/sci/ - Science & Math

IT'S BETTER TO SWITCH TO DOOR 4
THERE'S A REASON THE HOST DIDN'T PICK IT.

>>2236918
But im sure when i first learned of this problem a while ago, it's supposedly better to stick to the one you chose in the first place.

It's a 50/50 shot.

>>2236923
NOPE
ENJOY YOUR GOAT FAGGOT

50 percent because door one has a probability of 25% being the car.

>>2236923
why don't you check wikipedia yourself to see how wrong you are?

this is what you get for learning from hobos in the street begging for a mcdonald. Enjoy your goat.

>>2236924
>>2236924
>>2236924
correct. if you don't understand this you are fuckretarded.

the host must feel sorry for me picking a goat so he is giving me a second chance

>>2236932
>mfw "learning from hobos"

ITT: High-school kids who don't know the Monty Hall problem.

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

Chances are NOT 50/50.

If you stay with door 1, your chance of getting the car is 25%.
If you switch to door 4, your chance of getting the car is 75%.

>>2236934
LOL YOU GET THE GOAT TOO
THE PROBABLITIES OF THE OTHER 3 DOORS CONTAINING THE CAR IS 75%.
SO THEN 2 OF THOSE YOU DIDN'T PICK ARE REVEALED, AND THERE'S NOW A 75% CHANCE THAT DOOR 4 CONTAINS THE CAR
YOU FUCKING FAIL LOL

WHAT IF I LIVE IN THE DESERT AND I WANT A GOAT???
THEN WHAT???
HUH?

>>2236956

>>2236956
>>2236947
>>2236918
Painful samefag is painful

75%

now please let this thread die before 200 posts

>>2236960
INCORRECT
I AM
>>2236918
AND
>>2236947

>>2236956
IS JUST A FAG

Anyone who thinks it's 50/50 is fucking stupid and never took a probability course.

>>2236979
OP here, not asking if it's 50/50, wondering which door has a 75% chance

>>2236982
Door 1 dumbass.

ITT idiots

It all depends on whether the host knows which car the door is actually behind. If they don't know which door it is behind the chance is 50/50 but if they DO know, it's better to switch.

Why the fuck wouldn't it be 50/50?
Saging because trolls and tards, trolls and tards.

Whatever door you pick, you have a 75% to be correct.

When no door is shown it's contents, you have 25% to be correct, then they show you 2 doors, and so you have technically picked 3 Doors, which would be 75%, two are obviously wrong, the other might be right, but you have 75% chance that, the door that you have picked, has the car inside.

>>2237009
>It all depends on whether the host knows which car the door is actually behind. If they don't know which door it is behind the chance is 50/50 but if they DO know, it's better to switch.

This, faggots.
http://www.math.ucsd.edu/~crypto/Monty/monty.html
http://www.math.ucsd.edu/~crypto/Monty/montydoesnotknow.html

2 different versions of the same situation, in the first the game host knows which door it is behind and in the 2nd he doesn't know.

>>2237012
>2 doors left
>75% each
>150%
the fuck am I reading...

>>2237020
You didn't read well.

" magnet wire" how does it work? !!

After doors 2 and 3 are opened but before door 1 is opened there is a 50% chance of the car being behind door 4. At no point is there ever a 75% chance of the car being behind any particular door.

if you can't change your option, still 25%. if you can change your option, 50%.

>>2237057
No, if you switch it's nearer to 70% chance of being right.

It's funny because quite often you get people here screaming "2 OPTIONS DOESN'T ALWAYS EQUAL 50% PROBABILITY" but this thread has pointed out to me that a lot of people still don't understand how probability works.

>>2237012
I can't stop laughing.

Man, I hate these threads.

>>2237083
63% of the time i would agree with you 100%

>>2237057
What I'm saying is that you actually made 3 choices, having no control of the other two choices, let's say you choose door 4, and then they show you door 1 and 2, would you change to door 3 or stand by 4?
>Implying that the host knows where the car is.
I would stand, because I have 75% of being right, but if I change my mind to door 3, I only have 50% chances by making an arbitrary change of options leading myself by randomness.

>>2237083
I guess he gets what I'm trying to say.

>>2237097
No, by staying with your door you have a roughly 33% chance of winning.

