/sci/ - Science & Math

>>12141249
There are three doors. The car is behind only one of them. So Goat Car Goat = GCG
Now lets list the three configurations
GGC
GCG
CGG

Play out the gameshow in your head for each scenario

If I always pick door 1, and never switch, I win 1/3 of the time
If I pick door 1, then switch every time, I win 2/3 times

The examples for starting with door 2 and door 3 are an exercise left to the reader

>>12141249
imagine performing three trials of the monty hall problem. Before you pick, you have a 2/3 chance of picking a door with a goat. As it is more probable that you picked a goat door, when monty eliminates a goat, it is more probable to get a car if you switch every time in a number of trials that is equal to the number of ordered combinations of doors. In your two door scenario monty is not giving you information. The combinations of doors is also different. Consider my shit diagram. Each row is a trial, imagine you choose the left most door to begin with each time. The red door is what monty chooses. The blue door is the result of you switching. Compare this outcome with the second example and you can clearly see that in a given number of trials corresponding to the combinations of doors, they do not have equal probabilities of being the correct choice in n trials

The real Monty Hall problem is why the statistics on the show didn't match the theoretical statistics.

Call it Monty's massacre:
Person A selects a door, then Monty reveals the goat.
It is A's time to choose whether to switch.
Suddenly everyone dies. A year passes and the opened door and the bodies are removed.
Only two shut doors remain.
Now person B comes to the scene and randomly selects a door. This happens several times - several massacres and several B's.
The paradox dictates that the doors don't have a 50/50 chance of hiding the car, instead it's 1/3 vs 2/3.

>>12141381
fuck off and kill yourself you schizophrenic freak

>>12141387
This reminds me of the omniscient monty paradox

Monty puts a car behind a door. Monty knows which door the car is behind 100% of the time. Paradoxically, contestants are only correct, at most, 66.6...% of the time

Where did the remaining 33.3...% go?!

There is a 2 in 3 chance that you have forced Monty to open the only other door with a goat. Therefore there is a 2 in 3 chance that you should switch to the other door which had to be the car. If you suddenly forget which door you've selected then you lose this extra information and the probability reverts to 50 50.

>>12141249
That is to say, by making a choice you are affecting the system and therefore generating information contingent upon that choice. Forget the choice and you also lose the information.

>>12141407
But Monty does know where the car is 100% of the time. That's how the paradox works.

On first selection, the contestant has a 1/3 chance of selecting the car, and a 1/3 chance to select either goat. (2/3 total goat chance) Monty will never reveal the car by accident because that would totally cuck the contestant as he gets a goat whether he switches or not. (bad television)

If the contestant picked the door with the car initially, switching causes him to lose, whether .

If the contestant picked Goat #1, Monty has to reveal Goat #2. Switching gets the contestant a car.

Like wise, if the contestant picked Goat #1, Monty has to reveal Goat #2. Switching gets the contestant a car.

1/3 of the time switching gets you a goat, and 2/3 of the time switching gets you a car.

>>12141249
The odds get compressed into the one door you're allowed to switch to. Imagine there's 100 doors. You choose 1. 1/100 chance, right? Now the host opens 98 other doors, leaving only the door you chose and one other door. Do you think switching in this scenario would give you better odds? It's either a car behind your door, or a car behind one of those other 99 doors, and the host eliminated 98 of them for you.

>>12141249
>What's the difference between choosing if one should switch doors and starting with only two doors
because in the first case you start with 3 doors, not 2

>>12143131
To add to this, if you stick with the door you chose, it's a 1 in 100 chance. If you choose to switch, you're essentially picking all of the other 99 doors. If you could pick 99 doors or 1 door, the 99 doors would obviously be the better choice.

>>12143067
Yes
But if monty had to pick the car door, he;d be 100% right
But contestant is on;y 67% right at best
this is a paradox

>>12141249
Literally just work through the cases.
>pick goat (2/3 chance)
>>monty reveals other goat
>>switching gets you a car
>pick car (1/3 chance)
>>monty reveals either of the goats
>switching gets you a goat
Therefore if you switch you have a 2/3 chance of getting the car. Simple as.

