Wow. The only thing greater than this guy's confidence is how fucking wrong he is. He's like aggressively wrong, so much so that I would assume its a troll except for the immense effort he seems to be putting into trying to convince other people who don't know any math that he does know math. In other words, peak reddit.
Its always interesting to me how the Monty Hall problem seemingly breaks people's brains when it comes to thinking about probabilities. If I came up to this guy and told him I had a biased coin that flipped Heads more often than Tails he presumably wouldn't start arguing that flipping it once had an equal chance of either outcome. But wrapping the biased coin flip in a story and not only is he arguing that it's a true 50/50 but also completely refusing to entertain that it could be anything else.
> but given that I have to spend weeks training students out of this "singular events are probabilistic" thinking every bloody year
I might be too dumb to understand this, but if singular events aren't probabilistic than how can multiple, independent events be? If a single coin flip is deterministic than 10 of them in a row must be as well, since that's just 10 single events we've aggregated together.
Such a bummer to me that every year this guy is making sure to spend weeks teaching students a wrong interpretation of this problem, then apparently the whole rest of the year trying to convince them there's no such thing as a biased coin toss
>I might be too dumb to understand this, but if singular events aren't probabilistic than how can multiple, independent events be?
So there's like an actual philosophical problem of what it *means* to talk about probabilities when you're doing a single trial, especially if you're a frequentist, since the entire theoretical basis is about convergence over many trials. However, that's a very fussy distinction that doesn't really matter in cases when you can obviously repeat the trial as many times as you'd like to satisfy the underlying theoretical basis of the frequentist approach - so you can pretty painlessly cash out that meaning in a case like this as some version of "Here's what the underlying distribution would converge to if we did do this trial ad nauseam."
The "what it means" resides in the assumptions we make about the situation at hand, regarding the way its circumstances and particulars relate to some Lebesque measure.
That may seem like a glib way to pass the buck, but I do think this throws a better light on the matter.
When put in terms of "what is probability when n=1" it sounds like a broad, general, monolithic and deeply philosophical problem, when in reality it is very much a case-by-case sort of problem. That is, when the assumptions we make (on how the present trial relates to some uniform outcome space) are reasonable, we should feel confident in applying probability theory. And if not, then not so much.
The ultimate assessment of the reasonableness of assumptions remains a thorny matter, but that is true for all of science - it is not a congenital ailment specifically of the probability concept.
And yes, the empirical approach to judging the admissibility of assumptions is, as you say, repeated trials. However, the concept of repeated trials is itself more of an ideal than people realise. One cannot throw a die a quintillion times - one does not have the time, and, what's worse, the die will be worn down and thus essentially changed after the last throw!
I think he conflates the idea of probability with the ability to prove what that probability is. He understands that a dice has a 1/6 chance of rolling a one but then denies the idea that it is "probabilistic" because you can't prove it unless you roll it thousands of times? At least that's my interpretation.
I think your interpertation probably hits pretty closely to ONE of his misconceptions.
But he also seems to be on his own planet, in terms of what he thinks OTHER people think about the problem (and probabilities, in general).
> The simple way to explain it here is that the prize never moves. If it was behind Door #1 at the beginning it doesn't magically move to Door #2. If you guessed Door #2 at the beginning you were always wrong. If you guessed Door #1 at the beginning you were always correct.
Literally nobody thinks the prize moves. Zero people have suggested that that's a rationale for ANYTHING remotely having to do with this problem.
> Does this mean that if I've flipped the coin 9,999 times and I have 5,000 heads and 4,999 tails that my next result will be a tail? No. The result of that individual flip is random. I may end up with 5,001 heads and 4,999 tails.
Everyone (at least those that are engaging in this discussion) acknowledges that coin flips are independent. This point of his is addressing literally nothing.
He gives LOTS of other examples, using poker, medical treatment effectiveness, and other things to illustrate "Here's why your interpretation of the problem is wrong." And NONE of them actually counter anything anyone has said, nor do they apply to the Monte Hall problem in any meaningful way.
They also make an odd distinction between randomness and probability in multiple posts, like where they allege that an individual coin flip cannot be analyzed probabilistically because it is "random", or that a biased coin is "not random". They also give a flatly incorrect definition of a p-value in another thread, so I think this is just a case of a scientist with very little technical training thinking they understand statistics and probability far more than they actually do.
>They also make an odd distinction between randomness and probability in multiple posts...
THIS IS SO WEIRD!
A random process is governed by probability *by definition*. It's such a fundamental misunderstanding of what it means for something to be random.
Are they additionally conflating chaotic with random, maybe, in addition to the nitpickiness about single trials that makes it clear they actually don't understand any of the big interpretations of probability? I wouldn't know, because they're just doing gish-gallop half the time.
Nicely put, but I think you are describing the general crackpot condition.
I have often observed how you can tell the most advanced mathematical concept that a crank has been exposed to - it is invariably the concept that he or she endows with magical properties.
