cm of the inner wall of the appartment, because it's made to be pushed.

The problem is the wind always opening the washing room door. Must be a killer when trying to sleep. That and it being another door than the one you whose, basically mean you couldn't choose the washing machine room's door, reducing it to a 50/50 chance of finding the bathroom door.

Personally, I would change the bathtroom's knob to a unique one, and put a lock on the washing machine's. Switch that, Monty !

[SerialBeggar]

https://images.weserv.nl/?url=www.smbc-comics.com%2Fcomics%2F20130323.gif

[Noyjitat]

This guy ever make it to Texas? If so it looks like the titan website needs to be updated and the paypal button changed  8)

[eabrace]

He made it.  He's got a job to pay the rent and everything now.

We've pointed Tony in the general direction of getting the button updated.  :)

[GuyPerfect]

You guys were extraordinarily helpful and I continue to be grateful for all the aid you sent my way.

[TonyV]

I changed it from "Help Guy" back to "Donate Coffee".  (Metaphorically.  In reality, I hate coffee, and donated funds go towards maintaining hosting.)