/sci/ - Science & Math

>>9929494
Just draw the probability tree out you retard

>>9929494
Its because there's two stages of probabilistic phenomena. It doesn't reduce to one stage.

>>9929494
It's fascinating that when Marilyn Vos Savant (person with highest OQ ever) answered this problem in her magazine column (correctly), she got over 10,000 letters and e-mails, even from people with PhD's, that insulted her and attacked her for being wrong, while it was them who were brainlets and completely wrong. It's an interesting and very polarizing problem.

>>9929494
It's 50%. Monty Hall is 1/3.

>>9929551

its not that hard with a truth table

Imagine if there were 10000 doors
Chances of you picking the car randomly would be 1/10000
However, the host opens 9998 doors which reveals goats, and you can kind of be certain that the door he does not open definitely contains the car (as he knows where the car is unlike you).
Thus if you switch you would have a much higher probability than 1/10000 chance of winning the car.

>>9929494
Just imagine it like this - You initially have a ⅔ chance of picking the door with the goat, and a ⅓ chance of picking the one with the car. The host always removes a goat from the remaining two doors, so by switching there's now a ⅔ chance you have the car and a ⅓ chance you had the car to begin with and now have a goat.

>>9929569
thats...a pretty good way to explain it

No matter what anyone says, if theres two doors one with a goat one with a car you have a 50% chance of getting the car

>>9929615
So if I tell you that there's a 2/3 chance that the first door has a goat, there's a 50% chance that the first door has a goat?

If you have 3 options, each has a 33.3% chance. You remove one, now each of the 2 options has a 50% chance. Why is it so complicated?

>>9929659
Brainlets like to complicate things

>>9929578
Thanks

>>9929578
Basically this.

The chances the initial door you picked had the car was 1/3. Now one door is removed leaving only two possible options. Therefore if there are two doors and the one you picked originally had a 1/3 chance of being the right one, the remaining door has a 2/3 chance of being the right one. (By the right one I mean the one with a car... who the fuck wants to win a goat)

>>9929494
Your first choice shifts the odds, thats all you need to understand to accept its not 50/50

>>9929494
Your first choice has a greater chance of locking down a goat than locking down a car.

>>9929696
this. you dont even need a truth table, since the host didnt add any information about your door the odds of the car being behind her are still 1/3

>>9929494
>okay, there are three doors, one has a Ferrari behind it, and the other two have goats behind them
>so, if I pick one of the doors, then my chances of getting the car are 1/3
>wow, he is cool, he just told me that there is a goat behind a door I didn’t open
>I should use my knowledge of conditional probability to figure out how this changes the odds
>well, I can always find a goat behind a door I didn’t pick, no matter which door I select, so, the car being behind my initialy selected door is a subset of all the selections in which the host can open a different door to show me a goat, so the intersection of the two is equal to the narrower
>divide by the probability the host can find a goat behind a door that is not my first selection
>shit, how do I math......50%?
Okay, so, in your mind, you being told by the host that there is a goat behind some door you didn’t pick should increase the chances of your initial selection

Some intuition.

The reason your chances go up is because the host deliberately picks a door that is not your own and he knows contains a goat. By using his own knowledge in the selection, he leaks information into the system that you can then exploit.

What will really mess with your noggin is if the host picked a door at random and it happened to be a goat, the chances would remain at 50/50.

Does this problem work backwards too?

If there were two doors only, 1 goat, 1 car and the host added another door with a goat behind it, does that change the chance of winning the car from 50% to 66% now?

Can the host then add 98 more doors with goats behind them, knowingly to the chooser and improve their chances of winning the car from 66% to 99%? (98 added but revealed and 2 left with car and goat unknown as to which is which).

If the chooser chose at random then would they then win the car 99% of the time?

>>9929841
Are you pretending?

>>9929800
>leaks information
>excellent, now that he has shown me that there is a goat behind that door, I can confidently say the probability I picked the car has gone up 50 percent
>because, duh, 50% + 0% + 50% = 100%, so it works
>wait what do you mean the probabilities of success for the two doors I didn’t open need to be equal?
>what do you mean of the two doors I didn’t pick, telling me which of them doesn’t have the car behind it doesn’t change the sum of the probabilities of success for those two doors?

Okay but even if the chance is higher what if I just have a hunch my original door is right because I really liked the vibe it gave me and I wind up winning? Would you say God blessed me?

>>9929878
Yes

its 50/50
you either win, or you don't

>>9929494
just watch movie all day if youw ant to be smart
https://www.youtube.com/watch?v=Zr_xWfThjJ0

>>9929859
Care to tell me how that doesn't work?

The chooser knows in the original problem knows the door the host showed now has a goat, take the door away from the problem and its 50/50, add it, now its 2/3. How does adding a door with a known goat NOT keep increasing the chances of winning the car based on the problems solution?

