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You are currently reading a thread in /sci/ - Science & Math

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https://www.youtube.com/watch?v=4Lb-6rxZxx0

>Those comments

Why are people so stupid, /sci/?
>>
>This "problem" reminds me of a rant with my math teacher, back in school, where she just wouldn't agree that a coin could land on the edge. But this is not the point. You can't apply calculations to a chaotic system and expect predictable results.

What the fuck.
>>
>>6586390
fuck, I was about to post that exact comment.
>>
>>6586390

Is there a single part of this comment that isn't completely wrong? Even the coin falling on the edge thing should actually be impossible unless you basically threw the coin so it had no rotation.
>>
>>6586411
Why do you assume that? I'm 37 and I've seen it happen at least six or seven times in my life.

That makes it extremely unlikely, but not impossible.
>>
>>6586412

Hmm, I guess it would depend on the type of coin as well though? The assumption I made is that the coin was thrown like you would in a coin toss, that is it would be rotating quite fast. I agree that if you just chuck coins in a random fashion that some of them will end up landing on the edge. However I don't see how it can happen if the coin is rotating fast, there simply would not be enough time for the friction forces to stabilize it on the edge before it falls over. Do you recall what type of coin/surface this happened on?
>>
>>6586381
another example of the value of computer literacy
if kids were taught basic programming skills in school they'd be able to determine the correct answer convincingly and quickly with a simple monte carlo algorithm, even if they're absolutely terrible at math and critical thinking
>>
The hundred door example was very good. It's very intuitive when you think about it that way.
>>
>>6586390
>You can't apply calculations to a chaotic system and expect predictable results

*gauss tips your fedora*
>>
For some reason youtube comments section (no matter what video) is like first world human stupidity concentrated. Or maybe the world really is this stupid.
>>
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I suppose the troll threads will start popping back up around here.
>>
>>6586462
I'm surprised there aren't already.
Any problem involving probability is a goldmine of bait.
>>
>>6586381

The dirty trick of this problem is that it's all about information asymmetry.

Most people don't understand that "a door with no goat gets opened" means, that the other guy knows, where the price is.

I always thy to explain it with 1,000,000 doors:
After chosing one door, 999,998 (false ones) get opened - so unless your first choice is right (1:999,999) you should take the second one.


>>6586390
>You can't apply calculations to a chaotic system and expect predictable results.

I freaking hate it when plebs use words like "chaotic system"..
So you can't predict a Lorenz attractor, right?
>>
http://marilynvossavant.com/game-show-problem/

All the PHd mathematicians in the 90s couldn't even get it, lol.

>Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful.
Robert Sachs, Ph.D.
George Mason University

>You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame!
Scott Smith, Ph.D.
University of Florida

>Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem.
Barry Pasternack, Ph.D.
California Faculty Association
>>
>>6588061
please call them "american Ph.D mathematicians"
>>
>>6588061

>You made a mistake, but look at the positive side. If all those Ph.D.’s were wrong, the country would be in some very serious trouble.
Everett Harman, Ph.D.
U.S. Army Research Institute

lovin' every laugh
>>
What if the door accidentally opened on its own?

Would this change the answer? Why or why not?
>>
>>6588147
That isn't part of the scenario in any manner of thinking.

If you mean "if a goat is revealed without any intelligence behind it", then no. Nothing changes.

As long as 2/3 doors contain goats and 1/3 has a car its the same scenario.

Choosing at random, you are most likely to have chosen a goat right?

When a goat is revealed (by chance or by choice) it means that statistically it is more likely that the other door has the car, because you were more likely to have chosen a goat from the start.

The revelation of the goat is important. Its not necessarily to do with the "host" having knowledge.
>>
>>6586381
>http://marilynvossavant.com/game-show-problem/
you guys know she IS WRONG right...r-right

now I am really confused the 100 door example really just confused me more

my reasoning:

you cannot group the doors, each one a single entity, each door in effect is an un-like term, just like you cannot combine b + x

this lady treats all the doors as if they are x, how is this possible, the value of every door can either be g(goat) or c(car)

so the programs running this problem have an inherit problem if they treat all the doors the same


help me out guys, I sort of get her argument and I want to believe but I can't
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>>6586381
There is no reason to switch door when the third one is open.
>>
>>6588203
Three ( or N ) eggs are in the bowl.
Only one of them is hard boiled.
You select one egg, put it on the table.
The chance that the table egg is hard boiled is 1/3 ( or 1/N ).
The chance that the bowl has the hard boiled egg is 2/3 ( or (N-1)/N ).
The show host breaks one egg ( or N-2 eggs ) from the bowl.
The chance that the bowl has the hard boiled egg is STILL 2/3 ( or (N-1)/N ).

Note:

1)
The host does NOT open a random door, the opened door always reveals a goat.

2)
If the problem had 10 doors instead of 3,
after you pick a door, the host would open 8 doors instead of only 1 door.
>>
This thread just reeks of condescending. Hate to break it to you guys, but the result is not intuitive. The only reason all of you claim it is so simple is because you have seen it 50 fucking times, probably on this board alone.
>>
>>6586381
for fuck's sake, why can't people write scripts to check it themselves?

It's as if someone claimed that oil and water mix, and then everyone got their heads up their asses and started arguing with each other, instead of just putting oil and water into a container and seeing what happens.
>>
>>6588203
If you chose randomly from 100 doors, you would have a 99% chance of being wrong right? Right.

If 98 of those doors were then opened, you would have 2 doors left, a goat and a car right? Right.

Since you made your choice with no knowledge you still have a 99% chance of having a goat right? Right.

Therefore, it makes sense to change doors because its more likely that the car is behind the other door.

