/sci/ - Science & Math

Sensible chuckle.

>>7594349
>hear about the Monty Hal problem from some girl
>acquire a love for mathematics as a result
>girl keeps teaching me all summer
>specifically states that she wants no compensation
>leaves without saying goodbye because never gave her the specific compensation she really wanted
Fucking girls, man

>>7594363
Shoulda fucked her right in the pussy.

How does the monty hall problem contradict an orderly universe

>>7594349
>Study quantum mechanics
>Wonder if my cat is alive or dead when I can't see him, terrified I'll kill him by observing him.

>>7594406
https://en.wikipedia.org/wiki/Monty_Hall_problem#Vos_Savant_and_the_media_furor

It doesn't, it's just true and so counter-intuitive that people can't accept it.

>>7594363
sounds like she should be slapped

>>7594506
>slapping bitches
>not straight up koing them

not the gahara i know.

Don't read about the blue eyes puzzle then OP, it'll kill you.

https://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/

https://en.wikipedia.org/wiki/Common_knowledge_%28logic%29

>>7594527
But emma-bro, blues eyes is retard-tier. I expected better from you

I remember this fuggin my mind when I first encountered it but now its so logical I can't even trace my steps to revisit what it was that confounded me.

People I am a stat god. The monty hall problem is easy to understand if u expand the problem. classic example is 3 doors, make it 100 doors and you will see clearly what is happening. Enjoy

>>7594653
Random story from muh life: I (brown eyed) was at the house of a friend of a friend of a kid. I was alone with his mother in the kitchen at one point. Never seen this person before.
We talk for 1 minute, then she tells me she would never give a kid my name, as it's (appearently) the name of some dictator, and also: brown eyes people are all stupid, because cows have brown eyes.
>o-okay

>>7594773
I meant the puzzle, not people with blue eyes.

>>7594789
I am so fucking tired of mobile 4chan turning my pics 90 degrees

>>7594777
oh I see.

I actually don't like solving puzzles. But here's another one I know of
https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever

>>7594527
Scratch that. Try the sleeping beauty problem.
https://en.wikipedia.org/wiki/Sleeping_Beauty_problem

This is a fundamentally fucked up one that no one has an answer to.

>>7594349
It's just a game show trick, chill out.

>>7594842
Sadly, I already know all of Wikipedia by heart.
Btw. that one's funny:
https://en.wikipedia.org/wiki/List_of_lists_of_lists

I'd strongly argue that the sleeping beauty problem isn't one that than can be resolved, like a puzzle can. Any "solution" will fix the meaning of the notion of probability in some way.
In fact, I'd go as far and say theories of probability are a formalization of a human idea that's more unfounded in reality than much of physics, in particular because it involves (contrary to mere combinatorics) the problematic notion of time.

Thus I find the scenarios involving common knowledge more intriguing.

I like the movie in pic related, though.

>>7594363
>Never have anyone offer to teach me fucking shit, have to learn everything on my own
>Class time is a continuous lesson in how hard people can ignore me
>Read people like this getting all the luck of the Irish handed to them on a silver plate and then squandering it like a fuckboy

REEEEEEEEEEEEEEEEEE

>>7594973
In that case, I'm not gonna bring up my girlfriend, my genius friend with massive boobs, my tomboyish dyke friend that tries to feel me up, or the three little girls I've kissed and/or molested

>>7595035
>my genius friend with massive boobs

pics or GTFO

>>7594527
>>7594653
Why would the solution work if there are more than 2 blue eyed people? Wouldnt it already be common knowledge since you know that the brown eyes see 2 or 3, and that either of the blue eyes see 1 or 2?

>>7595419
If they see 1 or 2 then you have no way to tell what your eye color is.

>>7594799
Damn. qt as fuck.

>>7594973
Ah too bad, you must be stuck in that zone of too stupid to tutor hot dumb girls and too smart to be taken pity on by hot smart girls. I tutored one of the hottest girls in my high school in math. One day we decided to do a private session at her house and I got my dick sucked for the first time. Then there were numerous lab partners in college who needed me to do everything...

>>7594966

That movie was just old men having sex with passed out young women.

Did I miss something? should I watch it again?