>>9929578
i pick 1
so you're saying there;s 2/3 chance the goat is in the one i didnt pick. and the probabilty gets condensed into the door i havent picked. but can't i just draw these arbitrary groupings

>i pick 1 and say there's a 2/3 chance of the car being in 1 or 2, so when he removes the second door i say that 2/3 prob has been condensed into my starting door

problems?

>>9929925

>>9929925
Initially, there's 1/3 of picking the correct door and 2/3 of picking an incorrect door. If you picked the correct door initially then switch, you lose. If you picked an incorrect door initially then switch, you win

>>9929932

>>9929659
You have a 2/3 chance of having picked a goat. A goat you didn't pick is revealed. You still have a 2/3 chance of having a goat since Monty always reveals a goat you didn't choose. Why is it so complicated?

>>9929494
>its not 50/50
https://en.wikipedia.org/wiki/Independence_(probability_theory)
It's not an independent probability because the host can't choose to reveal a door that has a car behind it.
Think about what would happen if he did:
>OK anon, here's what's behind door #1... it's a car! Now do you stay with your original choice, or are you going to pick door #1?
That would be retarded because you'd be effectively asked to choose if you want to win or if you want to lose.
If they were independent probabilities you'd be right, but because the host cannot ever choose to show you the door with the car behind it that means the probability for the host's choice is absolutely dependent on your first choice as a contestant. If you pick a door with a goat, you have forced the host to open the one remaining other door with a goat. And because two out of your three options for the initial pick force the host to show you the one remaining goat, two out of your three options for the initial pick will lead you to a final pick where switching will be the right answer, while only one of your three options for the initial pick (picking the car) will lead you to a final pick where switching will be the wrong answer.

>>9929994
Cringe

>>9930004
How is that cringe? It's how the problem works, brainlet.

>>9930010
Writing a blog for a bait thread is cringe

>>9930031
How is that a blog? It's just an explanation of the problem, not a diary entry.
Are you using "blog" to refer to any post that has more than one line of text in it?

>>9930049
>Are you using "blog" to refer to any post that has more than one line of text in it?
Yes

>>9929494
The problem is how you assign probabilities. Think about it this way, according to you, before any information is given, each door has a 1/3 chance of having a car. Once the dude opens some random door, whatever door you choose has a 1/3 chance of being correct no matter what. However, the law of probability says all events must sum up to one. So if your door has 1/3, the door the dude opened is now 0, that means the last door has 2/3.

>>9929494
Ripped from Wikipedia, because apparently /sci/ is now too retarded to read:

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

>>9929494
You're completely right here. Since you only know THAT the host revealed that there is a goat behind door one, but not WHY, you don't have any guarantee that he would have necessarily revealed a goat at that point in all circumstances and hence can't model the problem with a probability tree that guarantees you don't have a 50:50 chance.

>>9929511
Kek at this. You're assuming that the problem statement would necessarily result in a tree in which you choosing a goat will always result in the host revealing the other goat when this information is not provided and he could have the option to do otherwise, meaning that being given the offer you're possibly given the information that you're more likely to have a car.

>>9929905
that explained nothing

>>9929494

>>9929494
But your choice guides his choice. Without your choice of door he can freely choose one of the goats, if you chose a goat he has no choice.

Because the more likely alternative is that you initially pick a goat, if he opens a goat door the other door must be a car. So, it will only not be a car if you initially picked the car

>>9930195
>you don't have any guarantee that he would have necessarily revealed a goat at that point in all circumstances
Yes you do.
If he doesn't reveal a goat that means he reveals a car.
Why would he reveal a car? It would make him asking you if you want to change your answer a meaningless question.
This all follows from the not at all controversial assumption that you're playing to win and not playing to lose.
If you're playing to win, then the host giving you knowledge of the door you can pick in order for you to win and then asking you if you want to pick that door would be nonsensical, it's equivalent to him telling you at that point that he's decided to make you win.

>>9930230
this makes sense. this is assuming the car is next to the door you didn't pick though. what if the goat was in door 2. would the 2/3 apply to door 1 or 3?

>>9930560
simulate any situation you want, by rearranging the door numbers before you start

>>9930560
>this is assuming the car is next to the door you didn't pick though
No it isn't.
A) You don't even know which door the car is behind in that picture, you just know that there's a 2/3 chance it's behind door 2 and a 1/3 chance it's behind door 3.
B) There's no such thing as "the" door you didn't pick. There are two doors you didn't pick.

>>9930568
>>9930570
So it's more about your odds than actually trying to get a car. Since 2/3 doesn't guarantee you get it on a 66% chance. It means you're more likely to get a car but there still could not be a car behind the door. If I say I chose door number 2 in that picture

>>9930576
>So it's more about your odds than actually trying to get a car

Distinction without a difference

>>9929569
I am lying to everyone about understanding this shit for four years
Holy shit, thank you

>>9930514
>Why would he reveal a car?

Because that means you lose, and it's part of the game show to sometime reveal that the player lost 'early' instead of giving the player the opportunity to switch every time, which would get boring quickly as it would be figured out by the players that switching is the better option in that case. Your logic doesn't hold for this reason.