Probability, how does it work?
http://www.math.ucsd.edu/~crypto/Monty/montybg.html

For idiots saying that it is 50%

Imagine you have 1,000,000 doors 999,999 have goats inside and the other one has a car.

You pick one door, other 999,998 doors open and reveal a goat behind them, would you switch?
So you still think that there is a 50% probability

>>2237113
hmm... fuck, I was refering to a 4 options problem, where you are shown 2 doors after you pick one, but still, I was wrong ;_;

It's 50%
You already know that it's not the two opened doors, so that leaves two doors a mystery. Well, only one has the car, so that means that there's an equal probability that 4 has the goat or the car....the answer is 50% because there are only two doors.

>>2237149
You're retarded, there are still only two choices, meaning only a 50% chance.
If there are three doors, and none are open, it;s a 1/3 chance that one has the car...if one is opened to reveal a goat, that leaves two doors and thereby a 1/2 chance at which has the car.

>>2237149
By opening 999.998 doors, you have eliminated 999,998 doors from the problem. Now there are only two doors in question.

>>2237198
>>2237171
>>2237185

If you switch, yes, you have a 50% chance, but if you stand, you will get much less, let's say about the 1'000'000 doors, if you don't change, it would have been the same as if no door had been open, so it would be a 1/1'000'000 probability to be right, although, if you switch, you make this completely random, thus making a 50-50 guess.

>>2237171
>>2237185
>>2237198
Oh man, this thread keeps getting better.

>>2237198
Yes, in a situation where you have two doors the chance is fifty percent.

However, the question of the original Monty Hall problem is phrased in a way that you can't simply disregard the other doors.

The probability (and switching being a better choice) is easily explained if you imagine a large number of people. Say, a 100 switching doors, and a 100 not switching. There will be more winners in the first group.

Try it, it's true.

But I know you be trolling.

Retards. One door has a 100% chance of holding the car, and the other has 0%.

>>2237212
The act of switching does not magically reset the probability distribution. You can only choose two doors at that point. Therefore one has to have the car, one has to have a goat. The probability was changed once you observed the other 999,998 doors being opened.

if you have 100 doors, pick one, 98 are opened, what is the chance of it being in the other door?

before, 1/100, so other door must be 99/100.

so it's 75% for this one.

>>2237223
If you stand by your door, you must remember that it is a door that you randomly picked from the rest, therefore having a 1/?? chances of being right, when there are only 2 doors left, and you stand, you have made no change, you still have a randomly chosen door whith a chance of 1/??? of being right, although if you switch, you become, once again, a random choice between only 2 doors, thus making it 50%.

>>2237239
That's what I'm saying.

>>2237244

so in general the probability of the car being behind the unpicked door is 1-p(first door)

>>2237239
>>2237240
>>2237244

Wait... this is somewhat different, but you improve your chance by switching.

This is an interesting problem, but I see no real world application for the train of thought being used to decipher it.

If host knows, 75%. If he does not, 25%.

Just read monty hall problem on wikipedia, there's a chart that shows you're factually wrong. Understanding how the math works is a little harder for me though.

I'm playing a monty-hall problem applet at the moment. I have switched doors 14 times, and of those games, I have one only five times. Going to play more for a better distribution, but the better chance by switching thing isn't looking good.

I'm reading the Wikipedia article on this right now, and I honestly don't understand how this works.

I'm sorry, but I don't get it.

wow this is retarded

2 doors
one has a car

if the car is placed behind a random door, then each door has a 50% chance of having the car behind it.

regardless of which door you pick, there will be a 50% change of finding the car :D

So far after 40 games, I have switched every time and only won 50% of the time. Still going.

>>2237271

>If host knows, 75%. If he does not, 25%.

You are 100% incorrect. Only doors with goats are opened.

>>2237279

If you play poker you know that having the best probability of winning does not mean you win. 14 times is too small of a statistical sample anyway, you can just get bad luck.

>>2237299
I'm up to 60 so far with no change in distribution. I'm still going.

>>2237284
Draw a picture. Three doors, one contender. Now copy it twelve times so you have one pic of twelve trios of doors. Got it?

Now 'assign' four contestants to door nr. 1, four to nr. 2 and four to nr. 3. The car, let's assume, is always in door 3.

