OK. If you stick, you're not going to win. We know that much. If you change, you have a 2/3 chance of winning, not a 1/2. You would think it was 50/50, right? It's not. If there are 3 doors and you've already opened one of them, that's 1/3 of the doors opened. There are 2 doors remaining. That leaves you with 2/3.
The problem with ALL of this, is that you're adding more and more complexities that weren't part of the original problem. You can't *assume* that these conditions are present. For example, what if the producers wanted to keep the car, and so they moved the car no matter what door you eventually chose to an unchosen door. Your probability just dropped to zero since there is always a door that is not chosen, and thats where they will put the car if you choose correctly. Original problem is fine.
This of it in the concept of ownership. The host OWNS 2 of the doors (probability the correct door is behind his 2 doors-2/3). You OWN 1 door (probability your door is correct-1/3). When he eliminates one of this OWNED wrong doors, the door remaining retains the 2/3 probability, while yours retains the 1/3 probability. Therefore, switching to the still 2/3 probable door is the RIGHT choice.
In the classical Monty Hall problem, where the car is behind a random door, and Monty Hall knows where the car is and always reveals a goat to the player (picking a door at random if the player picks the car right away), then the chance to win if the player switches is 2/3 and the chance to loose is 1/3.
ok. dont travel back and fowrd in time. is because you dont know that you calculate in the 1st place.3 doors to begin is concensual 1/3,ok.ok now imagine YOU choose twice, so if you dont get to see door n1 is a simple sequence of 2 like the coins. if you put in a breaking event, 1 door revelead, you have to refigure, not sequence now just single shot 50/50. what happens is pre test , post test and dependent event (sequence)are diferent concepts to really reajust your odds in dinamic situations
The likelihood of 1/3 changes to 1/2 when you do the choosing both times. The continuance of the 1/3 predicate is based on the person showing you the cups knowing what cup holds what.
it's one more different way to say it's the same. if you realise is a double negative meaning "switch and win"= "stay and loose"="inicial pick goat"=2/3.
We already know that from the start in a sequence of games. and getting it the same reversed only proves there's actually no advantage in switching in a certain game. is reduntant...
IOkay, so it's a 2/3 shot you got it wrong on your first shot and chose a goat. Then they show you a goat and offer a switch. Since all that is left is the car and a goat and that two out of three times you have chosen wrong on the first guess and given that the other door is the car, switch and your odds are increased. Granted you man be screwing yourself...but the odds are with you to switch. I don't get the argument.
well the argument is that you are chaining 2 events and what yu get in the end is the same partition you had in the start 1/3 vs 2/3. it's an ilusion to think there's an advantage of switching as what you get is dependent of your inicial pick in reverse- the "switch" matter. it is simply semantic and not probability, you are still refering to first event. god please get it!
In fact the second step beeing inocuous (meaning no advantage cause you can't tell what your pick was) leaves you with the inicial oods, presented in reversed as to "switch", instead of "2n pick". Obviously semantic isuae because if it was a "2nd pick" you wouldn't doubt to call it 50/50, now would you?
The two events ARE chained, because you are makeing TWO choices! If something is done in series the past effects the future. I flip a coin twice, each flip is a 50/50 as to heads or tail, but .the odds of me getting heads both times is 1/4 right? Because the previous event has influence. Otherwise I'd be an idiot and say it was 50/50. and (before I get any kind of hate filled response) I'm in no way calling you and idiot, but you ARE dead wrong this time.
Ok you call them chained and you exemplify with the coins. well as with the coins the are INDEPENDENt events, one does not influeence the other's oods. In fact it could if the first pick was disclosed, but it NEVER IS so you cant call it an event, and you only make one choise in the end, otherwise ....yes :). so your second pick is as good as the first. and swicthing back would be the same!!! try it!cheers
Okay, as far the coin flipping problem each flip is indepedent, however if asked about a coin being tossed x amount of times in y order...each flip is independent but the chance of a certain outcome or winning outcome depends on the previous cases. You ask me to try it....have you? Your numbers are ass backwards, you just don't want to admit it.. Infact, if you honestly believe your odds to be true...I have a poker game every Tuesday. Your MORE than welcome to come.
as to pocker if someone flashes a joker on you your oods remain the same. .. but you know what they say "players win and winners play".have a lucky day!
huh?! IF I'm reading this right I'd argue that first, any respectable game of poker will never use a joker. But more importantly, if you're flashed any card, joker, ace, seven, or anything really....that card being flashed should effect decision. There is a reason people try to hide their cards you know. Whether spades, nines or whatever you are drawing out of a defined set. So what you know showing can not be drawn again. Like this Monty problem, the past events should effect future choices.