Monty himself understood this.

https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html

The problem is fundamentally 'open' unless the host's actions can be determined to be unconditional.

>>9929994
Can you.
Please write in.
Proper paragraphs.

I would even.
Take double spaced.
Reddit shit.
Over this.

>>9929569
>>9929602
>>9930598

If you needed this 'explanation' in order to get it, then that means you don't really understand it at all.

The 'bazillion' door problem is fundamentally different from the three door problem, as in its case the probability of having all the doors picked such that it randomly happened to be the case that one of the two remaining doors has the prize is so low that you'd naturally assume that the doors were all deliberately chosen in order to not reveal the prize, which you almost certainly didn't pick either. It would be stupid in that case to not go for the other door.

In the original problem statement though, the chances of you initially picking the car and/or the host randomly picking a goat are high enough that it's meaningful to presume that either your being deliberately tricked or that the goat might have been chosen randomly, in which case you don't get a better than 50% chance. Whereas in the bazillion door problem the chances of either are so low a priori that you're right to naturally discount them.

>>9930605
>The problem is fundamentally 'open' unless the host's actions can be determined to be unconditional.
The host's actions work that way because the original problem was stated that way:
>She answered this question from a reader:
"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 No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"
https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html
Note that the quibble Monty Hall brought up late in that article doesn't apply to the problem as it was worded when first answered.
What he brought up was the possibility to simply tell a contestant they lost right away without giving them the option to switch, and the problem as it was worded when first answered by Marilyn vos Savant starts with the premise he's already given you the option to switch.
The fact Monty Hall didn't always give you the option to switch on his real life show has nothing to do with the "Monty Hall Problem." An abstract problem being named after some real life thing does not bind that problem to the rules of that real life thing. The rules are in the problem's stated premise, not in Monty Hall's head.

>>9930625
>trying this hard
2/10

>>9930613
It's perfectly acceptable and typical to put quotes and URLs on new lines, and there are only three sentences that aren't quotes or URLs in that post with their own lines, two of which are justified because they're sandwiching the quote line. It isn't really anything like your stupid attempt at parodying single line statements seven times in a row with incomplete sentences you fussy autistic faggot.

>>9930632
>Trying is lame, look at how cool and aloof I am.
Fuck off, idiot.

>>9930629
>She answered this question

This very problem statement, which is what we are discussing now, and which Marilyn vos Savant admits is worded ambiguously in the article, doesn't predetermine the host's possible actions. All it says is that the host "knows what's behind the other doors", and that IN THIS PARTICULAR INSTANCE, happens to have opened a door with a goat and offered a switch.

That is all.

>Note that the quibble Monty Hall brought up late in that article doesn't apply to the problem as it was worded when first answered.

It does and this is explicitly stated.

>Ms. vos Savant acknowledged that the ambiguity did exist in her original statement.
>Still, because of the ambiguity in the wording, it is impossible to solve the problem as stated through mathematical reasoning. "The strict argument," Dr. Diaconis said, "would be that the question cannot be answered without knowing the motivation of the host."

>What he brought up was the possibility to simply tell a contestant they lost right away without giving them the option to switch, and the problem as it was worded when first answered by Marilyn vos Savant starts with the premise he's already given you the option to switch.
Ok, it's really important to understand something, as what you've said here implies that you fundamentally do not get it. The premise is that YOU HAPPEN TO HAVE BEEN GRANTED THE OPTION TO SWITCH. This does not rule out the possibility of: [Monty acting so that he WOULD reveal the goat you chose, given you chose a goat, and WOULD offer the option to switch, given you chose the car. AND it also being the case that you chose the car]

If you want to talk about a stricter statement of the problem, then OK. But I've never seen the problem properly introduced in its strict, unambiguous, form, which requires a decent amount of rigor. The ambiguously worded problem is far more interesting anyway, as it has far more to teach us about thinking about probability carefully.

>>9930638
1 of the three is sandwhiching the prior 2 are not
>It's not an independent probability because the host can't choose to reveal a door that has a car behind it.
Think about what would happen if he did:
There is no reason to place both of these on separate lines. Additionally the following sentence
>That would be retarded because you'd be effectively asked to choose if you want to win or if you want to lose.
Should either be incorporated into the following paragraph or you should have left a space between it and same. Writing decently isnt just about being an autist, people are less likely to read your posts when they are formatted like garbage.

>>9930641
you're not trying, just bating
just saying you're bad at it, and boring

>>9930679
>sandwhiching
>isnt
If you're going to be a little bitch about formatting preferences you should at least figure out how to spell first. Also you don't understand what sandwiching means. Hint: There are two pieces of bread, not one. You fucking idiot.

>>9930681
The guy defending me is different, but I do want to clarify.

I'm not trying to insult people who didn't 'get it' until seeing the 1000 door problem. It's an unintuitive problem so there's no shame in that. The issue is that, if you did base your understanding off the 1000 door problem and couldn't otherwise reason about why the original works clearly, it's likely that you are actually misreasoning about the original problem and not fully understanding why it works the way it does.