Now imagine the 'opening'. Group 3 wins outright. Groups 1 and 2 don't, and the other door (2 or 1 respectively) is opened.

If they all switch, all 12 players win a car. If noone switches, only 4 people (group 3) have won a car.

>>2237289
Baphomet has eaten well, the fields will sway golden for harvest and the women will carry healthy babes.

>>2237300

Shit, don't ever play poker.
Either that or the random generator of the applet sucks.

>>2237308
Up to 122 games so far; I've won 60 switching every time. So slightly less than 50% so far.

>>2237301
Okay, yeah. I'm seeing that working. But I don't understand HOW it works.

I feel like someone has just told me human flight is possible, then done a Superman and flown away. I've seen it, but what the fuck how does that even work.

Rather than continue doing this by hand, I'm going to write a small program to do it and have it go through a few million iterations.

>>2237321
The host knows which door has the car behind it. He opens two doors he knows has goats and leaves the third closed, leaving just your door and that one.

Remember, he can't open your door. So either you are already on the car, or the final door is the one he left closed because he knew the car was behind it.

This is why it doesn't work if he doesn't know what's behind the doors.

>>2237300
Well, you see, the funny thing about mathematical truth is that it has probability 1 and anything contradicting it has probability 0. It doesn't matter how many times you "experiment" because you'd be only establishing greater and greater anomalies. You won't be advancing at all toward proving your erroneous proposition, because the prior probability of that proposition being true is 0.

Well, I guess this settles it.

And yes, I know, the code is shit. I haven't programmed in a long time and have forgotten some of the functions, and couldn't be arsed to look anything up.

>>2237434
This code is subtly broken. If the initial choice happens to be the valid choice, one of the remaining doors should be opened at random, but your simulation opens one deterministically.

It won't influence the outcome in this case, but strictly speaking, it's reason to disregard your results.

>>2237463
Yeah, I wrote it knowing it wouldn't affect the results. An easy fix would be to just have it choose one of the other two by generating another random number between the remaining doors.

>>2237475
While justified here, you should be very careful with that. The whole reason you're doing the simulation is that you aren't positive you understood the problem correctly, which usually means you also aren't qualified to judge whether such a simplification is valid.

>>2237434
A computer simulation "settles" it for you but a simple understanding of conditional probability does not?

Sure is engineering in here

>>2237500
Yeah, I'm aware. If this was being written for anything but a post of 4chan I would have done it differently. I know what the problem is and how to fix it, I just didn't bother since I knew I'd get the same results and this is just for a /sci/ post.

anyone have that nice picture that illustrated all the possibilities?

>>2237505
Hm? I understood it from a mathematical perspective, I just wanted to try it myself and see how things turned out. The sample from when I was doing it by hand was too small to have any reliable conclusion... so I scaled it up to 10,000,000 by simulating it on a computer rather than waste hours.

>>2236923

No, it a some guy's paradox.
In this case, when you chose door 1, there was 25% chance of being right.
However, when you open the doors, the chances of the car being on door 4 increase to 50%
The thing is:
When you chose door 1, you had the probability of 25% of being right, but if you choose door 4 now, the chances are higher because it has now a chance of 50% of being the right door

i still say it's 50/50

fuck you atheists

>>2237526

>>2237526

Atheism has nothing to do with it

host doesn't know which door the car is behind, yet magically picks goat doors to open

>>2237533
The premise is that the host knows what's behind every door.

Door 1 is 50%, Door 4 is 25%

>>2237532
>>2237529
of course atheism has everything to do with it

a omniscient infallible god implies determinism

1 2 3 4 S
g g g c c
g g c g c
g c g g c
c g g g g

MY table says 75%

>>2237535
i know, but not according to some in this thread

Exactly what would be expected with 3 doors: a 66% to 33% ratio.

Anyone who thinks it is 50% is an idiot. Read the wikipedia page on the Monty Hall problem.

People who say 50/50 are assuming the host doesn't know either, and in this situation, they are correct.

From the wiki that every asshole in this thread is telling the 50/50ers to go to:

. In this version, the host forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch.

the wording is not clear on wether 2 and 3 were eliminated because of them having goats, or without that knowledge.