This scenario is the same no matter how many doors (as long as there are 3 or more). The only difference between 3 or 10 or 1000 is the odds that you were correct to begin with.
>>
>>6588247
The major issue people are having is that they don't understand "why" the solution is real.

You can write a script for the problem and see the answer, but it doesn't really help to rationalise why that is true.

The issue is that the logic is less intuitive than the math. Until you wrap your head around it properly it can be difficult to figure out.
>>
>>6588061
>You are the goat!
Glenn Calkins
Western State College
>>
I never understood switchers.

Chances before of being correct door:
33% 33% 33%
Chances after reveal of being correct door:
50 % 50%

Both remaining doors have the same chance of being correct.
>>
I remember reading somewhere that in the real Let's Make a Deal Monty could choose whether or not to let you switch, and he could psychologically manipulate you into switching or staying. Like, if you knew it was better to switch, he would only offer you the chance to switch if it would make you lose.
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>>6588453
read
>>6588369
>>
>>6588469
>>6588369
>Since you made your choice with no knowledge you still have a 99% chance of having a goat right? Right.

See, that's the part of the argument where I call bullshit. What happened in the past doesn't effect the probability of this new choice. As far as I'm concerned there's two doors and one of 'em has a car behind it. Both doors have a 50% chance of being correct in this situation, changing doors will make no difference on the outcome.
>>
>>6588489
99 out of 100 times it will.
>>
>>6588489
You'll either live through the day tomorrow or die at some point. Since there's two possibilities, it's 50%.
>>
>>6588492
Help me out here, I don't see your argument.

>>6588493
Black or white fallacy
>>
>>6588453
>>6588489
>>6588498
Just write a simulation in your programming language of choice. The more doors you have, the less trials it will take to make it obvious that you should always switch assuming it's a fair game.
>>
>>6588498
>>Black or white fallacy
Yes, I was rephrasing your point to show how ridiculous it was.
Why would the door you pick suddenly jump from 1% likely to be the car door to 50% likely to be the car door once 98 other doors were revealed?
>>
>>6588498
I'll try to help. Think back to the three doors. How many different ways can you group what's behind them into groups of two? Goat-goat, goat-car, goat-car right?
So when you choose a door, you are leaving two doors unchosen. The chances that the unchosen group of two doors contains a car logically is 2/3. This does not change with the revealing of the goat.
>>
>>6588504
The 'other' door also had a one percent chance in the beginning. I fail to see what makes it different from the door I originally chose.

>>6588502
Will do tomorrow morning.
>>
>>6588498
It's like this: You have a 2/3s chance of picking the wrong door at the beginning, and if you did then the door the host doesn't open is always correct. It's very simple when you visualize each step separately.
>>
OH FUCK IT JUST HIT ME

still going to run a 50 door simulation tomorrow but I understand that every time a for it removes it ups the chance of the 'other' door but not the original (because the original cannot be opened by the host)

Thanks /sci/
>>
>>6588507
The thing that makes it "different" than that other door is this: you are right, in the beginning it is the same. When you choose a door even, nothing changes with the percents. The door that contains the car even has a 1% chance of having it as far as you know. It's when the host starts opening doors that things change, as the first door opens to reveal a goat, the chance that the car is behind the remaining 98 goes to 1.01% each, then 1.02% each as the next door is opened.
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>>6588513
It's my first day on this board and you're welcome, for my part at least. :-)
>>
Probability Concentration isn't real.
Proof:
A1/3 ... B1/3 ... C1/3
=
A1/3...BC2/3
-
B1/3
=
A1/3... C1/3
I don't care if who accepts or rejects it, but it is what it is.
Mathematical Conflation stop existing the second a necessary component is removed.
>>
>>6588522

Yes-huh
>>
I have N doors (N >= 2), where N - 1 contain goats.

No matter what door I choose, the host will ALWAYS open N - 2 doors containing goats. Therefore, no matter which one I choose, I will always have a 50% chance of being correct, even if N > 2.

How's this explanation wrong? Sounds fine to me. (I understand that initially you are more likely to pick a goat, which is why you should switch.)
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>>6588538
After the original l pick the host opens one of the other n-1 doors to reveal a goat. This action increases the chances of the group you pick but NOT the original pick because the original pick us exempt from the sheep culling process.
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>>6588541
original pick*
Group you didn't pick*
is exempt*

Duck smartphone keyboards
>>
>>6588544
Alright, that makes sense. Thanks for clarifying.
>>
>>6588502 here
I went ahead and decided to whip up a simulation because I have nothing else to do at 2 in the morning. This screenshot is from 1000 trials with a 50 door game.
>>
>>6588556

nice one. care to share the source code on pastebin?
>>
>>6586381
this video dont make it clear why you should switch, this explaine it clearly
https://www.youtube.com/watch?v=mhlc7peGlGg
>>
The big problem is that most confuse this game with a similar one:


>>6588147
>What if the door accidentally opened on its own?
>Would this change the answer? Why or why not?

If the False door opens then it doesn't change the game.

But let's assume a random door (also the price door) would open and the game would be lost if the price opens ba accident:
Then switching or not swichtching would be equal.

Let's say there are 10 doors and once the right door opens (by accident) the game is lost:
Then your chances woud be equal wether you switch or not.

Your chances that there are only two doors left (which is 100% in the first game, since only false doors get opened) would be 2/10.

So your chances that there are only two doors left, you switch and it's the right one would be 1/10.