Someone who understands the original through the 1000 door problem is less likely to intuitively understand why it's important that the host is guaranteed to both choose a goat and offer you the option to switch to it, and that simply happening to be given this option without that guarantee doesn't net you the 2/3 chance on switching.

>>9929914
Because he has already chosen and adding a door with a goat behind it doesn’t add any new information about where the car is you fucking spasticated inbred cunt that hasn’t had pussy since pussy had you

Imagine this game with 1,000 doors. You pick one. The host reveals 998 goats. Do you switch? Why?

Repeat with 999 doors.
Repeat with 998 doors.
...
Repeat with 4 doors.
Repeat with 3 doors.

>>9930705
1000 door example is good at one thing:
revealing that Monty opens (n-2) doors, not just 1 door - just a coincidence that 3-2=1

>>9929511
>>9929515
>>9929569
>>9929615
>>9929659
>>9929698
>>9929800
>>9929841

No, fucking stop. I'm stopping this meme NOW.
AFTER THE DOOR IS REVEALED, YOU ARE NOW MAKING THE CHOICE BETWEEN TWO DOORS. "DON'T SWITCH" IS EXACTLY THE SAME AS SAYING "DOOR 1". THEY'RE BOTH 50/50. STOP THE FUCKING MEME

>>9930773
Not how it works fag

>>9930774
yes. it. IS.

You open door number 1. A goal is revealed. There is no, NO difference between Monty Hall swapping you out with another person and saying "choose between these doors" and just asking you to switch or not. ITS THE SAME CHOICE WITH DIFFERENCE WORDS.

Clearly, if you aren't some terminally autistic fake mathematician, you'll recognize that both doors are 50/50 once one door is opened.

>>9929494
That part is 50/50. But the overall chance of winning is 2/3 because it's possible to just pick the car's door off the bat.

As a weighted sum of probabilities:
(1/3 * 1) + (2/3 * 1/2) = 2/3

>>9930776
>There is no, NO difference between Monty Hall swapping you out with another person and saying "choose between these doors" and just asking you to switch or not.
First of all I'll say you can technically have a somewhat valid argument for 50/50 IF you allow the host to decide not to open a door and give you a switching option or allow the host to do weird shit like opening the door with the car in it and asking if you want to switch to it. That said, IF you stick to the premise the host is always going to offer you a switching choice and is never going to open the door with the car behind it in giving you this choice, then there definitely is a difference between asking someone to "choose between these doors" vs. revealing where the goat is after your first pick and asking if you want to switch.
The difference is that with the constraint the host can't pick the car door to show you, the door he does pick is going to be dependent on the door you initially pick. The door you initially pick is 1/3. If you pick a car door initially, then switching would make you lose, but if you pick a goat door initially, then switching will always make you win, and there are two goat doors out of three doors total for a win probability of 2/3 when you switch every time.

>>9929557
This. I think everyone here has the reading skills of a 5-year-old. OP's problem is not Monty Hall.

>>9930868
OP didn't mention the part where you pick a door before the host opens a door, but it was close enough otherwise and most (adult) people tend to start with a holistic notion and then automatically gloss over errors or gaps when it comes to reading. It's great if you can overcome that tendency and spot problems other people would miss, but it's kind of shallow-minded to suggest people have poor reading skills for behaving according to a well established psychological tendency towards holistic inference. That's a lot like saying people have bad spatial judgement skills if they misjudge circle size in an Ebbinghaus illusion picture. It's not really a poor skills issue, these are both consequences of useful features our cognitive processes operate in terms of.

goats are named Tom and Jerry, and theres a car

Here are the possible setups:
1. T J c
2. J T c
3. T c J
4. J c T
5. c T J
6. c J T

if you chose the leftmost door initially; games 1,2,3 and 4 are won by switching. 4/6 games are won by switching. 2/3
+Setup#1: pick left, have Tom, Jerry is removed@mid, switching wins
+Setup#2: pick left, have Jerry, Tom is removed@mid, switching wins
+Setup#3: pick left, have Tom, Jerry is removed@right, switching wins
+Setup#4: pick left, have Jerry, Tom is removed@right, switching wins
- Setup#5: pick left, have car, Tom is removed, switching loses.
- Setup#6: pick left, have car, Jerry is removed, switching loses

4/6 win by switching.
2/6 win by staying.

Switch or stay, you don't win 100% of the time.

>>9929551
Proves that having a phd means nothing

>>9930894
>Switch or stay, you don't win 100% of the time.
Nobody claimed you win 100% of the time though? Your win probabilities (2/3 for switching, 1/3 for staying) are the consensus right answer for this problem, you're not disputing the consensus.

>come to this thread expecting the good minds of /sci to eloquently agree with OP and see truth behind the Monty meme
>it's filled with brainlets spouting the usual autistic drivel in defense of the meme
wew

>>9930897
I always thought of graduate degrees less as intelligence indicators and more as ambition / productivity / high stress tolerance indicators.