>>7595501
Who the fuck would watch that spare rapists

>>7594966
Well, whether it's solvable or not it would have applications, mainly in answering the anthropic principle and doomsday hypothesis:
https://en.wikipedia.org/wiki/Doomsday_argument

>>7595502

I didn't know what it was about when I watched it. But I couldn't look away, it was all so... eww.

>>7594432
You obviously don't study quantum physics if you think a macroscopic object independant and not entangled with a microscopic particle can be in a superposition

>>7594349
I just now read about it. It's stupid, you create two separate odds as soon as you open the new door as an option completely disappears when you in fact get the car as the second door option. Probabilities will then change to independent tasks.It doesn't contradict an orderly universe at all, just divides the order into two separate pieces

>>7594973
Topkek. You're autistic
>>7595035
>genius friend with massive boobs
Go back to /tv/, fam. .

>>7595639
I think that once you fix your idea of how probability works (if you don't drop it altogether), then now surprising such arguments will be trivial or silly.

>>7595661
I think a reading is this: There is no good thing in the main characters life, she just goes on with no aim - her wake state is when she's dreaming. She is completely passive and doesn't value herself in any way (does medical experiments for money, may it be pic related or the odd mansion thing where she sleeps). She is only really in the present when she's not - i.e. when she's on drugs. She leaves the waking state to get away from the nightmare she only can stomach by being stoic.
At the end of the movie she wakes up (literally and figuratively)
https://www.youtube.com/watch?v=XwQzq-E4Np0#t=5m20s

>>7595639
I think that once you fix your idea of how probability works (if you don't drop it altogether), then now surprising such arguments will be trivial or silly.

>>7595661
I think a reading is this:
There is no good thing in the main characters life, she just aimlessly goes on. She is completely passive and doesn't value herself in any way (does medical experiments for money, may it be pic related or the odd mansion thing where she sleeps), the life is 100% without joy or purpose. She can stomach this "nightmare" only by being stoic - her wake state is when she's really asleep. She is only really in the present (awake, if you will) when she's not, i.e. when she's on drugs. At the end of the movie, literally and figuratively, she wakes up
https://www.youtube.com/watch?v=XwQzq-E4Np0#t=5m20s

>>7594349
I've just now come across this thought experiment in your OP.

Yeah, it does seem counterintuitive but the problem lies here.

1. He ALWAYS shows you 1 door that doesn't have the prize.

2. From the very start, Its always a 2/3 chance you picked the WRONG door already.


Chances are you originally settled on the wrong door since its only one prize and three doors.

So we know you most likely picked the wrong door. Now the guy reveals 1 of 2 doors and its ALWAYS a non winning door.

So now you most likely settled on the wrong door from the beginning. Then the man eliminates the second wrong door.

Odds are the door you didn't pick is the winner. Really nothing mind shattering in it from my perspective. Check out quantum suicide if you want a true mindfuck grounded in reality.

what are other good probability mindfucks?

He's right, you know.

>>7597577
>http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/
>Some PhDs in mathematics confirmed information regurgitating retards

>>7597577
>you are either right or you are wrong

this is why stats majors should take at least some basic math courses

>>7595676
Yes that was obviously a serious post

>>7594711
>classic example is 3 doors, make it 100 doors and you will see clearly what is happening. Enjoy

If switching in the the Monty Hall problem has a 2/3 chance of picking the car, then switching in the Hundred Door Problem has a 99/100 chance of picking the car by the same logic.

>>7597603

yes, and?

>>7597604
If you don't switch, you have still opened up 99/100 doors. Your choice has no impact on the number of doors opened and therefore no impact on the odds.

>>7597609
you are not choosing between one door.

the choice is between one door. or all other doors

>>7597613
You get all the other doors regardless. Monty Hall opens all the other doors BEFORE you make your choice.

Let me simplify this for you. Let's say Monty Hall offered you a different choie:

>Stay with the door you chose
>Open both the other two doors and win if the car is behind EITHER of them

Compare this to the actual Monty Hall Problem, where the third door is already open BEFORE making the choice between two doors.

>>7597620

then you still have a 2/3 chance in switching. i'm not sure what you're arguing for/against here.

>>7597623
So you admit that your odds of winning are 2/3 because you open TWO doors?

Then how do you rationalize claiming that your odds of staying in the actual Monty Hall Problem are 1/3 if the third door has already been opened?