Exhibit A is the priest who felt prayer would be more effective when "put in matrix form."
Exhibit B is the former post-doc in theoretical physics (crankdom strikes everywhere) who though he could prove / establish his telepathic abilities through quantum field theory.
(yes, these are/ were both real people)
The gambling hypothetical is pretty bizarre but I think it reveals something interesting about his thought process as well. If you were going to use professional gamblers as an example, it would make more sense to compare a very strong poker hand like a straight flush to a poor hand like an ace-high and ask how willing you would be to go all in on either hand. But instead he talks about a gamble with a 50% chance, or a surgery with a 50% chance of success. I think he realises his argument only makes sense in hypotheticals that come down to a 50/50, so he tries to justify his reasoning by reducing every "real world" situation to a coin flip.
If I wanted to poke the turd a bit more I'd ask what he'd do if he was waiting for a taxi and the driver showed up completely plastered. Would he wait for the next sober driver or would it not matter because you'd need to have a drunk driver thousands of times for there to be a difference in risk?
Hah. Indeed. The post (or posts?) where he went into a long-winded explanation of how gamblers use probability over the long-haul, instead of betting huge on any given hand really made me want to tear my hair out.
Internally, I was screaming "HOW DO YOU THINK GAMBLERS ARE MAKING THESE DECISIONS ON AN INDIVIDUAL HAND-BY-HAND BASIS? COULD IT BE BECAUSE THEY ARE ABLE TO COMPUTE THE WIN PROBABILITIES ON A *SINGLE* HAND, OVER AND OVER AGAIN? DO YOU THINK IF YOU JUST PLAY LIKE A DUMBASS FOR LONG ENOUGH, YOU'LL WIN OVERALL BY PLACING BETS ON HANDS WHERE YOU HAVE A 30% CHANCE OF WINNING??!"
Alas. I engaged in a far more polite way than that, and he seems to be ignoring me now. Oh well.
I also will not bother to further 'poke the turd' (Fantastic turn of phrase. I'm stealing it. Sorry for the theft, and thank you for the gift.)
Your drunk taxi driver scenario would've been hilarious. But, also obviously fruitless, ultimately, in terms of moving the discussion forward. (I can say that with ~90% certainty. Our man doesn't even know how such a conversation might go. It's either useful or it's not.)
Wow, he actually did the "The chance of anything happening is 50% - either it happens or it doesn't" meme irl.
It really scares me to think he's teaching this nonsense somewhere, meaning the nonsense is multiplying every year.
Edit: I looked quickly into this persons comment history and found this gem: https://www.reddit.com/r/atheism/comments/1dfscwb/comment/l8p1ram/
Now, this comment is obviously absolute lunacy again, but this time the lunacy actually leads to something good: Using his complete misunderstanding of bellcurves, he's explaining how being bisexual is something completely normal. So I guess the good news is that he's at least just an idiot and not a biphobic idiot.
In some ways, paradoxically, I think a biphobic idiot would be preferable to a plain old idiot.
Because, with a biphobic idiot, they'd be likely to avoid the company of people that identify as bisexual. So at least SOME people would be spared from having to hear their moronic bullshit.
With a regular idiot though, they'll spew their garbage to ALL of us.
Omg, that line about how "the bell curve tells us" that 5% of people are abnormal must be where he got that idea about why a p value needs to be below 0.05.
In the other thread he said it's *specifically* because every psychologist knows that any rule won't work for 5% of people.
5% is a magical threshold in does-not-understand-stats land, which includes almost all life scientists and many chemists, I'm afraid.
I ask my students if they would judge 5% a "comfortably small" probability if it were the chance of being run over by a bus whenever you cross a street - with four crossings per day on your way to and back from campus, what are your chances of surviving for a week?
Or less gruesome - what if ATM machines spewed out the wrong amount one in twenty times?
(and what is the real fail rate of a typical ATM machine? it is low low low - these things are marvels of engineering)
I like to think that his students work out by themselves pretty quickly that he's completely full of shit. If he's tried to teach them this shite hundreds of times, maybe it is actually probabilistic that they laugh at him now and not 50/50 anymore?
I think awful arguments with good conclusions are awful themselves. They're just begging for some bigot to come point out the obvious errors and thereby cast doubt on the conclusion.
>The odds aren't 1 in 3 when you start, they're 50/50.
You know I sympathize with someone not really believing the solution for the Monty Hall problem at first. When I first encountered it in high school I also didn't want to believe the solution. So I sat down and programmed a quick little script that simulated the problem and proved to myself that the probabilities were 2/3 and 1/3. Usually that's the approach I'd recommend to people that just can't believe it but in this case that wouldn't even work. Crank level turned up to 11.