>>9930898
You tell people they have a better chance of winning by switching and they get it in their heads its a surefire win. It also doesn't solve that basically everyone who ever played the game only got to play it a single time. Being told switching is a better chance, only to lose because 66/33 isn't really too great of gap from 50/50, would probably feel shitty.
>evil science man said switch and now I don't get a car

>>9930904
>You tell people they have a better chance of winning by switching and they get it in their heads its a surefire win.
What? Why would anyone interpret "better chance" as "surefire?"

>>9930936
Probably cause the solution is usually presented as a winning tactic.

think of it like this monty hall with 100 doors.

you choose one and 98 doors with goats get revealed.

the probability that your first choice was a goat DOES NOT CHANGE, there is a 1/100 chance that you picked the one with the car, so the unrevealed door has a 99/100 chance of being a car.

going by the 50-50 logic, you have a 50% of winning a car anytime for an infinitely large number of doors

>>9931078
I've already pointed out that this analogy doesn't actually work and that it's completely reasonable to hold that doors randomly being picked out naturally results in a 50:50 chance for the one-of-three door version, with an only 1/3 chance of the car being randomly picked by the host (if he's acting randomly), and a decent chance the host is trying to bluff you out of the car if that's his strategy and reasons for offering the switch.

When the doors are increased to hundreds, the chances that the host isn't picking the doors specifically to give you the car on switching decreases greatly, as you'd only not switch if you suspected that the prior probability of the host being benevolent was less then the chance that you've won the car outright.

Monty hall is only a 50/50 winrate if switching and staying are chosen randomly. If you just flop from switch to stay to switch ad infinitum, over a large enough sample size of games, there will result in 50% wins for the total of all games together.

if however you also run a counter only for switching, it will be 66% wins, and only for staying would be 33% wins.

OP you have the action order wrong.
The person first chooses one of the three doors, then another one without the prize gets opened.
The chance to get the prize is still 1/3 if you don't switch.
Imagine if the first door gets opened for someone else, but you're the one who still has to make a choice, not knowing which of the other doors got opened.
Now imagine that you'd have the opportunity to ask for the other person's opinion on which door to open. They would recommend you to switch, because they have more information than you do.

>>9930776
Enjoy a lifetime of poverty because of your inability to grasp high school math.

>Host: Here are 100 doors, behind one is a car. Pick a door:
>You: 35.
>Host: All right. Since I'm being nice today, if you give me $5, I'll let you switch your bet and have the car if it's in any of the other 99 doors that you didn't pick. But if you actually guessed right the first time, you get nothing. How's that sound?
>You: No way fag, I know the probability is 50/50

>>9930690
Now you are just assblasted because you cant reasonably deny the point has merit.

>>9930941
Nobody except you has even brought up this bizarre idea that "having a better chance at winning" is equivalent to "being guaranteed to win." Are you literally mentally ill?

>>9931234
I did reasonably deny it. Because you don't understand what a sandwich is.

>>9930195
The post is titled "Monty Hall problem." The standard assumptions of "the Monty Hall Problem" are:

1. The host must always open a door that was not picked by the contestant (Mueser and Granberg 1999).

2. The host must always open a door to reveal a goat and never the car.

3. The host must always offer the chance to switch between the originally chosen door and the remaining closed door.

If these cannot all be assumed, then we're not talking Monty Hall, dipshit.

You can easily write a Monte Carlo simulation to prove that the correct answer is, in fact, correct.

> prizes are random assortment of [False, True, False]
> contestant picks one prize randomly
> host selects one False prize that wasn't selected by contestant
> rinse and repeat 1e6 times
> sum and calculate mean of switching and keeping your original choice

Probability that you win on switching: 0.666689
Probability that you win on keeping your original choice: 0.333311

>>9929494
The OPs issue with this summed up clearly in his greentext. OP completely ignores the part where you pick a door first before the host removed a goat. It's this 3 door choice that starts you off at a 33% chance. The removal of a goat from the other two doors is where it gets complicated. Simply put the odds become better that the other door has the car. OPs scenario has the host remove a choice from the 3 doors, he's not limited to the 2 doors you didn't choose, in this brainlet situation the choice is obviously 50:50 and not even worth the post...

You guys dont understand. There is a 33 percent chance, because even though one of the doors are already open, you are so retarded, that there is a chance you pick the open door.

>>9931264
>If these cannot all be assumed, then we're not talking Monty Hall, dipshit.

Then why, whenever people start talking about Monty Hall, do people never actually state these conditions at the outset and instead only introduce them after people give the 'wrong' answers? It's standard for the 'standard assumptions' to not be expressed in the problem statement, and then for this omission to never be acknowledged afterwards.