>>7597625
you are just not getting this

go do the experiment

after you get the results you can reconcile it however you want.

>>7597620
>You get all the other doors regardless.
No you don't, dude. You first choice is choosing between doors with 1/3 each.

Your second choice is choosing between your first 1/3 door and the door that becomes 2/3 when monty opens the goat.

>>7597629
There is no logical argument for why one unopened door should become 2/3 while the other unopened door should remain 1/3. If opening the goat door raises the odds of the unopened door to 2/3, then both unopened doors are now 2/3 because there is no difference between the two doors.

>>7597625

with 3 doors you will ALWAYS have a 1/3 chance of getting the correct door on the first pick without having any prior knowledge of what doors have goats and what do not. the odds are greater that you did not pick the correct door on the first try (2/3); it is more probable that the other door, which monty does not open, holds the car, because, again, your first pick had a greater probability of being wrong.

>>7597634

your second choice is choosing between your first 1/3 door and the door that becomes NOT 1/3

hence either right or either wrong

>>7597634

read: >>7597636

>>7594349
I'm no math genius but this is how I understand the problem:

The first time you chose its a 1/3 chance to get the right door. After one bad option is removed you now have a 1/2 chance. Its not like anything magically changes, if you picked the right door at the start it will always be the right door, however there's a good chance your first choice was not right and that's why its best to switch.

Am I not understanding it right? It seems logical to me, the first choice was probably wrong and that's why its best to change.

>>7597634
It's because 2/3 of the time, your first door is a goat. Then the door that monty doesn't open is 3/3 a car.

The other 1/3 of the time, your first door is a car. Then the door that monty doesn't open is 0/3 a car.

So for switching,
2/3*3/3 + 1/3*0/3 = 2/3

>>7597639
>you now have a 1/2 chance

no.

>there's a good chance your first choice was not right

yes, 2/3.

>>7597644
Ok I don't understand how its not 1/2 but isn't the fact that you were probably wrong the first time enough to justify changing?

Have they modeled this? Seems simple. Make a program based on this scenario, run it 100 times where it doesn't switch then run it 100 times where it does switch, compare results.

>>7597647
>Ok I don't understand how its not 1/2
Because it's 2/3. If your original door was 1/3, the other door must be 2/3.
>the fact that you were probably wrong the first time enough to justify changing?
Yes, this is key to understanding the paradox. You just estimated the probability a little low.
>Have they modeled this?
Yes, and switching got the car 66/100 times, while not switching got the car 33/100 times.

>>7597647
it is 1/2 if there are two doors because the choice is 1/n door or n-1/n door

its not 1/2 because is NOT about 1 out of two choices you are given (stay or not stay) you are given a binary choice this choice is NOT the problem

the problem is about the doors

>>7597647

just because he opens a door doesn't automatically take away from the fact that, in the beginning, you had a choice of 3 doors. the door monty does not open has now taken on the 1/3 chance from the door that he did open--resulting in 2/3 of a chance of being the correct door.

as another anon said, putting it in the scheme of 100 doors makes it a lot clearer. choose one door out of 100, and you have a 99/100 probability of being wrong. monty comes along and opens the 98 doors that have goats, leaving your door (which may have a goat), and 87th door that he did not open. while it may seem like you now only have a 1/2 chance, in reality your first pick was wrong 99/100 times, so pick the door monty leaves open.

>>7597657

my bad, i mean leaves closed.

>>7597653
>>7597654
>>7597657

Thank you I get it now. Why do people argue about this then? That's pretty logical and models show switching to be better as well. Is it autism?

>>7597663
Because dumb people keep forgetting about the first part of the problem and thinking that 1 car in 2 doors means both doors are 1/2.

>it's 50/50, it either happens or it doesn't

>>7597665
>implying you're smarter than erdos

just play the freakin' game:
http://www.stayorswitch.com/

>>7594349
Monty Hall problem made me lose faith in humanity. There are always people who go full retard over "But statistics can't explain my individual chance, that is 1/2" or "but If I only do it once its 50/50 etc." and its weird how its mostly the kind of people who believe in creationism or that relativity is a jewish conspiracy.