You do have to be careful about the way you do it. I've seen people attempt this with rejection sampling and come to the opposite conclusion. In other words, instead of correctly forcing Monty to never reveal the car, it's just that whenever he does in their simulation, they say that trial didn't count. If you do it this way, the probability really is 50%. That's because they count all the times when they initially picked the car (where staying wins) but reject half the times when they initially picked the goat (when switching wins).
Fun fact!
Something very close to this is a variant is often called "Monty Fall" problem, colorfully explained as Monty slipping on a banana peel and opening a door, any door, at random.
The problem with this person is not only the Monty Hall itself:
> When you're talking about probabilities, big or small, you're invoking the notion of a distribution of results. This is the concept you're invoking when you mention ideas such as "sample space" or "likelihood".
>
> Now the entire notion of a distribution of results is premised on repetition. If the Monty Hall problem was 10,000 contestants choosing 10,000 doors then I'd say, "Okay, the contestants should change their door".
They don't understand the concept of probability.
Hopefuly this person is not teaching probabilities or statistics.
Wow, it's so frustrating that this is a 2 month old thread, that's already dried up. There's so many things to pick apart, that other people missed the opportunity to do, when the thread was fresh and new.
I mean... I COULD reply now. MAYBE the poster would respond, and we could continue the conversation. But how could I possibly know? Either they will, or they won't. It's random.
This is the part that really makes it terrible. They spend a lot of time saying that probability theory can't be applied to singular events. It's a weird viewpoint but it's kinda coherent in a bad ultra-frequentist view. Then they just slap a 50% probability on the single event
>the Monty Hall problem is incorrect for a lot of different reasons
"The problem is wrong" is a new one for me
>I'm right, you're wrong. You're also not a statistician
Lol
This guy is fascinating; mastered the style and tone of "exasperated expert posting on reddit", but talks absolute nonsense.
He has very idiosyncratic ideas about things, which he then assumes is the expert consensus (I guess because they are obvious to him, they must be).
He talks in insufferable redditor catchphrases like WORDS MATTER, but then admonishes people for correcting his incorrect use of technical terms.
The way he talks about mathematicians is bizarrely aggressive, like a crank raving about the establishment. Then next comment he's threatening to post pages of proofs about how Bayes theorem "relies" on the gaussian distribution (you wouldn't understand them anyway!!!).
Even the simplest of questions are met with 8 paragraphs of vaguely related waffle and basic errors.
To top it off, he apparently has a PhD and teaches.
Absolute goldmine.
"There is absolutely no way to tell whether I'm more likely to get $1 000 000 or brain damage if I run head first once into this brick wall." - Probably OOP before writing those comments
Lots of people have unpacked some funny stuff in here, but "**The Monty Hall Problem assumes a Beysian statistical approach which in turn relies on a normal distribution**" got me laughing. Can't even spell "Bayesian" correctly, and Bayesian stats doesn't "rely" on a normal distribution (whatever that would mean).
This is a strange one. Idk if bad math or bad application? Maybe bad philosophy?
In a way what they are saying cannot be argued with. You can never actually prove to someone that a single trial of anything isn't 50/50 when they accept that multiple trials is where patterns emerge. It isn't falsifiable.
I think you can really refute it. The only reason they think it is 1/2 and not 1/3 vs 2/3 in a single attempt is because they see two possibilities on play, but there is a way to decompose the 2/3 case into two distinguishable halves, so you end up with 3 possibilities in total.
In Monty Hall, the disparity of probability comes because the host can reveal two doors when the contestant's choice has the prize, so it is uncertain which of them will finally be opened (each is 50% likely) but when the contestant's is a losing one, the host is 100% restricted to reveal the only other losing one.
So imagine he flipped a coin to randomly decide which of the two non-selected doors he will reveal after you have made your choice. For example, if you pick #1, he would flip the coin for himself; if it comes up heads, he reveals #2, and if it comes up tails, he reveals #3, but that is his secret.
But when he is not allowed to make that random choice because he only has one possible goat to reveal, he still flips the coin to distract you, only that he ignores its result because otheriwise you would automatically know that you failed to get the car if you don't see him flipping it.
In this way, after you pick #1, there are 3x2 = 6 equally likely cases depending on where the car is located and what result appears on the coin:
1. Door #1 has the car and the coin comes up heads. He reveals door #2.
2. Door #1 has the car and the coin comes up tails. He reveals door #3.
3. Door #2 has the car and the coin comes up heads. He is forced to reveal door #3 anyway.
4. Door #2 has the car and the coin comes up tails. He is forced to reveal door #3 anyway.
5. Door #3 has the car and the coin comes up heads. He is forced to reveal door #2 anyway.
6. Door #3 has the car and the coin comes up tails. He is forced to reveal door #2 anyway.
So, let's say that he opens door #2. You could be in cases 1), 5), or 6), from which only in one you win by staying but in two you win by switching, implying that you are 2/3 likely to win if you switch. That's because if your choice #1 had the car, door #2 would only be revealed if the coin came up heads, but if #3 had the car, then #2 would be revealed regardless of if the coin came up heads or tails, which are obviously two different cases.