If you don't switch you also have the 1/10 chance.
>>
>>6586381
"I DISAGREE.
In the game, you are effectively given TWO chances to choose your "winning door".
Choice 1 is between 1, 2 and 3 and you have a 1/3 chance of picking the correct door. So you pick door 1 with a 1/3 chance of winning.
You are then asked to choose again, after Monty opens door 2, and you have to choose door 1 or 3 and you make this choice by either staying with door number 1 or switching to door number 3. So you switch, or stick, but the odds remain at 50% chance of door 1 or door 3.
The odds of 1/3 are now irrelevant now you know that door 2 is not a winner.
The odds of picking the correct door on the second choice are ALWAYS 50% or 1/2, EVEN if you had a million doors, and Monty opened 999,998 of the other doors, the second choice is the same risk.
UNLESS you are assuming that these doors are all analogous to Schrodinger's cat, where the car AND the zonk are both behind ALL doors - until you open it, when it is forced to choose and present itself as containing either the car, or the zonk."
OH GOOD NONEXISTANT GOD!
>>
>>6588556
C'mon, share source so we can close he discussion.
>>
Here's another way of seeing it. If you were given the choice to either open one or two doors you would always go with two for a 2/3 chance of winning opposed to 1/3. You would also know that one out of the two doors you chose will have a goat. So the reveal of one goat doesn't convey any new information. Switching doors in the original problem is equivalent to picking two doors resulting in 2/3 chance.
>>
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>>6588195
This is false.
>>
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So many snot-nosed kids here in need of some education. So let's find a general solution to the Monty Hall problem...

Let p be the probability that Monty reveals a goat, given that the prize is not behind your first-choice door. Let q be the probability that you switch doors, given that Monty reveals a goat.

Note that when p=1, we have traditional Monty Hall. When p=1/2, we have random Monty. When p=0, we have Evil Monty. The value q describes your strategy, with q=0 and q=1 in particular being the "never switch doors" and "always switch doors" strategies, respectively.

(1) Find the probability P of your winning, as a function of p and q.

Answer:
P = 1/3*(1-q)+2/3*q*p
=1/3 -1/3*q + 2/3 q*p
=1/3 + (2/3*p - 1/3)*q

(2) Using the formula for P, find a strategically optimal q as a function of p, i.e. find a strategy q that gives you the greatest chance of winning.

Answer:

If p>1/2, then q=1 is best, i.e. always switch doors. P=2/3*p

If p=1/2, it doesn't matter what you do. P=1/3.

If p<1/2, then q=0 is best, i.e. never switch doors. P=1/3.

Put that in your pipe and smoke it.
>>
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>>6588717
Fixed the image. Basically after the first choice pathways 2 and 3 are the same. As a circuit this could be optimized by eliminating option 3 (which the host graciously does for us). So for practical purposes, your first choice is always 50% probability of a goat or a car regardless of redundancy in the initial question.

Monty Haul isn't even a question if it's written optimally. There are two doors, one has a goat, the other has a car. You pick one. It is either a car or a goat and you are given the option to switch. So throughout you have a 50% chance of getting either regardless of switching.

Either way, goats and cars are pretty awesome. 100% chance of winning something cool.
>>
>>6586381
I have a python script who simulate the game, so you could make your own experiences.
If you guys want it, I will post it.
T
>>
>>6588507
>I fail to see what makes it different from the door I originally chose.
Oh Lord....
It's different because Monty CHOSE that door based on his knowledge of what's behind each door.
Put yourself in Monty's shoes: the contestant (most likely) picks the wrong door.
You now open all the doors that don't have a car.
The contestant should switch.
In the less likely scenario, the contestant picks the right door, and you open all doors but one, any one.
In the more likely scenario, the contestant is better off switching, in the less likely scenario the contestant is better off sticking.
Which scenario we're in doesn't change after the contestant picks the first door.
>>
>>6588758
>Basically after the first choice pathways 2 and 3 are the same.
Yes, but between them they are twice as likely to happen as choice one.
Maybe you belong on /pol/ or /b/ instead of /sci/.
>>
>>6588805
I want it!!
>>
>>6588882
http://pastebin.com/cKe08usX
Suit yourself
>>
>>6588888
God i forgot to delete line 25.
>>
>>6588758
Goddammit you fucking retard. What prevents you from switching at option 3?
>>
So here is the original statement:
>Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
Note that it says "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat".

It does not say, "the host, who knows what’s behind the doors, chooses another door which he knows to have a goat behind it..." nor does it say, "the host, who will do this regardless of what's behind the door you've chosen...".

The explanation of the "answer" changes the scenario.

It's a riddle, not a problem of math or logic. In problems, the answer follows from the question, in riddles, you can justify the answer in a way that makes it seem as if it is the best response, but if you don't know the answer beforehand, you're guessing.

Riddles are a classic way to make people feel or look stupid when they haven't committed any actual errors. Marilyn vos Savant a shit.
>>
>>6588900
It says "He opens another door, which has a goat". He WILL ALWAYS choose a goat based on the original wording. It doesn't say maybe has goat, or could have goat, it say he picks a door which has a goat, excluding any possibility of choosing a door which has the car. The only thing that doesn't matter here is the number of the door, which why it says "say #3".
>>
>>6588929
>It says "He opens another door, which has a goat". He WILL ALWAYS choose a goat based on the original wording.
No, the original wording doesn't specify what "WILL ALWAYS" happen all, it just asks you what to do if this happens.

You're interpreting it through what you already know of the solution. Read the original wording neutrally.

There's no explanation of the host's reason for opening the door, no statement that he always does so after the player makes his initial choice, no claim that this is even a regular feature on the show.
>>
>>6588935
Except it doesn't matter. Whether it was on purpose or by chance, if he picks a door with a goat behind it, the odds of switching to the car will be 2/3.
>>
>>6588939
Oh my god, how can you think that?

We know he knows what's behind the doors. His motivation or criteria for opening a door isn't given.

He might only open a door, show you a goat, and offer to let you change your choice if you've already picked the car.