Even in the initial paper the 'standard formulation' is introduced independently of the problem statement, and makes constrains on behavior that aren't given by the actual scenario (in which the host and contestant barter 'freely').

https://www.jstor.org/stable/2683689?seq=1#page_scan_tab_contents

>>9931328
The problem is the same given its name. It is only necessary to restate the conditions of the problem when it is obvious that erroneous results stem from modification of these conditions, in which case we either correct them or focus on the "new" problem instead.

You'll receive no sympathy from me when you can just search "Monty Hall problem" and find the conditions of the problem - in fact, you did just this. Good job.

>>9930723
Just a coincidence, goyim. Keep switching

>>9929551
i was unironically shocked when i found out about those letters. I understand this is sorta like counter-intuitive problem and shit, but with a short explanation it is so fucking obvious and simple that i can't even

>>9931328
This is a distraction. If you look at most of the actual responses people sent to vos Savant you'd have a hard time finding many that were wrong specifically because of someone not assuming the right starting conditions. The real reason why almost everyone who was (or still is) wrong about this were (or still are) wrong about this is because they refused / still refuse to believe a choice between two doors could be anything other than 50/50 in chances. You *could* come to a 50/50 conclusion because you don't realize the host is supposed to offer to let you switch after picking and you don't realize the host can only ever show you a door that both wasn't picked initially and doesn't have a car behind it, but honestly those alternative lines of thinking are even less intuitive things to assume than the standard problem itself is.
Marilyn vos Savant by the way specifically mentions this as the case, that she would've been fine with people objecting to the starting conditions not being established clearly enough but that this is a non-issue because the actual responses she read through were mistaken for an unrelated reason.

>>9931379
I feel a similar way, anon. The best I can come up with is that all of us in general spend lots of time behaving in irrational ways. I don't think most of the people who got so upset about this and insistent that vos Savant was wrong were operating from a place of logical soundness. It was more like they latched onto the notion "2 doors = 50/50" and shut down any further attempts to think about the topic. So in a way it's not that they were being stupid, it's that they were deciding to not even think about it.

>>9931212
But, that naturally has nothing to do with this, because there are three instances, not ninety nine. Ofc with ninety nine doors while only one car the chances will be far far lower.

>>9931367
>The problem is the same given its name.

But this is backwards. The problem stems from the scenario given, the probabilistic model was then developed afterwards to model and reason about the problem, which is derived form the scenario given by the problem statement. In no instance have I seen a scenario statement where it is even remotely implied that the host couldn't have decided whether or not to reveal one of the booby prizes based on the contestant's initial actions; the very context of the show implies the possibility of these kinds of decisions. The whole issue here is that the model is being retroactively interpreted as the 'real' problem and substituted for it, when there is no standard scenario statement I am aware of that it is a good model of.

>>9931387
>The real reason why almost everyone who was (or still is) wrong about this were (or still are) wrong about this is because they refused / still refuse to believe a choice between two doors could be anything other than 50/50 in chances.

This is the case for many of those among the responses, and I don't deny that. But, not having gone out of my way to check them out myself, I have little doubt that many were right in spirit to criticize her for her own hasty bluntness.

It is important to note that the case that many people who 'know' the 'right' answer don't understand that it is strongly dependent on the unstated "standard assumptions", and hence mistakenly think that the host revealing a goat couldn't give information that could increase the chances of their initial choice being right. This deserves to be criticized.

>>9931428
In the paper cited above, the scenario was given. It doesn't matter if the host COULD reveal a losing choice or not, this is only the Monty Hall problem IF the host DOES, as occurs in the problem statement.

While the show in reality may differ from the ideal scenario, you're literally the only person here who gives a fuck about how this would play out if they were on a game show. Why not argue that the probabilities would be different if the doors were boxes and one contained keys while the others were empty? Because we aren't high school drop outs who solve problems with the mental equivalency of particularly stupid ten year old.

>>9931296
Fucking this. Glad I read through the thread cause I was about to post this. Utterly pointless if you don't specify that you've already picked a door

>>9931141

jesus christ your basically arguing that math is flawed because it doesn't agree with your intuition

your argument is basically "it's 50-50 because there's 2 doors left!!!"

high school math condition on switching

P(win if you switch) = P(win if you switch | choice was car) + P (win if you switch | choice was goat) = 1/3 * 0 + (2/3) * 1 = 2/3

just because you reveal that one of the doors was a goat DOES NOT make your original choice have had a 1/2 of being a goat

you ALREADY chose the door before you revealed there was a door with a goat

logically, if there was no reveal would you say that 1/2 the doors you picked were goats? no, it's still a 2/3 chance of goats, the "reveal" doesn't change that

>>9929494
You have to think about it in terms of switching and staying. Think about the the number of cases when you win by staying and compare that to the number of cases when you win by switching.

The whole premise makes no sense to me at all.
Either the host knows *nothing* about what's behind the doors, in which case it's 1/3 before and 1/2 after, or he *does* know what's behind the doors, in which case probability never comes into it.

>>9931618
>or he *does* know what's behind the doors, in which case probability never comes into it.