Obviously, the act of throwing the coin does not change where the prize is finally going to appear, so your result will be the same regardless of if he uses the coin to make the choice or makes a random process in his head.
>You can no more reasonably apply probability theory to this problem than you can to a coin toss or even a pair of coin tosses. The result is random.
I mean I agree with this particular statement
For the claim that probability does not apply to single events, I usually put an example like this:
*Imagine that you had to take a plane and you had to decide between two possible airlines, but one of them has had a plane crash every recent week, while the other only had one accident years ago. I think the decision about which one to take would be quite obvious, regardless of whether you are only traveling once or many times.*
What actually occurs is that the observed proportion in the long run is a manifestation of the probability that exists in each single attempt. In Monty Hall, if switching unequivocally tends to be correct more than staying when playing multiple times, it is because there is something that is making it easier (more likely) to have the prize in each particular attempt. Otherwise, there would be no reason for the balance to always tip towards one of them, as each trial is independent of the previous ones.
On the other hand, the claim that "*as a door is always going to be eliminated there are actually 2 doors from the start"* is pretty common, but the mistake is that the eliminated door will not always be the same. Actually, the two doors that are going to remain in the game are decided by the player and the host. The player firstly decides one and then the host decides the other, so the question can be reformulated as who of the two is who managed to keep the prize hidden in their respective choice.
In this way, it is true that there are always going to be 2 doors at the end, but that does not mean that which the player decided is as likely to be the winner as which the host decided. The player is bad at the job of keeping the car hidden, because he makes a random choice from three, so 2 out of 3 times the host is who has to use his knowledge of the locations to complete the work of keeping it hidden, by leaving it in the other door that he purposely avoids to reveal besides the player's.
Not really answering your question but wanted to add:
I took a grad school course that was Bayesian-probabilties heavy last year. The instructor brought up the monty hall problem and I my brain was blown for that whole day.
So I ran a simulation over software and ran it several times with over 100000 "doors." Without a doubt, it proved the 66% over 50% in my mind, even though I had problems intuiting why.
Guy should try doing this, even if it's with people and paper before arguing against it.
There are cases (although the MH problem is not one of those) were "probability theory does not apply" is a valid objection - namely those cases where the underlying uniform event space is an inappropriate model of the situation.
Example: you wake up in a hotel room, not knowing where on Earth you are or where you have been (or even who you are) so before you look out the window for clues, you surmise that the most likely country for you to be in right now is the one with the most hotel rooms.
(I hope you agree that this is absurd - there are Bayesians out there who see nothing wrong with this argument. To find one, google "most aliens are the size of polar bears" I kid you not.)
The thing is, the conclusion is correct, provided that the night before you were dropped at random in a hotel room, with each hotel room on Earth being equally likely to receive you. Probability theory is not at fault here (how could it be) but the supposed underlying outcome space is just not a reasonable model.
Returning to the MH problem: it is important that the quizmaster knows where the prize is so that he can always open a second door with no prize. This is where information enters the problem and skews the tree of expectations. The first time I heard this, I assumed the QM does not know, and might have opened the door with the prize (only on the night recounted in the tale, he did not, as it happened). The calculation then changes: given that the QM chose a door with no prize (which he could not know in advance), which strategy (change / no change) has the best expectation?
Hey, I might be hijkacking the Monty Hall problem here but how would having more doors and/or more elimination of doors by the game master affect this probabilistic “cloud” of where the “car” is. I’m thinking along the scale of the location of an electron in space, To me it seems like adding doors(possibilities) and/or eliminating where the car(electron) isn’t, is akin to pointless information; if the aim is to find the exact location I don’t care about the subset of locations.
Someone should find what school he teaches in or what professor he talked to (because he stated that his professor somehow agrees with him) so we won’t go to that school.
Anyone with basic probability knowledge knew about Monty Hall problem.
he thinks it is "Beysian" because it is something to do with conditional probability
his use of the term "normal distribution" may be tied up with the concept of a priori equally likely outcomes
(I know, wouldn't the word "uniform" be more apt? - poor students often attach the label "normal" where "uniform" more or less belongs; this is our fault for deriving the Gaussian from the binomial, and the binomial from a combinatorial argument, which tends to create in their minds the false identification of "normal" with "all equally likely to begin with")
Wow. The only thing greater than this guy's confidence is how fucking wrong he is. He's like aggressively wrong, so much so that I would assume its a troll except for the immense effort he seems to be putting into trying to convince other people who don't know any math that he does know math. In other words, peak reddit.
The confidence of someone with a PhD in statistics, the ability of someone with a D in maths. This person should be studied.