This way, switching is 0%. You can't possibly win if you're going to take an offer to switch. If you steadfastly refuse to switch, you have 1/3 odds, which can't be improved.

Or he might have a goat all dressed up funny he wants to show the audience. Let's say the showgoat is behind door A, a less interesting goat is behind door B, and the car is behind door C.

If you pick door A, he says, "You win a goat!" game show over.
If you initially pick door B, he opens door A "Hey, look at this goat everybody! Do you want to stick with your choice or switch to door C?" switching wins, staying loses
If you initially pick door C, he opens door A etc., staying wins, switching loses

This way, there's no way to improve your odds. It's completely random, regardless of your strategy.

Or he might want you to win, because audiences prefer a happy ending. If you pick the car on your first prize, he shows one goat... but doesn't offer to let you change, tension mounts... he has a dramatic pause opens the other door with a goat behind it... then the big reveal of the car you won. If you pick a goat, he reveals a goat, and then offers to let you change.

This way, switching isn't just 2/3, it's 100%. You can win every time by switching if he offers. It's completely non-random, if you know what he's doing.
>>
>>6588959
Well yeah if you arbitrarily change the situation so that now he may not let you switch at all despite that never being a part of the original question, then yeah things will be different. I have no idea why you bring up completely irrelevant things though.
>>
Everytime the host opens a door the chances for the closed doors being right increases. People just don't realize that he doesn't open your door too
>example with 3 doors
>Monty opens one
>now you have 50/50 chance to win if you choose a door
>but you have already chosen a door with 50% chance (the first one)
>changing your choice doesn't make sense
>>
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>>6586415
I drew you a picture, it's perfectly possible for a coin to land on the edge.
>>
I always find the most intuitive way to demonstrate it is:

There's 100 doors, 1 with a prize behind it, and you're the guy who knows which door that is.

You're paid each time someone gets the prize, but all you can do is remove doors they haven't picked bar 1, and offer them a switch.

When someone picks a door, and it's not the prize door, what do you do? You remove the 98 prizeless doors they haven't picked. What are the odds they win if they switch? 100%.

Now that's what happens when they pick a prizeless door. 100% win rate when they switch. What are the odds they pick a prizeless door again?

What advice are you gonna give the contestants before they go in? FUCKING SWITCH NO MATTER WHAT.
>>
This discussion is closed.
>>
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>>6588995
>When someone picks a door, and it's not the prize door
>Now that's what happens when they pick a prizeless door.
>>
>>6588593
>>6588700
Sorry, I fell asleep immediately after posting that. Here's the source if you still want it .
http://pastebin.com/1e5MGgfH
>>
>>6588968
>if you arbitrarily change the situation so that now he may not let you switch at all despite that never being a part of the original question
In the original question, you're not given his motivation for offering to let you switch, or any set of rules by which he chose to make that offer. You're only given one situation which arises after you've chosen a particular door.

I've explained why that matters. If you don't understand, go back and read it again, and think harder about it until you do.
>>
>>6589005
Yep, that's what happens if they pick a prizeless door. They win if they switch, they lose if they don't. 99/100 times they will pick a prizeless door.
>>
>>6589009
Now that I'm awake and looking at this, the doors[] array is entirely useless and I don't know what I was thinking when I put it in. Code's sloppy but it works.
>>
>>6589004
/thread
>>
>>6588995
>FUCKING SWITCH NO MATTER WHAT.

Only because of this stupid stipulation that you added:

>You're paid each time someone gets the prize

That's not the case with every host. It's hardly the case at all usually.
>>
>>6589065
How is it stupid? That's the whole point to make it intuitive (I use this for 12-13 year olds).

When it's just "98 of the other doors without the prize open" the kids find it harder because their intuition doesn't like raw numbers without the human element .

The host's motivation makes no difference, it could be a random number generator. As long as the contestant knows none of the doors opened had the prize, it's still a 99% chance the other door has the prize.
>>
I guess the main reason people give wrong answer is that they misinterpret the question.

They don't think about the first gate revealed. They treat it like a new situation e.g. some new player arrives with no prior knowledge where he chooses between gate A and B.

Of course some people are clearly wrong while understanding the question.
>>
>>6589086
If it isn't clear "a human being is trying to help you out because they win too" helps people grasp the statistics better than just "98 of the other doors accidently open and reveal none of them had the prize"
>>
im late but: http://pastebin.com/6MFKCFHW
from 100000tests:
>>>
win by not swapping 16.86%
win by swapping 33.41%
lost by not swapping 33.17%
lost by swapping 16.55%
first picked door win 33.42%
second picked door win 66.58%
>>
>>6589019
>http://pastebin.com/1e5MGgfH

thanks, appreciate it!
>>
>>6589095
>They don't think about the first gate revealed. They treat it like a new situation e.g. some new player arrives with no prior knowledge where he chooses between gate A and B.

That's not misinterpreting the question. That's just getting it wrong.
>>
>>6589101
And the two last lines are perfectly relevant
>first picked door win 33.42%
>second picked door win 66.58%

The sad thing is your code is ugly.
>>
"Either get the car if it's behind the door you pick, or get the car if it's behind a door you didn't pick."

Your choice.
>>
>>6589100
>"98 of the other doors accidently open and reveal none of them had the prize"
This isn't the same situation at all. If it's accidental, and they didn't open specifically because there's no prize behind them, then there's no reason to switch.

Look at it this way: if you pick a door, and 99% of the time you're wrong, then the host specifically picks the one with the prize behind it, and opens all the others, 99% of the time, the host is showing you where the prize is.