>>12141249
It's not the same, since Monty won't reveal your door. If you chose a goat initially then Monty must leave the car as your other option. Since there is a high chance you initially chose the goat, this gives you an advantage over just choosing between a goat and a car.

It should go from 1/3 chance to 1/2 chance. When the one door is revealed before the option to switch, it's no longer relevant.

>>12144772
hurr durr

>>12144428
I don't understand what your paradox is.

just imagine it with a 1000 doors, you pick one, and 998 of them are removed for you, and then you get to choose whether to switch to the penultimate remaining door or not.

when the wrong doors are removed for you, you gain information about the doors that AREN'T removed because they CAN be removed, but AREN'T removed. The door you pick from the start CAN'T be removed even if it's the wrong door.

basically you want to switch to the door that has the added chance of the car, via monty choosing not to open it

>>12141249
>What's the difference between choosing if one should switch doors and starting with only two doors?
Since the host avoids choosing the door with the car and you avoid choosing the door he chose, your second choice is affected by the position of the car, while your first choice is not.

>>12141381
Post data and analyses

>>12141249
The car in question is a Pontiac goat. So no matter what you win a goat.

>>12146188
Kek

cute gote

>>12144435
and if you start with 2 doors?

>>12141249
Because in no case will Monty open the door to the car.

>>12147531
You're asking if you start with two doors, a car behind one goat behind the other, you pick one at random, and you're asked if you want to switch? It's 50/50.

Again work through the cases.
>pick door with car (1/2 chance)
>>switch, get goat
>pick door with goat (1/2 chance)
>>switch, get car
So it's the same whether you switch or not.

I know your original question was
>Why does having a prior choice effect the outcome?
The answer is literally just that the situations are different. Analyze the choices, as above, and you see that they are different.

I understand the math and everything but you all have to admit if you switched and got a goat you'd feel like an even bigger tit than if you stayed and got a goat because it'd feel like you lost through your own action rather than through inaction.

>>12147920
>they are different.
are they really >>12141387

>>12147999
Persons A and B don't face the same scenarios. Person A has a 2/3 chance of holding onto a goat door. Person B picks fresh, 1/2 chance.

>>12147965
psychfag leave

>>12148013
>fresh
how _exactly_ does that change anything?

>>12148013
>fresh
how _exactly_ does that change anything?
it's the same two doors.

>>12148071
Different anon.
Imagine there are three doors. One of them is open with a goat.
You know of the two closed doors, one has a car, and one has a goat.
You are asked to pick one of the two closed doors, you therefore have a 50/50 chance to pick the car.

Imagine then that everyone in the studio is killed, and the open door is shut.
A new person comes in, and sees three closed doors, and is asked to pick which door has a car. They are not given the option to switch.
Only one of the three doors has a car behind it, so from their perspective they have a 1/3 chance of choosing the car door.

But the first person knew a better probability distribution. They knew one of the doors had a goat behind it, so the probability for:
Open Closed Closed
having a car behind them was:
0 0.5 0.5
A total of 1
The third person doesn't know about the previously open door, to them they see:
Closed Closed Closed
Which has a probability distribution of
0.33... 0.33... 0.33...

Why does the probability distribution differ depending on the observer? I think you can understand why without me having to explain.

That's what i was trying to meme here >>12141407
Monty looks at the doors, and knows the car probability distribution is actually
0, 1, 0
But the first contestant sees
0, 0.5, 0.5
The second contestant sees
0.3.. 0.3.. 0.3..

It's not difficult to understand

>>12148116
tl;dr
explain the >>12141387
instead

>>12148151
no
i'm not going to spoonfeed a brainlet

>>12148159
>i can't
thought so

>>12148170
It's easy.
That anon (>>12141387) is making a joke
Anyone who isn't retarded could see this
Sorry kiddo

>>12148211
how is it a joke?

>>12148252
>Anyone who isn't retarded could see this
You wouldn't understand lmao

>>12148267
>can't explain
k

Holy shit i finally figured out how its 1/3 verse 2/3. Thanks bros

>>12148274
shit bait
kys

>>12148280

>>12148284
>>12148274

>>12148071
Person A picked thier door when they had a 1/3 chance of winning, person B picked when they had 50/50.
The solution to the Monty hall problem becomes pretty obvious if instead of three doors you imagine it as a hundred or something. When YOU make the choice your odds are ninety nine to one, if all the other doors are opened but one switching is essentially being given 98 chances to open doors and fail for free.
It would help if you pointed out which part of this you don't understand.