Seriously ask the next conspiracy nut about the monthy hall problem, chances are high they will insist that the true answer to it is 50:50.
Its like a litmus test for crazy.

>>7597674
Can you prove that this game determines the location of the car and two goats at the beginning of the game before you've clicked on any doors?

>>7597694
the results of the game is correct therefore the implementation is correct

>>7597702
Literal definition of begging the question lad

>>7597674
Told ya'

>>7597694
Can you prove this game is rigged somehow?
Or are the voices telling you it's a conspiracy?

Imagine one million doors.
999 999 contain goat
1 contains car
choose one

999 998 goat doors are opened
two left
you are allowed to switch

if you don't switch, you're either a retard, or a goat herder.

>interested in /sci/ because of animu

>>7595676
I mean, well, technically it's entangled with all of the microscopic particles around it and within it. So, if all of them were to collapse in a funny way, that would probably kill the cat.

>>7597758
>10 samples
>Worth noting anything
Return when you have played at least 100 times.

>>7594349
>be me
>mathematics phd
>after years of studying just realize that all the mathemathical beauty and order is just a brief moment before entropy devours almost averything
>start actually believing in the mythos
>every night is a suffering
>nightmares
>sleep paralysis
>going to a psychologist
>"anon you should know how to separate reality from fantasy"
>now fearing that if I tell anybody about my thoughts I would be take as a madman

Ignorance is a bliss...don't twist your sanity with those mind experiments...

I>>7598487
Explain, how does entropy even exist?

>>7598839
How can entropy be real if thermometers aren't real?

>>7598839
No no no, are you even reading anon?
WHY entropy exist is exactly the kind of question that will make your mind twich and scream in insanity if you go too deep. We could define it and analize it for sure. We could even try to prevent it in a certain way, but don't ask why anon....

I never understood why people get confused by this.

It becomes more obvious the more doors you add.

>1000 doors, pick one.

>host oppens 998 other empty doors, asks if you want to switch.

do you stick to your 1/1000 chance, or go for the new 1/2?

>>7600479
>go for the new 1/2

>>7597786
Now I get this. Using bigger numbers should make it clear for all people.

It's bigger change to pick wrong door on your and leaving correct one in un picked ones.

Not switching is relying on your lucky pick only. Now I would switch all time. Same reason I pick random results when doing lottery.

People probably so confused because of stuff like having 1/2 change to have tails in coin flip even if all previous results were tails.

>>7600583
>People probably so confused because of stuff like having 1/2 change to have tails in coin flip even if all previous results were tails.
So if I give you a coin that always lands tails you will still bet that it has 0.5 chance of landing heads?

>>7594842

The 'deabte' is nothing but philosophers making noise.

If the coin comes up heads the person will be woken once, if it comes up tails the person will be woken twice.
So any "ideally rational epistemic agent" is going to know that if she gets woken up,
there's a 1/3 chance the coin came up heads, and a 2/3 chance it came up tails.

>three doors
>car is randomly behind one door
>we know it's not behind door 3
>50/50 chance of it being behind door 1 or 2

I KNOW it's wrong and yet I can't make my brain understand why.

Why do the doors inhereit the probability of the first half of the problem? Why is the second choice not an isolated chance?

>>7600659
see
>>7597786

>>7600693
Increasing the number of doors doesn't change my confusion.

I still don't understand why all those doors pass their probability through time to the second choice.

>>7600751
Nothing is being transported. The right door is the right door and the wrong doors are the wrong doors.

You might chose the right door on your first guess but you probably didn't, the odds are against you. So look at it this way, with 3 doors you probably chose a goat, that's the most likely option, then he shows you the other goat, that means the remaining door is probably the car.

Not 100% of the time since sometimes you will choose the car first but most of the time you won't so switching gives you the best chance. The whole thing is based off the fact that your first guess is probably wrong.

>>7600766
>The whole thing is based off the fact that your first guess is probably wrong.

But that's what I mean.

In the end, I have two doors, behind one of which (at random) is a car. That should be 50/50.

But, because I "chose" one of the doors when there were three options, somehow that alters the probability of the current situation. My first guess alters the probability of the second guess.

And I don't understand why. I accept that it happens, I'm not dumb enough to refuse evidence just because I don't understand it, but I don't get it.