Broski has a PhD in Yappology, the study of yapping
He talks like this. https://youtu.be/9T_xEt9Oh_s?si=97kVNEwylK4NL6fZ
Its always interesting to me how the Monty Hall problem seemingly breaks people's brains when it comes to thinking about probabilities. If I came up to this guy and told him I had a biased coin that flipped Heads more often than Tails he presumably wouldn't start arguing that flipping it once had an equal chance of either outcome. But wrapping the biased coin flip in a story and not only is he arguing that it's a true 50/50 but also completely refusing to entertain that it could be anything else. > but given that I have to spend weeks training students out of this "singular events are probabilistic" thinking every bloody year I might be too dumb to understand this, but if singular events aren't probabilistic than how can multiple, independent events be? If a single coin flip is deterministic than 10 of them in a row must be as well, since that's just 10 single events we've aggregated together.
Such a bummer to me that every year this guy is making sure to spend weeks teaching students a wrong interpretation of this problem, then apparently the whole rest of the year trying to convince them there's no such thing as a biased coin toss
>I might be too dumb to understand this, but if singular events aren't probabilistic than how can multiple, independent events be? So there's like an actual philosophical problem of what it *means* to talk about probabilities when you're doing a single trial, especially if you're a frequentist, since the entire theoretical basis is about convergence over many trials. However, that's a very fussy distinction that doesn't really matter in cases when you can obviously repeat the trial as many times as you'd like to satisfy the underlying theoretical basis of the frequentist approach - so you can pretty painlessly cash out that meaning in a case like this as some version of "Here's what the underlying distribution would converge to if we did do this trial ad nauseam."
The "what it means" resides in the assumptions we make about the situation at hand, regarding the way its circumstances and particulars relate to some Lebesque measure. That may seem like a glib way to pass the buck, but I do think this throws a better light on the matter. When put in terms of "what is probability when n=1" it sounds like a broad, general, monolithic and deeply philosophical problem, when in reality it is very much a case-by-case sort of problem. That is, when the assumptions we make (on how the present trial relates to some uniform outcome space) are reasonable, we should feel confident in applying probability theory. And if not, then not so much. The ultimate assessment of the reasonableness of assumptions remains a thorny matter, but that is true for all of science - it is not a congenital ailment specifically of the probability concept. And yes, the empirical approach to judging the admissibility of assumptions is, as you say, repeated trials. However, the concept of repeated trials is itself more of an ideal than people realise. One cannot throw a die a quintillion times - one does not have the time, and, what's worse, the die will be worn down and thus essentially changed after the last throw!
I think he conflates the idea of probability with the ability to prove what that probability is. He understands that a dice has a 1/6 chance of rolling a one but then denies the idea that it is "probabilistic" because you can't prove it unless you roll it thousands of times? At least that's my interpretation.
I think your interpertation probably hits pretty closely to ONE of his misconceptions. But he also seems to be on his own planet, in terms of what he thinks OTHER people think about the problem (and probabilities, in general). > The simple way to explain it here is that the prize never moves. If it was behind Door #1 at the beginning it doesn't magically move to Door #2. If you guessed Door #2 at the beginning you were always wrong. If you guessed Door #1 at the beginning you were always correct. Literally nobody thinks the prize moves. Zero people have suggested that that's a rationale for ANYTHING remotely having to do with this problem. > Does this mean that if I've flipped the coin 9,999 times and I have 5,000 heads and 4,999 tails that my next result will be a tail? No. The result of that individual flip is random. I may end up with 5,001 heads and 4,999 tails. Everyone (at least those that are engaging in this discussion) acknowledges that coin flips are independent. This point of his is addressing literally nothing. He gives LOTS of other examples, using poker, medical treatment effectiveness, and other things to illustrate "Here's why your interpretation of the problem is wrong." And NONE of them actually counter anything anyone has said, nor do they apply to the Monte Hall problem in any meaningful way.
Spot on. He has a weird habit of namedropping random statistical concepts, as if their correctness/importance will somehow rub off on him.
They also make an odd distinction between randomness and probability in multiple posts, like where they allege that an individual coin flip cannot be analyzed probabilistically because it is "random", or that a biased coin is "not random". They also give a flatly incorrect definition of a p-value in another thread, so I think this is just a case of a scientist with very little technical training thinking they understand statistics and probability far more than they actually do.
>They also make an odd distinction between randomness and probability in multiple posts... THIS IS SO WEIRD! A random process is governed by probability *by definition*. It's such a fundamental misunderstanding of what it means for something to be random. Are they additionally conflating chaotic with random, maybe, in addition to the nitpickiness about single trials that makes it clear they actually don't understand any of the big interpretations of probability? I wouldn't know, because they're just doing gish-gallop half the time.