>>9931240
Why the fuck do you think people find monty hall so hard to grasp?

Its cause they can still lose despite the winning strategy. The numbers arent what they care about, its the car you dumb cuck. They dont get the car, they dont comprehend the strategy. Ultimately if the game is only played a single time as any real contestant ever got the chance, they're better off just fucking guessing and not adhering to any strategy cause they will either win or lose.

>>9931902
>1/99999999 chance of winning if you stay
>well you only play once so just guess
I can't tell if you're retarded or trolling.

https://www.openprocessing.org/sketch/480963
Heres some code that runs monty hall 100,000 times. You can check the source with the </> button to see how it works.

>>9929696
But I like goats.

>>9931905
Thats not the game you dumb cuck.

>>9931555
>In the paper cited above, the scenario was given.

Yes, and that's exactly what I'm talking about. I'm doing nothing but arguing from the problem scenarios as given, with no further assumptions, unlike the standardization. I'm not 'borrowing' anything from the show that isn't already implicit in the problem statement.

>It doesn't matter if the host COULD reveal a losing choice or not

Yes, it does, this matters immensely and that has been shown. The 2/3 chance to win on switching depends on all the standard assumptions. If Monty can freely bluff you then he can make the probability of giving up your container resulting in something better arbitrarily low; this is perfectly compatible with all the scenario statements I've seen and both Monty himself and Maria agree that this is the case, regardless of what actually happens on the show. If Monty can do different things depending on on whether or not I have the car, then you can construct numerous completely different probability trees that result in Monty's behavior affecting the likelihood of a given outcome in various ways.

However, I'll be fair and admit that the original problem statement does certain things that make it more interesting that the other variations I've seen. It's interesting because the contestant is the one who brings up the switch, implying that they are assuming that Monty's behavior is giving them more information about the contents of the box they have then Monty himself likely realizes, and this may actually be the case. This doesn't actually imply a consistent 2/3 probability to win and requires Bayesian reasoning to be made 'mathematical', but there is a serious argument to be made that attempting to switch is a good idea here, depending on how clever Monty actually is, and that IS interesting and not incorrect.

>>9931618
You're completely correct but most people here are attached to the idea that they know the right solution because they've been told it even if they can't think about it clearly themselves.

What about the explanation that the first guess was 1/3 and the second guess was 1/2, so the second guess always has better odds? I've seen it written and heard it said that this explanation for why it is better to switch is not ok, but I think it is. The probability of winning by switching is 2/3, so the other solution has that for it: it tells what is better *and* what the odds are. However, I think my reason for why it is better is sufficient to show it is even while my reasoning doesn't quantify the odds.

>>9931618
Let's say the player goes with a strategy. All games have strategy. So he decides that no matter what, he is NOT switching. He's sticking with his initial choice.

There's one car and 2 goats. You follow?

The host then reveals one door which has the goat. So far for good, the game is played.

The player is asked by the host if he wants to switch or stay.

And as previously state, the host says fuck it, sticking to the plan. NO SWITCHING. Stick to the guts.

Alright what are the odds he got a car? It's 1/3. Therefore 2/3 for getting goats.

Remember he said he wasn't switching. So in order words, not switching is exactly how the game is played if there was no host revealing no goat.

But being allowed to change the guess, means that the player has a higher change of success.

So not switching, i.e sticking to your first try, means 1/3 chance of winning.

Let me rephrase it to you. When you roll a dice, aiming for a specific number, and you fuck up the first roll. And the the host says you can roll the dice again: Is rolling the dice again mean the odds of getting what you want going to increase? Of course.

Well it's the same idea. Switching in the Monty Hall problem means the player is playing again. They are rolling the dice again. And so the probability is going to increase.

Thus switching is what a player should do.

Now you can retort with "well in the dice example you know you didn't get the number". True and with the Monty Hall problem,it's not certain that the player fucked up but odds (2/3) are that the player didn't pick the car. And so they should switch.

>>9930709
That's irrelevant. Imagine there's 100 doors in the original problem and the host opens 98 doors with goats and asks if you want to switch. It's the EXACT same as the original problem so please tell me how switching doesn't grant you a 99% chance at winning?

>>9932250
So the question would be about the different possibilities up to the player being asked about switching, because it's right before the player switches that they need to know the probability of success. In the following:
>What are the odds that the person chooses the Car and gets shown Goat #1?
>What are the odds that the person chooses the Car and gets shown Goat #2?
>What are the odds that the person chooses Goat #1 and gets shown Goat #2?
>What are the odds that the person chooses Goat #2 and gets shown Goat #1?

The answer for each, with respect to the order shown above is:
>1/6
>1/6
>1/3
>1/3

Why 1/6, because it's 1/3*1/2. When you're asking the probability of X and Y, the result is the probability of X times the probability of Y. There's 1/3 chances that the car gets picked and 1/2 for either goats to be shown after. So far it's 1/6.

Then there's next event of the player deciding whether to switch or to remain.