If you pick a door, and 99% of the time you're wrong, then 98 doors open at random, 98% of the time, one of those doors is going to show the prize. The 2% of the times that the doors don't reveal a prize include the 1% chance that you got the door right, and the 1% chance that you got the door wrong and all of these randomly opening doors failed to show the prize. It's a 50% chance whether you switch or not.
>>
>>6589108
We've been through this, the original question actually doesn't specify enough information to justify the "correct" answer: >>6588900
>>
>>6589117
What does autism feel like?
>>
>>6589114
constructive/10
>>
>>6589116
Nope. It's the same.

>98% of the time, one of those doors is going to show the prize

That's irrelevant.

>"98 of the other doors accidently open and reveal NONE OF THEM HAD THE PRIZE"

It's just stats. I flip two coins, one of them is heads, that means there's a 1/3 chance the other is heads. I pick a door, 98 of other doors open, none of them have the prize, 99% certainty it's behind the door you didn't pick. Doesn't matter why those 98 doors open.

For the coins, 3 possibilities, 2 of which have a tails.

For the doors, 100 possibilities, 99 of which have the prize behind the door the contestant didn't pick.
>>
>>6589117
No, it has all the information you need for the correct answer. The post you quoted is bullshit.

As long as the door revealed has a goat behind it, it's 2/3 chance the other unpicked door has the car.
>>
>>6589124
'kay
You don't initialyze all variables on one line, it is messy and hard to read.
You're using list when they are not needed, only because you are too tied to the mechanics of the game : we don't care to know where there's nothing/a goat, you shouldn't stock. A simple variable or a dictionnary would have been more efficient.
Plus the way you construct your list is messy : two variables to change to increase the number of doors is too much. his may sound ridicule in something as little as this, but it will be important on bigger projects.
Why is swap a number where it could have been a boolean.
"pick" is not a clear name for a variable.
win_noswap, win_swap, lose_swap, lose_noswap are irrelevant for the experience.
And your commentaries are stupid.
>>
>>6589141
And by the way, this is >>6589086 demonstrated perfectly.

You grasp it when it's a human being doing the picking, but an accident does the same thing and suddenly you've lost sight of the probability.
>>
>>6589160
>You don't initialyze all variables on one line
Might be hard to read for some people, but its faster to understand what the variables are intended for and it doesnt wastes lines for nothing
>using list when they are not needed
>dictionnary would have been more efficient
they function the same in this problem
>A simple variable
how?
>two variables to change to increase the number of doors is too much
Im not increasing the size, it is initialized as a 3element long list. Too much? Should i put it in a single line?
>it will be important on bigger projects
Havent have problems sofar.
>"pick" is not a clear name for a variable.
Yet you understood what it does.
>Why is swap a number
Was easier to randomize, but 0 and 1 translates to bool to be frank
>... are irrelevant for the experience
You meant experiment?
Nothing is irrelevant, its just less irrelevant, it just shows how the probabilities work out.
>And your commentaries are stupid.
I agree, but "on bigger projects" the work like a charm to understand whats going on.
>>
>>6589137
Are you just completely stupid then?

>It's just stats. I flip two coins, one of them is heads, that means there's a 1/3 chance the other is heads.
You've understood this puzzle very badly. It only works in a contrived situation where you somehow get the exact amount of information, "at least one of them is heads", and you would get that information every time it was true.

If you flip two coins, and look at one of them, and it's heads, that means there's a 1/2 chance the other is heads, just like if you flipped one coin, got heads, and then flipped it again. The one doesn't affect the other.

Even in the case where you flip two coins, and someone looks at both and says, "At least one is heads", you have to know why he's doing so, and what he would do in other cases. For instance, what is he going to say when two tails come up? Does say, "Neither one is heads."? Or does he say, "At least one is tails." If he can say, "At least one is tails." which does he pick when it comes up one heads and one tails? Does he reflip the coins if they both come up tails?

This all matters. If he only says "At least one is heads." when both are heads, then it's not a 1/3 chance the other is heads, but a 100% chance. You need to know the full scenario.

>I pick a door, 98 of other doors open, none of them have the prize, 99% certainty it's behind the door you didn't pick. Doesn't matter why those 98 doors open.
This is completely wrong.

If 98 doors are opened, chosen at random from among those you don't pick, it works out this way:
1% of the time, the correct door is the one you chose
1% of the time, the correct door is the unopened one you didn't choose
98% of the time, the correct door is opened randomly

The 2% of cases in which the opened doors don't reveal the prize are distributed equally between you having chosen the correct door, and you having not chosen the correct door, on your first guess.
>>
>>6589141
>As long as the door revealed has a goat behind it, it's 2/3 chance the other unpicked door has the car.
How can you think this?

It matters what his rules are for deciding whether to open a door, and which door to open: >>6588959

Given the original wording of the question, it isn't specified whether or not he only opens a door and offers to let you change when you've picked the car on your first guess.

Nor is it specified that he, despite knowing where the car is, specifically chooses to open a door with a goat behind it, rather than picking at random.

All we are told is that, in this specific case, he has happened to open a door which has a goat behind it. Without knowing the decision-making process which led to this action, this tells us nothing about whether we should switch.
>>
>>6589188
>Might be hard to read for some people, but its faster to understand what the variables are intended for and it doesnt wastes lines for nothing
YOU. NEVER. WASTE. LINES. Whatever you'll do. There will always be enough lines. And more lines = more space = easier to read.
>they function the same in this problem
No. They seem to but if you take 1000 doors, you'll have 999 doors that will mean literally nothing. But in a dictionnary you'll always have two keys : userChoice and treasureDoor.
>how?
treasureDoor = <nbOfTheTreasureDoor>. You will only have to compare it with the <nbOfUserChoice> to see if it is the same.
>Im not increasing the size, it is initialized as a 3element long list. Too much? Should i put it in a single line?
You have to think about modulability. To make the problem clearer lots af poeple have talked about increasing the number of doors to 100 or 1000. It should be more easy, just stock it in a nbDoors variable.
>Havent have problems sofar.
Then you'll have some later
>Yet you understood what it does
Think about everyone else being stupid
>0 and 1 translates to bool to be frank
Not in an interpreted language. You have to make some optimizations a compiler would make by yourself.
>You meant experiment?
Forgive my French.
>I agree, but "on bigger projects" the work like a charm to understand whats going on.
Wouldn't do it with my coworkers, but well if you didn't had any problems by now, you'll have some later.
>>
>>6589221
>more lines = more space = easier to read.
Oh god, you are a horrible programmer, and I'm glad I don't work with you.

more lines = more space = you have to scroll while reading a function instead of just moving your eyes.