>>12148304
>imagine it as a hundred
who cares, irrelevant.
Explain how do the same two doors change from 0.333/0.666 to 0.5/0.5 in >>12141387

>>12148450
A is given information about which door is likely to have the car that B doesn't have. Since A is twice as likely to have chosen a goat, Monty is twice as likely to reveal the only goat not chosen, leaving the car as the other option. But since B didn't see which door A chose, he doesn't have that advantage.

>>12148469
>human-centrism
same two doors, sounds like gaia hippie /x/ consciousness mysticism

>>12148475
So someone who sees the result of a coin flip and someone who doesn't has the same information about the results? No, it's not human-centric, it's information-centric. You could do the same problem with computers that calculate every possible state and the answer would be the same.

>>12141249
The problem with nerds is that they always think about the same questions without getting ANY new information about the subject.

Who cares about different methods on how to answer this question. Try it 100 times with a dice or something and see the results and in future just accept that u have to change the door.

Lol fucking useless nerds

>>12141249
Think of it this way. Say there were a million doors and there is a car behind only one of them. The rest conceal goats.

You make your pick. Monty opens one of the other doors, revealing a goat, as you knew ahead of time that he would. Now you have the option of switching to any other of the 999,999 remaining closed doors.

Do you want to guess again? Sure, why not, since you almost certainly guessed wrong the first time!

>>12148760
this isn't very helpful since you will almost certainly guess wrong the 2nd time as well

>>12141249
My fuckbuddy goat died, so I would be happy anyways

>>12141249
I never understood this paradox honestly why would Monty offer you to switch a door if you picked the wrong door? I think the correct answer is staying with the door you picked because Monty wants you to switch a door and pick the door with the goat.

I just don't get it why people come up with shitty riddles like this that don't clarify everything, the solution would've been alot clearer if in the paradox it would say if Monty Python wants you to lose or not.

>>12148806
the stupid, it hurts

>>12148913
Mind explaining your stance chief?

>>12148806
That's exactly what Monty would WANT you to think. So, you should pick the opposite and switch.

>>12141249
Just use 100 doors instead of 3, makes it much more obvious
>99 doors have goats, 1 has a car
>you choose 1 out of 100 doors
>Monty opens 98 other doors which he knows are goats and goats only
>there are two doors left: Your original door you picked, and the one door monty did not open
Do you switch?
Reduce it down from 100 to 10 doors, to 6 doors, all the way to 3 doors- still the same mechanism

>>12141387
If B is asked to just pick a door, its 1/2, because they have no knowledge of which door was A's original pick and both are equally likely to have been.

Door 1 = A's pick, B picks door 1 = 1/3
Door 1 = A's pick, B picks door 2 = 2/3
Door 2 = A's pick, B picks door 1 = 2/3
Door 2 = A's pick, B picks door 2 = 1/3

If B is asked if they want to stick with A's choice or switch, its 1/3 or 2/3.

>>12141249
If you don't switch, you pick a goat 2/3 of the time and the car 1/3 of the time, and you get a goat 2/3 of the time and the car 1/3 of the time. If you switch, you either pick a goat (2/3) and switch to the car or pick the car (1/3) and switch to a goat, since out of the choices you have, one's a goat and one's a car. Simple as.

>>12141249
it's 50/50, either it's a goat or it's not

>>12141249
Good work anon. I think we've been more than a week without a Monty Hall thread. I was starting to twitch.

>>12148304
wouldn't it still be 50/50?

>>12148956
Alright then so he wants us to win so that means we are in favor and we should change with a chance of 2/3 of guessing right if that's the case after he reveals the door with a goat.