If they stay for the first two scenarios as shown in the questions before, then they get the car. So stay has two for cars for so far.
To find out the odds of success, the odds of each event happening for the player, wherein they still win by staying, need to be added. There are two events where the player chooses to stay with a success, i.e when they chose the car in the first place.

So stay success odds is: 1/6+1/6 = 1/3

Then there's switching and the success of that. The only way to switch and get a car is when the player switches is when the events stated in the last two questions happen. Because that's when they chose either Goat #1 or Goat #2. So the player can switch for two events and get a car.

The success of staying and getting a car is: 1/3 + 1/3 = 2/3

2/3 > 1/3 so the player should switch

>>9932288
Exactly. It could be a million doors. It's always better to get another shot at rolling the dice, or picking the car, or door or rolling the lottery thing.

>>9932250
So the question would be about the different possibilities up to the player being asked about switching, because it's right before the player switches that they need to know the probability of success. In the following:
>What are the odds that the person chooses the Car and gets shown Goat #1?
>What are the odds that the person chooses the Car and gets shown Goat #2?
>What are the odds that the person chooses Goat #1 and gets shown Goat #2?
>What are the odds that the person chooses Goat #2 and gets shown Goat #1?

The answer for each, with respect to the order shown above is:
>1/6
>1/6
>1/3
>1/3

Why 1/6, because it's 1/3*1/2. When you're asking the probability of X and Y, the result is the probability of X times the probability of Y. There's 1/3 chances that the car gets picked and 1/2 for either goats to be shown after. So far it's 1/6.

Then there's next event of the player deciding whether to switch or to remain.

If they stay for the first two scenarios as shown in the questions before, then they get the car. So stay has two for cars for so far.
To find out the odds of success, the odds of each event happening for the player, wherein they still win by staying, need to be added. There are two events where the player chooses to stay with a success, i.e when they chose the car in the first place.

So odds of getting a car by staying is: 1/6+1/6 = 1/3

Then there's switching and the success of that. The only way to switch and get a car is when the player switches is when the events stated in the last two questions happen. Because that's when they chose either Goat #1 or Goat #2. So the player can switch for two events and get a car.

The odds of getting a car by switching is: 1/3 + 1/3 = 2/3

2/3 > 1/3 so the player should switch

>>9931615
holy fuck i get it now
the issue i had is defining the numerator and denominator
the numerator is the amount of goats you can choose.
the denominator is the total amount of doors.
the reason the numerator is that is because all the other goats are going to be eliminated, so you need to only choose a goat to guarantee a win on the switch.

>>9929935
Most intuitive argument so far.

>>9929494
Switching door gives you a slightly higher chance of getting the car. Here's why:
>there's three doors, 1 with a car and 2 with goats.
>you choose door number 1.
>before you open your own door, the host is nice and opens door number 3, which reveals a goat, and gives you the option to either stick with door number 1 or to switch to door number 3.
>when you first chose door number 1, you had 2/3 chances of getting a goat.
>but now that one of the goats is eliminated, you are left with 2 doors, one of which, your initial choice, had a 2/3 chances of having a goat.
>So while door number 1 has 2/3 chances of getting a goat, that number would never increase your chances of getting anything because that's literally how odds DON'T work.
>Tl;dr switching doors increases your chances of getting a car by 1/3.
Thing to notice: that doesn't mean the first door doesn't have a goat, it just means you are more likely to win a car by switching.

>>9929494
>No one said anything about the law.
Of course, because if you look at the facts then your lies dwindle away.

The fact is that the only structure in society holding anyone down based on race is AA.

You have no proof other than emotional rhetoric to the contrary.

>even though we're all the same.
Yes, this is true then why are you not advocating that everyone be treated equally under the law? Is it because you're using your race as an argument to squeeze advantage out of society?

It's kind of sick, honestly, that the only reason there is so much hate in this country is because people with high melanin skin have convinced themselves that people with white skin are somehow below them, even though we're all the same.


And for the record I am Asian.

>>9933593
Everyone keeps repeating this as if it makes sense. That when you get rid of one goat (because no one would choose the opened goat door) the chances dont get better. However assuming you dont know what is behind what door, and the fact that "switch or not" and "choose the door" is the EXACT same thing, just worded differently, how the hell have the chances not improved?

>>9934997
If you picked car first then switch, you lose. If you picked goat first then switch, you win. Picking car is 1/3, picking goat is 2/3. So switching is 2/3 win rate

>>9929714
>you dont even need a truth table
>making sure you never see the flaw in your thinking

>>9929994
>>OK anon, here's what's behind door #1... it's a car! Now do you stay with your original choice, or are you going to pick door #1?
>That would be retarded because you'd be effectively asked to choose if you want to LOSE or if you want to lose.

FTFY.

>>9930679
>1 of the three is sandwhiching the prior 2 are not

Learn 2 comma and full stop.

>>9930897
"This is US, we can't have professors being smarter than joe hillbilly"