You can overdo cramming shit together, but you can also overdo spreading things out.
>>
>>6589242
If you have to scroll while reading a function, your function is definitely too long.
Also
>you are a horrible programmer
>i haven't ever read a single mine of your code
and
>i can't code properly
>but i can judge other people's code
I hope next time you'll get some advices you won't try to shit on the face of the person who's trying to help you.
>>
>>6589221
I suddenly feel sad wasting my time on my previous reply
>>
>>6586411
Well sometimes you don't have a desk, so you catch the coin an place it on your hand. Earlier today I flipped a coin, caught it between my fingers, so it was on its side, and then placed it on my hand. It was on its side.
>>
>>6589251
>one-size-fits-all thinking about things where flexibility is more practical
>dogmatism toward trivial things like whether to put more than one variable on a line
Confirmed for horrible programmer, accomplishes nothing on own aside from following texbook examples, negative productivity when placed on team.

This is just not how useful programmers think.
>>
>>6588118
Go usa
love how I said "have any of you ever heard of monty hall problem" to my hs math class the other day and they all raised their hands
>>
>>6589251
>If you have to scroll while reading a function, your function is definitely too long.
not the person you replied to, but have you ever done any real programming? Or do you just make nifty little python scripts and call it "muh programming"
>>
>>6589324
Everybody fucking laughing about the people who "got it wrong".

Nobody paying attention to the fact that the way it was originally explained, there wasn't sufficient information to justify Marilyn's answer.

Original question:
>Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

>the host, who knows what’s behind the doors, opens another door, say #3, which has a goat

Original answer:
>Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?

>the host, who knows what’s behind the doors and will always avoid the one with the prize
>will always

It's the "will always" that makes her answer work. The "will always" isn't in the question. That's something she made up, not as the person posing the problem, but as the person proposing an answer.

It's an unjustified assumption. That's what all of those PhDs wrote in to correct her about. She snipped down their letters, removing their explanations, to make them look foolish.

In the original question, we don't know whether the host "will always" avoid the one with the prize. We don't know whether he'll always offer to let you change. All we know is that this one case, he chose to open a door, and it happened to reveal a goat. He may only choose to do the reveal and make the offer if you've chosen the right one.
>>
>>6589353
>The "will always" isn't in the question.
Yes it is. Here:

>the host, who knows what’s behind the doors, opens another door, say #3, which has a goat

If there wasn't a second comma, after "#3", you'd be right
>>
>>6589353
In the Monty Hall problem the host will always pick a goat. While this may not have technically been stated originally it was what was intended, and is what people mean when they say "Monty hall problem".
>>
>>6588744
This is probably the best post in this thread.
>>
>>6589357
>>the host, who knows what’s behind the doors, opens another door, say #3, which has a goat
>If there wasn't a second comma, after "#3", you'd be right
This doesn't matter at all. He knows what's behind the doors. He opens another door. The door has a goat.

Not "regardless of what you choose, he will always open a door which has a goat". Not "he will always" anything. It's just a statement of what he has done in this particular case. There's nothing to firmly establish that he's following a fixed procedure.

>>6589363
>In the Monty Hall problem the host will always pick a goat.
...and always offer the choice. Sure. As long as it's stated that way.

But if you fuck up the definition of the problem, you don't get to mock people for getting the "wrong" answer. And if someone only asks you a question that sounds *mostly* like the Monty Hall problem, but changes or leaves out key details, then giving the answer to the Monty Hall problem is just wrong, as Marilyn was.
>>
>>6589383
>There's nothing to firmly establish that he's following a fixed procedure.
To an autist such as you, this is correct.

The rest of us realise the example explains the general case.
>>
>>6589383
>There's nothing to firmly establish that he's following a fixed procedure.
Why are you picking on this part of not giving a fixed procedure.

Maybe next time there'll be four doors, and two goats? I don't see you being worried about this change?
>>
>>6589194
>Are you just completely stupid then?
>>6589200
>How can you think this?

lol. Think of the coin example again. AT LEAST ONE vs THIS ONE. 1/3 vs 1/2. Two very different pieces of info.

Say it's A B C behind the doors.

A random host reveals B, then it's 1/2 you've got A in your door.

A random host reveals not-A (but doesn't reveal if it's B or C), then it's 1/3 you've got A in your door.

Not-A is interchangeable, B is not. The host picks B, knowledge or no, it means it's favored A and C statistically, even if A was the only thing the host wouldn't pick or if it was a random choice. Hence equal odds. The host picking not-A means it's favored A but hasn't favored B or C, so A becomes weighted. Since you know the range of possibilities falls under "98 non-A doors you didn't pick are randomly opened" when you see no A behind the doors, you also know only your door can't be opened in any of those possibilities, so only the other door left unopened receives the favor towards A. Hence it becomes 99/100 if you do the math.

ANN
NAN
NNA
all x2 does not mean ANN vs NNA if the non-A picking host reveals the middle door to be N (otherwise it's 1/2 which you rejected). The door position doesn't matter, because N's are interchangeable (so 98% 1% 1% is bullshit, and the whole reason this is the go-to unintuitive problem in the first place).