>>12141249
because you are more likely to choose a goat at first

why the fuck do you still talk about this

>>12149176
to add to this

Just imagine there was 1000 goat doors, and 1 car door. Host opens all goat doors leaving just 2 doors. Do you switch? Of fucking course you switch

>>12148450
>Irrelevant
It's completely relevant, it accurately describes how the first person has a lesser chance of picking the right door whether it's 3 doors or a hundred.
When the first person picked a door they picked from three doors so thier chance of being right is 1/3, opening a non winning door doesn't change the fact that when they picked they had that exact chance of winning, so switching is essentially picking the open door and the closed door at once.
When person 2 comes in they're just picking between two doors with no prior choice, it's not like the probability "sticks" to the doors in some magical way the probability depends on what the chooser had available.

>>12148806
It's based on a real show that would do this.
You'd pick from three doors then one of the wrong doors would be opened and you'd have the chance to switch.

>>12141249
Hall adds information when he selects a door that isn't a goat

>>12149130
But you know from before that what you've picked is probably a goat, so that gives the other door a higher probability of being the right one.

>>12149130
Let's take an extension to describe why you're a fucking moron, shall we?
There's a hundred thousand doors. 99 999 goats, 1 car.
You pick a door.
The gameshow host opens 99 998 goat doors.
This leaves one door somewhere in there closed, and the one you picked blindly.
Of these 99 998, they're nothing but goats, as per the problem's statement. The gameshow host will only reveal goats, not the car.

Consider that there's 100 000 doors and 1 car. There is a 99.999% chance you picked a goat initially.
Conversely this implies a 0.001% chance you picked the car initially.
That leaves two options:
- a blind guess out of a hundred thousand
- of the other 99 999 doors, the one that wasn't opened
Thus, we can state that the door left closed has a 99.999% chance of being the car.
We therefore can conclude anon is a brainlet.

>>12150648
Don't try to help him, it's futile. Just sell him lotto tickets and take his money, it's the natural way of life.

>>12149008
This. Something about knowing certain bits of information changes the probability just from the knowledge of that information.

>>12150648
sounds like 50/50 to me

>>12150648
gambler's fallacy

>>12151339
No, cretin. The gambler's fallacy is expecting that the probability of an independent trial will be affected by the outcomes of previous independent trials. This is not at all related

>>12151759
sounds like you have a problem with gambling, the first step is acceptance

>>12151766
My gambling addiction is of no more relevance to the Monty Hall problem than my alcoholism.

If your talking about probability and statistics then your looking at a overall question of "what is the chance of getting cool new red car twice"but if you are the person actually going through the doors you have the same chance of getting it as last time. Probability of getting it twice is (1/3)(1/3) so 1/9

>>12151993
wouldn't it be 1/3 and 1/2?

>>12141249
It's just a two stage problem. First stage, the probability of finding the prize by selecting a door is 1/3. So you're stuck with that. Now sthe latent states are unknown and independent from your choices and you are given the possibility, at the second stage, of choosing a door again. If you do not play, your probability of winning stays 1/3 because you played on the first stage, and anything that happens between your choice and the showdown is irrelevant. If you play, you have 1/2 probability of winning. You obviously make a choice at the second stage.

>>12152041
I have to specify that this one is the 'Monty Fall' variation of the problem. The original problem solution depends on the peculiar behavior of the show's host.

>>12151993
I think you're playing a different game, anon.

>>12141249
OP chooses door 1. Then host opens door 2. The host never opens the door chosen by OP and never opens the door with the car. This means that

P(Host=2|Car=3,OP=1)=1 <- this means that if the car is in 3, host will certainly open 2 because OP chose 1.
P(Host=2|Car=1,OP=1)=0.5 <- this means that if the car is in 1, host may open door 2 or door 3 with equal probability, as he will never open door 1.

Now

P(Car=1|Host=2,OP=1) = P(Host=2|Car=1,OP=1)P(Car=1|OP=1)/P(Host=2|OP=1)

P(Car=1|Host=2,OP=1) = 0.5*(1/3)/(0.5) = 1/3

P(Car=3|Host=2,OP=1) = P(Host=2|Car=3,OP=1)P(Car=3|OP=1)/P(Host=2|OP=1)

P(Car=3|Host=2,OP=1) = 1*(1/3)/(0.5) = 2/3

Therefore OP chooses 3 once the host opens door 2.