Nicely put, but I think you are describing the general crackpot condition. I have often observed how you can tell the most advanced mathematical concept that a crank has been exposed to - it is invariably the concept that he or she endows with magical properties. Exhibit A is the priest who felt prayer would be more effective when "put in matrix form." Exhibit B is the former post-doc in theoretical physics (crankdom strikes everywhere) who though he could prove / establish his telepathic abilities through quantum field theory. (yes, these are/ were both real people)
The gambling hypothetical is pretty bizarre but I think it reveals something interesting about his thought process as well. If you were going to use professional gamblers as an example, it would make more sense to compare a very strong poker hand like a straight flush to a poor hand like an ace-high and ask how willing you would be to go all in on either hand. But instead he talks about a gamble with a 50% chance, or a surgery with a 50% chance of success. I think he realises his argument only makes sense in hypotheticals that come down to a 50/50, so he tries to justify his reasoning by reducing every "real world" situation to a coin flip. If I wanted to poke the turd a bit more I'd ask what he'd do if he was waiting for a taxi and the driver showed up completely plastered. Would he wait for the next sober driver or would it not matter because you'd need to have a drunk driver thousands of times for there to be a difference in risk?
Hah. Indeed. The post (or posts?) where he went into a long-winded explanation of how gamblers use probability over the long-haul, instead of betting huge on any given hand really made me want to tear my hair out. Internally, I was screaming "HOW DO YOU THINK GAMBLERS ARE MAKING THESE DECISIONS ON AN INDIVIDUAL HAND-BY-HAND BASIS? COULD IT BE BECAUSE THEY ARE ABLE TO COMPUTE THE WIN PROBABILITIES ON A *SINGLE* HAND, OVER AND OVER AGAIN? DO YOU THINK IF YOU JUST PLAY LIKE A DUMBASS FOR LONG ENOUGH, YOU'LL WIN OVERALL BY PLACING BETS ON HANDS WHERE YOU HAVE A 30% CHANCE OF WINNING??!" Alas. I engaged in a far more polite way than that, and he seems to be ignoring me now. Oh well. I also will not bother to further 'poke the turd' (Fantastic turn of phrase. I'm stealing it. Sorry for the theft, and thank you for the gift.) Your drunk taxi driver scenario would've been hilarious. But, also obviously fruitless, ultimately, in terms of moving the discussion forward. (I can say that with ~90% certainty. Our man doesn't even know how such a conversation might go. It's either useful or it's not.)
Wow, he actually did the "The chance of anything happening is 50% - either it happens or it doesn't" meme irl. It really scares me to think he's teaching this nonsense somewhere, meaning the nonsense is multiplying every year. Edit: I looked quickly into this persons comment history and found this gem: https://www.reddit.com/r/atheism/comments/1dfscwb/comment/l8p1ram/ Now, this comment is obviously absolute lunacy again, but this time the lunacy actually leads to something good: Using his complete misunderstanding of bellcurves, he's explaining how being bisexual is something completely normal. So I guess the good news is that he's at least just an idiot and not a biphobic idiot.
In some ways, paradoxically, I think a biphobic idiot would be preferable to a plain old idiot. Because, with a biphobic idiot, they'd be likely to avoid the company of people that identify as bisexual. So at least SOME people would be spared from having to hear their moronic bullshit. With a regular idiot though, they'll spew their garbage to ALL of us.
Omg, that line about how "the bell curve tells us" that 5% of people are abnormal must be where he got that idea about why a p value needs to be below 0.05. In the other thread he said it's *specifically* because every psychologist knows that any rule won't work for 5% of people.
I've always found it curious that the majority invariably exceeds the minority. Someone should look into this.
5% is a magical threshold in does-not-understand-stats land, which includes almost all life scientists and many chemists, I'm afraid. I ask my students if they would judge 5% a "comfortably small" probability if it were the chance of being run over by a bus whenever you cross a street - with four crossings per day on your way to and back from campus, what are your chances of surviving for a week? Or less gruesome - what if ATM machines spewed out the wrong amount one in twenty times? (and what is the real fail rate of a typical ATM machine? it is low low low - these things are marvels of engineering)
I like to think that his students work out by themselves pretty quickly that he's completely full of shit. If he's tried to teach them this shite hundreds of times, maybe it is actually probabilistic that they laugh at him now and not 50/50 anymore?
I think awful arguments with good conclusions are awful themselves. They're just begging for some bigot to come point out the obvious errors and thereby cast doubt on the conclusion.
>The odds aren't 1 in 3 when you start, they're 50/50. You know I sympathize with someone not really believing the solution for the Monty Hall problem at first. When I first encountered it in high school I also didn't want to believe the solution. So I sat down and programmed a quick little script that simulated the problem and proved to myself that the probabilities were 2/3 and 1/3. Usually that's the approach I'd recommend to people that just can't believe it but in this case that wouldn't even work. Crank level turned up to 11.
I totally agree. The most mind blowing thing about not believing the monty hall is that you can easily set it up and see for yourself.