My mind views probability as an island- the previous coin flip doesn't affect the odds of the current coin flip- and this invalidates that.

>>7595035

Fuck off back to /a/.

>>7600787
OK but this isn't a coin flip.

You choose a goat (most likely)

He shows the other goat

Remaining door is probably the car.

Idk any other way to explain it I don't see how that doesn't make sense to you.

>>7600479
It's 999/1000 odds you fuckwit.

>>7600787
Take you door, or all the others. That is basically the situation, since the gameshow host doesn't open doors at random.
Switching or staying, whether the host tells you before or after your decision which doors (of the ones not chosen initially) are definitely goats, why would it make a difference?

>>7600792
>You choose a goat (most likely)
>He shows the other goat
>Remaining door is probably the car.

But why?

I could have chosen the other door from the start, and the situation would be reversed (in terms of doors).

Why does choosing a door affect its future probability of being the correct door? The right door had a 1/3 chance of being correct originally too, but because I didn't choose it, it doesn't keep those odds. The wrong door, however, does keep them, because I chose it.

Why? Why does me choosing affect the probability? It's like some Schroedinger shit. If I don't pick either door, after he reveals one, they've got an even chance.

>>7600809
>Why does choosing a door affect its future probability of being the correct door?
No.
Monty opening doors does not affect a door's past probability of being correct.

>>7600809
Your over complicating this. Do you agree that 2/3 times your first choice is a goat?

>>7594349
Great blog, would subscribe.

>>7594349
this got me so mad. FUCK

>>7594349
>glimpsed unknowable terrors of the unfathomable abyss
I felt like that when I started getting deeper into abstract algebra and analysis.

>>7594794
That's just your shit phone.

>>7600221
all why questions are subjective.

just cause, because sure

>>7600809
It has nothing to do with quantum mechanics, and everything to do with the fact that the host is giving you more information by opening a door.

>Why does choosing a door affect its future probability of being the correct door? The right door had a 1/3 chance of being correct originally too, but because I didn't choose it, it doesn't keep those odds. The wrong door, however, does keep them, because I chose it.

No. The right door had a 100% chance of being correct because it is the correct door by definition. You had no information about the situation, however, so you could only give it a 1/3 chance of being correct along with each other door.

Keep in mind that if you picked a different door, the host might have opened a different door in response. You convey information to the host by choosing, and he conveys information back by opening one door.

Monty Hall works because 1) the host knows where the car is, and 2) the host knows which door you have picked. If either of those assumptions fails, then the probability of winning is only 1/2 because no information can be conveyed.

>>7600924
(continued)

If you always pick door 3 and then switch, and the host doesn't know where the car is, we can list out all the possibilities like this:
1. Car is behind 1, host opens 1: null result (host has messed up)
2. Car is behind 1, host opens 2: you win
3. Car is behind 2, host opens 1: you win
4. Car is behind 2, host opens 2: null result
5. Car is behind 3, host opens 1: you lose
6. Car is behind 3, host opens 2: you lose

All of these are equally likely: P1=P2=P3=P4=P5=P6=1/6. (Also note that P1+P2=P3+P4=P5+P6=1/3. This will be important later.) Given that you do not see the host mess up, #1 and #4 can be eliminated and you will win 2/4=1/2 of the remaining possibilities.

If the host does know where the car is, the probabilities are no longer equal (P1=0, for instance, since the host will never intentionally mess up). However, it is still true that P1+P2=P3+P4=P5+P6=1/3 because the car is equally likely to be behind each door. Because P1=P4=0, P2 and P3 must increase to match: both must become 1/3. Essentially, knowing that the host knows where the car is provides information about the host's actions, and that in turn provides information about the car's location.

>>7595785
i tried to break it down into the simplest sentence:

>since its a 2/3 chance you will choose a goat, you should swap

that seems fine. but im having trouble understanding why the other way isnt also right.

>revealing a goat just eliminates a door and you are left with a 1/2 chance

they both seem right to me. some one want to explain why the 2nd sentence is wrong?

>>7600787
I'm with you. both 1/2 and 2/3 chances seem acceptable answers. how is that possible?

>>7601009
>>revealing a goat just eliminates a door and you are left with a 1/2 chance

The other door you didn't choose inherits the 2/3 chance when the goat door is revealed.