Now I'm going back to a forum where people understand this shit.
>>
>>6589353
>In the original question, we don't know whether the host "will always" avoid the one with the prize.

Once again, DOESN'T FUCKING MATTER. Switching is still better.

The ambiguity in the original question is that it isn't clear whether the contestant knows it was a goat behind the door or not. And only autism would see a problem with that.
>>
>>6588758
>Two events are similar, so therefore it is correct to only count it once!
Try again.
>>
>>6589390
>hurf durf he's right I'm wrong I'm embarassed
>better call him an "autist"

>>6586381
>https://www.youtube.com/watch?v=4Lb-6rxZxx0
This annoys the fuck out of me, because she heavily implies that this is how Let's Make A Deal actually worked. It's not. I used to watch Let's Make A Deal when I was a kid. This is a made-up problem.

I'm not sure Monty Hall ever acted out "the Monty Hall problem". His name was just used to make a scenario:
http://www.jstor.org/discover/10.2307/2683689?uid=2&uid=4&sid=21104146785477

It's pretty annoying, because she actually comes out and says that people watched the show for years, and saw this problem acted out time after time, and thought there was no strategy (i.e. all of these slack-jawed yokels didn't notice that the people who switched won twice as often as the people who didn't). So isn't it special and clever that mathematicians found the answer?

Well no, this was never a real life problem, it was originally a riddle posed by a mathematician (a professor of biostatistics), and in quite a different form. The contestant asks to switch doors (boxes), without being being offered the choice. Monty's (Monte's) response is "That's weird!" It's not clear he's going to be allowed to change his choice.

In this version, you're not asked to assume that Monty's either ignorantly or deliberately making the game easier to win, in ways that will quickly be noticed and become a boring part of the show. He's just trying different things to make the game exciting, and a contestant catches him probably giving away useful information, and tries to take advantage.
>>
>>6588061
I'm pretty sure any mathematician worth his salt already knows the answer to the Monty Hall problem. Marilyn vos Savant probably paid these guys to pretend to be stupid so that she appears even smarter to dumbasses. She's already spent her whole life trying to appear as smart as possible to everyone.
>>
>>6589406
>>6589395
Jesus guys, it's even on the Wikipedia page:
https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors

>The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door, or always offer a choice to switch, or even never open the door revealing the car. However, vos Savant made it clear in her second follow-up column that the intended host's behavior could only be what led to the 2/3 probability she gave as her original answer.

>Possible host behaviors in unspecified problem
>"Monty from Hell":The host offers the option to switch only when the player's initial choice is the winning door. = Switching always yields a goat.
>"Angelic Monty": The host offers the option to switch only when the player has chosen incorrectly = Switching always wins the car.
>Ignorant Monty": The host does not know what lies behind the doors, and opens one at random that happens not to reveal the car = Switching wins the car half of the time.
>>
>>6589406
See >>6588744

Intentions matter here. If Monty's intentions are unknown, all you can say is that switching gives you some probability between 1/2 and 2/3.
>>
>>6589446
yeah, and the place is edited by autists.

if phrased as intended completely legallistically, people still claim 2/3rds is wrong. the criticism of the original description is basically damage control as people don't like to feel stupid.
>>
>>6589486
>if phrased as intended completely legallistically, people still claim 2/3rds is wrong
Sure, some people.

>the criticism of the original description is basically damage control
Now this is just bullshit, because the fully-specified scenario is utterly contrived and implausible.

As I pointed out before, if this was actually done, it would become obvious very quickly to people who watched the show that the switchers win twice as often. Realistically, they'd catch that in playtesting, and it would never get aired. It's not an interesting game when the correct strategy is so obvious after watching people play for a while.

If your intuition tells you that a situation should exist, where a game show host repeatedly offers people a choice where one option can be determined to be consistently twice as good as the other by watching it a few times, your intuition sucks.
>>
>>6589435
>i.e. all of these slack-jawed yokels didn't notice that the people who switched won twice as often as the people who didn't

Why would you think they would? Do you think anyone would keep a running tally of all the results? For anyone completely ignorant of the math behind it all it would take quite a few games worth of remembering the results before they clued in.

Fuck, you're acting like the average TV viewer is like that guy who memorized the pattern on Press Your Luck.
>>
>>6589439
vos Savant's article is what popularized the problem. While most mathematicians know about the problem now, they were unlikely to have heard it back then. It's easy to get it wrong unless you are paying attention close to the wording and it is worded correctly to begin with.
>>
>>6589596
When everyone's attention is on this one big decision in the game, and choosing one way wins twice as often as the other, people wouldn't have to keep a tally of the results. They'd just notice.
>>
Can somebody explain the correct /sci/ approved view of the problem to a normalfag?

If there are three doors
I pick door one, 1/3 chance of getting the right one

He reveals three to be a loser. I have two options. Door one (stick with current) or door two (change). 1/2 chance

Why does the original choice matter? How is choosing door one different than sticking with door one?
>>
>>6586470
But sticking with the same door is an active choice. You say it like you are choosing between choices in different system. You have two choices, one could win.
>>
>>6589648
>How is choosing door one different than sticking with door one?
Because if you were wrong originally, of which there is a 2/3 probability, then the host ensured that the remaining door is the right one.
>>
This whole riddle is a non-problem

The only thing you learn from the guy revealing a door is that you DIDN'T NOT choose the car.

I don't give a shit about what these pompous faggots think they have cleverly discovered.

End of story. This post is 100% true.
>>
>>6589658
This is just proof probability is a fake math.

Lets say you make the first decision on door 1. He reveals door 3 to be a goat.