Anyone giving a clear answer is assuming things when there is no basis to do so..

On another note, you could interpret the text as 2 and 3 having goats in all instances, which makes door 1 and door 4 each 50% all the time.

make program doing this millions of times

percentage
staying: 49.9807%
changing: 49.9808%

nope.avi

>>2238240 program

you must have an error in your program.

Can you assume that two doors with goats were always going to be opened? That is, if door 2 had the car behind it, doors 1 and 3 would have been opened instead? If so, then it's 3/4. If not, 1/2.

>>2238274
always 2 goat doors opened. never the car door.

Isn't being right with the original choice in this case 12.5%? And then door 4 would be 50%?

>>2238240
You wrote a really shitty program that doesn't do its job then. Try doing a trial with a few cards, having a friend know what they all are, you have to guess which one is one suit while the other three are all a different suit. Go through the entire process.

>>2238415
Is 2 possible outcomes. is in door 1. 25% is in door 2,3,4 75%

we get told is not in door 2 and 3. so is in door 1 25% is in door 4 75%

>>2238425
I understand very little of what you're trying to say, but I'm pretty sure you're either a troll or you don't understand a goddamn thing about probability.

>>2238431
Well, he actually is right.

There's actually a 50/50 chance when only 2 doors remain. The opened doors are not relevant to the problem.

Here's another scenario to explain: Say you have 3 doors, one of them is open showing a goat. One closed door has a goat, the other has a car. You can pick either closed door.

The opened door is clearly irrelevant to your choice. The only difference in the two scenarios is that mine started after the door was already opened.

1/3 or 33%

yes, it's the same probability as the original problem.

>>2238481 only difference/already open
that is a huge difference, and completely changes things.

Hey guys, if you flip a coin there will be fifty percent chance of getting heads. My clearly different problem should be applied to yours.

>>2238481
>The opened doors are not relevant to the problem.
Yes they are. Read the fucking thread before you post stupid shit that just makes you look like a dumbass. The host knows that the 2 doors he opened doesn't have a goat.

>>2238525
Fuck, I meant doesn't have a car

Relevant diagrams for the original problem here. http://awoscience.blogspot.com/2010/11/glen-explains-some-mathematical.html

>>2238512
Actually it doesn't change anything, unless you do multiple trials.

There are 3 possible locations for the car. If you only do this "wager" once, you are effectively left with only 2 doors to choose between for the location of the car, since the 3rd is eliminated. However, if you do this wager multiple times, the car's location is expanded to 3 locations, and then switching becomes favorable.

G G G C: choose door 1; host selects two doors with goats; switching doors wins car

G G C G: choose door 1; host selects two doors with goats; switching doors wins car

G C G G: choose door 1; host selects two doors with goats; switching doors wins car

C G G G: choose door 1; host selects two doors with goats, switching doors loses car

This thread is full of people who learned about this problem a while ago, without fully understanding it, and now call everyone who doesn't get it an idiot.

It's not complicated..

Whenever you hear this problem though no one EVER points out the KEY information. I suspect it's because they want to turn a very simple problem into a trick question, that is all this is.

Once you realize that the two doors are NOT completely random, and that the host will NEVER open the door with the car behind it, then it becomes obvious that there is a higher chance of switching...

HOWEVER, in the OP's original problem he never mentioned there even was a host, all he said is that two doors where opened, we don't know that the two doors were chosen such that the car was not revealed.
Therefore in THIS CASE the correct answer is 50/50.

The probability only changes when you add a person who makes a conscious decision about what two doors to reveal so that they purposely don't open the door with the car.

If anyone disagrees then you need to reread the monty hall problem and make sure you truly understand why that happens, and compare that situation to the situation the OP gave.

monty hall problem is retarded because of the hidden premise which is the whole trick anyways. well fucking duhhhhh if the host knows which doors to open then you switch.

etc etc.

C G X
He can't open your door or the car's door, so the remaining door is the one he opens. After he opens it, you have a 50/50 chance of getting the car.

G C X
Again, you are left with a 50/50 chance.

G X C
Again, you are left with a 50/50 chance.

Now, look at all 3 together, and your chance (when not switching) falls to 1/3.

Clearly, when over a single trial, your chance is 50/50. When over multiple trials, your chance is 1/3.