>>7600787

Because the person choosing the second door is not guessing.

He knows.

An intuitive explanation is that if the contestant picks a goat (2 of 3 doors) the contestant will win the car by switching as the other goat can no longer be picked, while if the contestant picks the car (1 of 3 doors) the contestant will not win the car by switching

/thread

When you select a door, you have
a group of two doors with P=2/3
vs a door with P=1/3.

In other words, a door vs a group.

When Monty reveales the goat,
it's *STILL* a door vs a group.

The only thing Monty changed is that
the group's original P=1/3+1/3
is now P=0+2/3 instead.
In both cases the group's P=2/3.

So, when you switch, you are trading
the door's P=1/3 to the group's P=2/3.
Of course this is the best thing to do.

>>7594448
>it's just true and so counter-intuitive that people can't accept it.

>it's just true and usually stated so poorly that people get annoyed with you when you tell them the only right answer is the one that fits your unstated assumptions.

You have to be VERY specific about Monty's behavior for the standard answer, and its analysis, to be correct, and it's almost never adequately specified.

- he knows where the prize is (or at least where two non-prizes are)
- he always opens a door, no matter what's behind the door you chose
- he always opens a door with a non-prize behind it
- he will always let you change to another door

So you need to know that he's following rules, and what those rules are. These rules are outside of the actual "Let's Make A Deal" rules, and were not mentioned either in the original version of the puzzle or Marilyn vos Savant's version.

If you don't know that he's following rules, and what the rules are, then changing doors doesn't bring any clear advantage. That makes it a game of guessing his thoughts and motives, which isn't a logic puzzle anymore.

>>7600627
But probability is fake as shit except in theory, so wouldn't an average person answer their belief to be the exact same every time they're woken up, unless given different stimuli by the person interviewing them?

>>7600787
Think about it like this. There are only two solutions at the start: The door you pick, and not the door you pick. The door you pick has 1/total probability, and 'everything else' has total-1/total probability. The act of opening the other doors only a formality. You're still basically choosing to open one door, or open all the other doors BUT that door.

The sticky presence of this thread is a trolljob right?

No one could be so stupid they don't get the monty hall explanation.

>>7600627
To invoke further discussion:
before falling asleep it is known that the probability of heads is 1/2 but after having her nap she deduces the probability of heads to be 1/3. Has she changed how the coin worked in the past with some time traveling witchcraft or what's going on here?

Keep in mind the question here is about estimating that the coin landed heads, not about what she'd bet her money on each time she's woken.

>>7594794

Just screencap the pic and delete the original, bro.

>>7597740
ur mum begged 4 my dick m8

Ok, here is my interpretation of the monty hall problem in a sort of informal proof format, tell me if it is stupid or not.

We have three doors. Behind two of them there is one goat each, behind the third there is a car.

If I were to choose one of the three doors at random I would have a 1/3 chance of finding a car and a 2/3 chance of finding a goat. It is important that there are only two distinct possibilities here and that added together we get 3/3. (I don't know how a mathematician would explain this but if all the chances of your distinct possibilities don't add up to 1/1 something has gone terribly wrong, right?)

Now I choose one door at random. The probability of me having chose the door with the car is still 1/3 and the probability of me having chose a door with a goat is still 2/3 at this point. 1/3 + 2/3 is 3/3. All remains right with the world.

Now, one of the other doors is revealed to have been a goat. This isn't very surprising. We always knew there were two goats and we could only choose one door. Of course one of the remaining doors was a goat.

Now we are allowed to change our guess to the remaining door. Naively we think that since it is a choice between two doors then it should be a 1/2 chance that the other door has a car because there are two doors and one of them has a goat and one of them has a car. But we already established that our first guess had a 1/3 chance of being the car! Revealing a goat that we already knew existed doesn't retroactively change this.

Assuming our initial naive calculation of a 1/2 chance of their being a car in the other door we add together our probabilities: 1/3 of our original guess plus 1/2 of our new possibility equals... 5/6.

The total of all possibilities should equal 1/1. The second door must have a 2/3 chance of having a goat behind it because that is the only value that would fulfill this.

>>7601009
Just draw it out on a piece of paper. It's really fucking obvious. If you draw out all the possible scenarios

>>7595035
Shut the fuck up anon