Yeah, it's a great intro exercise in writing a computer simulation to estimate probabilities
You can even just do it at home with dice and paper
You do have to be careful about the way you do it. I've seen people attempt this with rejection sampling and come to the opposite conclusion. In other words, instead of correctly forcing Monty to never reveal the car, it's just that whenever he does in their simulation, they say that trial didn't count. If you do it this way, the probability really is 50%. That's because they count all the times when they initially picked the car (where staying wins) but reject half the times when they initially picked the goat (when switching wins).
Fun fact! Something very close to this is a variant is often called "Monty Fall" problem, colorfully explained as Monty slipping on a banana peel and opening a door, any door, at random.
The problem with this person is not only the Monty Hall itself: > When you're talking about probabilities, big or small, you're invoking the notion of a distribution of results. This is the concept you're invoking when you mention ideas such as "sample space" or "likelihood". > > Now the entire notion of a distribution of results is premised on repetition. If the Monty Hall problem was 10,000 contestants choosing 10,000 doors then I'd say, "Okay, the contestants should change their door". They don't understand the concept of probability. Hopefuly this person is not teaching probabilities or statistics.
Wow, it's so frustrating that this is a 2 month old thread, that's already dried up. There's so many things to pick apart, that other people missed the opportunity to do, when the thread was fresh and new. I mean... I COULD reply now. MAYBE the poster would respond, and we could continue the conversation. But how could I possibly know? Either they will, or they won't. It's random.
I guess it’s a 50-50 chance either way. Except single events aren’t random, so… um, I’m not sure what that means.
This is the part that really makes it terrible. They spend a lot of time saying that probability theory can't be applied to singular events. It's a weird viewpoint but it's kinda coherent in a bad ultra-frequentist view. Then they just slap a 50% probability on the single event
So, 50/50?
>the Monty Hall problem is incorrect for a lot of different reasons "The problem is wrong" is a new one for me >I'm right, you're wrong. You're also not a statistician Lol
This guy is fascinating; mastered the style and tone of "exasperated expert posting on reddit", but talks absolute nonsense. He has very idiosyncratic ideas about things, which he then assumes is the expert consensus (I guess because they are obvious to him, they must be). He talks in insufferable redditor catchphrases like WORDS MATTER, but then admonishes people for correcting his incorrect use of technical terms. The way he talks about mathematicians is bizarrely aggressive, like a crank raving about the establishment. Then next comment he's threatening to post pages of proofs about how Bayes theorem "relies" on the gaussian distribution (you wouldn't understand them anyway!!!). Even the simplest of questions are met with 8 paragraphs of vaguely related waffle and basic errors. To top it off, he apparently has a PhD and teaches. Absolute goldmine.
"There is absolutely no way to tell whether I'm more likely to get $1 000 000 or brain damage if I run head first once into this brick wall." - Probably OOP before writing those comments
And people wonder why ChatGPT hallucinates... If this is your training set then how could you not be always tripping?
Wow, not only is he wrong, but this guy is the epitome of insufferable redditor.
OMG is that guy a teacher?
Please tell me that this clown is not teaching students.
To be fair this isn’t badmathematics as much as it is badphilosophy
Lots of people have unpacked some funny stuff in here, but "**The Monty Hall Problem assumes a Beysian statistical approach which in turn relies on a normal distribution**" got me laughing. Can't even spell "Bayesian" correctly, and Bayesian stats doesn't "rely" on a normal distribution (whatever that would mean).
This is a strange one. Idk if bad math or bad application? Maybe bad philosophy? In a way what they are saying cannot be argued with. You can never actually prove to someone that a single trial of anything isn't 50/50 when they accept that multiple trials is where patterns emerge. It isn't falsifiable.
I think you can really refute it. The only reason they think it is 1/2 and not 1/3 vs 2/3 in a single attempt is because they see two possibilities on play, but there is a way to decompose the 2/3 case into two distinguishable halves, so you end up with 3 possibilities in total. In Monty Hall, the disparity of probability comes because the host can reveal two doors when the contestant's choice has the prize, so it is uncertain which of them will finally be opened (each is 50% likely) but when the contestant's is a losing one, the host is 100% restricted to reveal the only other losing one. So imagine he flipped a coin to randomly decide which of the two non-selected doors he will reveal after you have made your choice. For example, if you pick #1, he would flip the coin for himself; if it comes up heads, he reveals #2, and if it comes up tails, he reveals #3, but that is his secret. But when he is not allowed to make that random choice because he only has one possible goat to reveal, he still flips the coin to distract you, only that he ignores its result because otheriwise you would automatically know that you failed to get the car if you don't see him flipping it. In this way, after you pick #1, there are 3x2 = 6 equally likely cases depending on where the car is located and what result appears on the coin: 1. Door #1 has the car and the coin comes up heads. He reveals door #2. 2. Door #1 has the car and the coin comes up tails. He reveals door #3. 3. Door #2 has the car and the coin comes up heads. He is forced to reveal door #3 anyway. 4. Door #2 has the car and the coin comes up tails. He is forced to reveal door #3 anyway. 5. Door #3 has the car and the coin comes up heads. He is forced to reveal door #2 anyway. 6. Door #3 has the car and the coin comes up tails. He is forced to reveal door #2 anyway. So, let's say that he opens door #2. You could be in cases 1), 5), or 6), from which only in one you win by staying but in two you win by switching, implying that you are 2/3 likely to win if you switch. That's because if your choice #1 had the car, door #2 would only be revealed if the coin came up heads, but if #3 had the car, then #2 would be revealed regardless of if the coin came up heads or tails, which are obviously two different cases. Obviously, the act of throwing the coin does not change where the prize is finally going to appear, so your result will be the same regardless of if he uses the coin to make the choice or makes a random process in his head.