Now, you must leave the stage. Your friend comes up and makes the final decision, not knowing what you decision was, only knowing theres a choice between door one and two. He chooses door 1.

Probability says that your friends choose was more educated. But you made the same decision based on the same data: none at all.
>>
>>6589667
But the friend is missing a key piece of information that you do possess when you're offered the option to switch: the fact that the host opened door 3 *when you chose door 1*. This critical piece of information changes the probabilities involved, which allows you to make a more informed decision than your friend could.
>>
>>6588834
>Yes, but between them they are twice as likely to happen as choice one.

It's just stuffing in an extra option that isn't actually a different option from the two that's there. This is highlighted by the fact that one can add as many extra meaningless doors as one likes and it still comes down to a car or a goat. In game design this would be like advertising a million different endings when 999,999 lead to the same cutscene. Or like having an FPS that touts a million different guns, when 999,999 are shit variations of the same gun or even literally function/look the same.

So yeah, you can artificially weight a scenario like this one with as many false choices as you like. You still only have two endings.
>>
>>6589763
>You still only have two endings.
Yes, but not two endings with the same likelihood.
>>
>>6586381
Thread hidden.
>>
>>6589648
>explain problem to a normalfag

>>6588235
>>
I was a grown ass man when someone first showed me the Monty Hall problem. I swore that they were retarded for thinking it was better to switch. I swore it was 50/50 either way. I wasn't convinced until I wrote a program to play the game a thousand times and saw the probability work out to 2/3. I learned a lesson about being closed minded when something seems non-intuitive.
>>
>>6589363
Well, if he doesn't reveal a goat, then he reveals the car, so I guess you could probably reason out which door to pick in that scenario.
>>
If the host opens a door, lets say door 3...

You are now left with either door 1 or door 2, you can switch and do all the fancy shit that you want but that will always be a 1 in 2 chance, one half.

Is there something I'm missing because this two thirds thing doesn't seem realistic.
>>
>>6590309
let the car be behind door 2.
scenario 1:
you pick door 1. the host opens a goat door, showing a goat. if you switch, you get the car.
scenario 2: you picked door 2. the host opens a goat door. if you switch, you get a goat.
scenario 3: you picked door 3. the host opens a goat door. if you switch, you get the car.

notice three outcomes, and two of the outcomes leading to a car.

if you pick a choice, and the chance of the choice being a certain outcome was 1/3, if you get to do the opposite of your choice the other outcome is 2/3. picking a car the first time round is the 1/3 chance.
>>
I just love how pretentious everyone one is, regardless of whether or not they are correct.
>>
>>6588678
>dat end
[Inception noise intensifies]
>>
>>6590366
Oh, the irony.
>>
>>6590326
But anon, what if the doors are made of glass or there's no wall. Switching from s correct choice has a probability of winning approaching zero.
>>
The answer is wrong because goats don't like Mormon fags knocking on their door every fucking day.
>>
>>6589645
They wouldn't. You'd need to observe and remember many games before the pattern became clear because sometimes people would switch and lose and sometimes people would stay and win. You might be able to pick up on the pattern more quickly if every single participant used one or the other strategy, but with a mix of strategies and results you'd need at least a few dozen before the pattern began to crystallize. And nobody's going to fucking remember dozens of results just by passively watching.
>>
These people just need to learn Bayes' theorem.
>>
Holy shit, I just realized.

The morons who don't understand the money hall problem probably also think that the probability of flipping two coins and getting both a heads and a tails is 1/3.

After all, three possible results "2 heads" "1 head 1 tails" and "2 tails".

Therefore, 1/3 probability for each.
>>
are you all done jerking each other off for being so smart because you had someone explain the monty hall problem to you before someone else did?

i guarantee you not a single one of you would have been able to solve the problem independently
>>
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>>
to prevent any discussion in this topic from emerging:
car at A
choose: C
switch = win
stay = lose
choose B
switch = win
stay = lose
choose A
switch = lose
stay = win
so fucking easy
>>
Fucking embarrassing. Mark my words, the transhumans in 200 years will point at the inability of most humans to not understand the simple logic behind the Monty Hall problem why we as a species were doomed to be replaced.
>>
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>>6592069
>>
It boils down to thinking it like this.
Ignore the whole door opening shit. You have two choices.
You pick door A. And you keep with that door.
Or you can pick both doors B and C and if you get the wrong choice once, you can ignore it and pick a second time.
Because that is what is happening. If you pick two doors to choose from, you get one free get out of the jail card. That skews the probabilities in its favor.
>>
The most concise statement of explanation is that the only time you lose while switching is if you originally picked the correct option. Which happens 1/3 times.
>>
>>6586381
Is she trolling or stupid?
>>
Fuck, they're right, but they explain it like morons.

Initial statement - if you choose a goat and you swop to the unopened door, you will get the car.

THEREFORE, the P of getting the car is 2/3.

The fucking morons explained it as if the opening of the door would change the probability, which it does not.
>>
>>6586381
>Wow, it can be frustrating reading these comments... Am glad this helped some people and sorry others remain perplexed.
oh lord
>>
>>6592571
Yeah nothing 'absorbs' any probability fuck.
>>
>>6592601
What's your problem?
>>
>>6588978
Don't forget the edge of the coin bouncing when it hits the ground. Gotta account for the forces in that collision.
>>
>>6589819
you know its b8 right m8?
>>
>>6588235
I see the reasoning. But why does the probability stack? Shouldnt it merely revert to 50/50 since the 2/3 probability went out the window when one egg was cracked? And having a 2/3 probability on a set with only 2 options seems counter intuitive
>>
>>6591986
Why does the probability stack?
Once the 3rd door is removed its no longer a x/3 chance. It becomes a half since theres only 2 options regardless of the initial open door
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