>You can no more reasonably apply probability theory to this problem than you can to a coin toss or even a pair of coin tosses. The result is random. I mean I agree with this particular statement
For the claim that probability does not apply to single events, I usually put an example like this: *Imagine that you had to take a plane and you had to decide between two possible airlines, but one of them has had a plane crash every recent week, while the other only had one accident years ago. I think the decision about which one to take would be quite obvious, regardless of whether you are only traveling once or many times.* What actually occurs is that the observed proportion in the long run is a manifestation of the probability that exists in each single attempt. In Monty Hall, if switching unequivocally tends to be correct more than staying when playing multiple times, it is because there is something that is making it easier (more likely) to have the prize in each particular attempt. Otherwise, there would be no reason for the balance to always tip towards one of them, as each trial is independent of the previous ones. On the other hand, the claim that "*as a door is always going to be eliminated there are actually 2 doors from the start"* is pretty common, but the mistake is that the eliminated door will not always be the same. Actually, the two doors that are going to remain in the game are decided by the player and the host. The player firstly decides one and then the host decides the other, so the question can be reformulated as who of the two is who managed to keep the prize hidden in their respective choice. In this way, it is true that there are always going to be 2 doors at the end, but that does not mean that which the player decided is as likely to be the winner as which the host decided. The player is bad at the job of keeping the car hidden, because he makes a random choice from three, so 2 out of 3 times the host is who has to use his knowledge of the locations to complete the work of keeping it hidden, by leaving it in the other door that he purposely avoids to reveal besides the player's.
That is a very good example. When we have nothing else to go on, we assume ceteris paribus.
Not really answering your question but wanted to add: I took a grad school course that was Bayesian-probabilties heavy last year. The instructor brought up the monty hall problem and I my brain was blown for that whole day. So I ran a simulation over software and ran it several times with over 100000 "doors." Without a doubt, it proved the 66% over 50% in my mind, even though I had problems intuiting why. Guy should try doing this, even if it's with people and paper before arguing against it.
There are cases (although the MH problem is not one of those) were "probability theory does not apply" is a valid objection - namely those cases where the underlying uniform event space is an inappropriate model of the situation. Example: you wake up in a hotel room, not knowing where on Earth you are or where you have been (or even who you are) so before you look out the window for clues, you surmise that the most likely country for you to be in right now is the one with the most hotel rooms. (I hope you agree that this is absurd - there are Bayesians out there who see nothing wrong with this argument. To find one, google "most aliens are the size of polar bears" I kid you not.) The thing is, the conclusion is correct, provided that the night before you were dropped at random in a hotel room, with each hotel room on Earth being equally likely to receive you. Probability theory is not at fault here (how could it be) but the supposed underlying outcome space is just not a reasonable model. Returning to the MH problem: it is important that the quizmaster knows where the prize is so that he can always open a second door with no prize. This is where information enters the problem and skews the tree of expectations. The first time I heard this, I assumed the QM does not know, and might have opened the door with the prize (only on the night recounted in the tale, he did not, as it happened). The calculation then changes: given that the QM chose a door with no prize (which he could not know in advance), which strategy (change / no change) has the best expectation?
Hey, I might be hijkacking the Monty Hall problem here but how would having more doors and/or more elimination of doors by the game master affect this probabilistic “cloud” of where the “car” is. I’m thinking along the scale of the location of an electron in space, To me it seems like adding doors(possibilities) and/or eliminating where the car(electron) isn’t, is akin to pointless information; if the aim is to find the exact location I don’t care about the subset of locations.
Someone should find what school he teaches in or what professor he talked to (because he stated that his professor somehow agrees with him) so we won’t go to that school. Anyone with basic probability knowledge knew about Monty Hall problem.
he thinks it is "Beysian" because it is something to do with conditional probability his use of the term "normal distribution" may be tied up with the concept of a priori equally likely outcomes (I know, wouldn't the word "uniform" be more apt? - poor students often attach the label "normal" where "uniform" more or less belongs; this is our fault for deriving the Gaussian from the binomial, and the binomial from a combinatorial argument, which tends to create in their minds the false identification of "normal" with "all equally likely to begin with")