The odds of getting heads 2 times in a row is 1/3. The chance of getting 2 heads in a row is 1/4. Its confusing i know. There are never good sources to learn about words or math. Good thing i could help out :D.
no mather what your name or alledged I.q. is , it's wrong.breaks rules of statistic. pre-test and post test recalculation of probabilities enters altering events and not solutions, that circles it. it's amazing how such illusion can crack people. best pre and post test or "event" probabilitie calculation e.g would be a couple of coin trous. 2 equal at start would be 0.25. 1 equal afterthe first would be 0.5. the "head or tails" result is irrelevant (always0.5) get it??? ok rest is romance
but what if monty doesn't know where is the car and randomly opens a door? if it opens a door and you see that there is the price then there is nothing you can do, but what if you see a goat and you know that monty did not know if there was a goat? does it make any difference if you change the door when that goat is revealed? i think that it does not make any difference.
aslong as monty opens a door with a goat, it is always your best option to switch, it does not matter if he knew where the prizes were or not. However, if he doesn't know where the prizes are placed and he opens a door with a car you're screwed.
it does matter if monty knew where the prize was. if he opens a door with a car you're screwed, i agree to that, but if he opens a door with a goat then it doesn't matter if you switch or not. I know that it looks strange but trust me that this is true. I made a program simulating this. You don't have any advantage (or disadvantage) if you switch in this case.
If Monty picks at random, (the assumption that he does not know where the car is), the chances of success in switching returns to 50% or 1/2. When he is forced to reveal the goat, 2 out of the six possibilities are eliminated, because he cannot reveal the car. Taking this into account, her conclusion is correct, that you have two-thirds a chance of winning the car, if you switch, when in the beginning you have two-thirds of a chance to pick a goat. Clear as mud??
Most of her explanation is correct, except when, at 2:22, she states the premises by which the monty hall paradox is predicated. She states that this problem must be predicated on two premises: 1) Monty Hall picks at random the door to reveal after you make your choice, and 2) He offers you the option to switch. She got the first premise wrong. In fact, this problem only works when Monty knows what is behind each door and deliberately picks a door with the goat.
You're cute. You have a 66% chance of going on a date with me. so gimme an email. Are you part Irish and part cute? Yhat's a 66% probability that you qualify for a date. This means you have a good chance that we are compatible. I can even do math with you in spare time.
Its not simple at all if the host selectively offers swaps or follows a pattern of which of two loss doors to open. If events are NOT random, statistics become worthless or even less than worthless.
Well for me this is math and basically it is just about itself. It's fun being able to go through the possibilities - but they are just that: possibilities. In reality the gameshow host - if possible - uses reverse and multiple-reverse psychology. But of course the contestant figures that out, so a mind game is the result. This scenario is a little hard to break down to hard data. So you have a strong point here. Still these problems are fun seen as pure math: they keep our brains active.
The big issue is how to value statistics. Statistics require RANDOM samples. Getting random data is extremely difficult. For instance in polls, you are never random because certain groups of people would be more willing to participate in a poll than others.
Same in physics (=applied math): is an experiment representative? Most of the time not; so you have to make more experiments and include as many parameters as possible. To fully understand any process we need an infinite number of experiments and include the full analysis of an infinite number of parameters in each. Meaning: we will never fully understand anything, including my post ;-)
This is pretty simple problem. I am taking an intro statistcs class at UCSB and this would have been about as hard as the simplest problem on our first test. I dont understand why this is difficult for people to understand.
Absolutely. It took me quite some time to go through this problem step by step (some of the most complex added-on scenarios still have me lost). If one sees this vid without knowing and understanding the others, it's a big: Huh???
I suspect people also get duped by thinking you have three doors to choose from. Well, you dont...you have just TWO doors to pick from because Monty eliminates one...ALWAYS!
you are tard math wins. learn what probability is dumb ass. you have a 2/3 or 1/3 (depending on switching or not) chance of winning cause it starts with 3 doors. they even draw pictures and explain the probability yet you still dont get it. let me guess you are bad at math?
Let me guess, you didn't realize that this post of mine was 28 days old? Its counter intuitive so many people think its 50-50 until they replay the scenario in their own head.
I don't buy it! The two doors that are left both have an equal chance of holding the car. That equal chance used to be 33% versus 33% and after eliminating the third door that equal chance has now become 50% versus 50%. I know people say its just intuition but its intuition + logic as I just explained.
I have recorded attempts of this. It seams you always ahve a 50 50 chance when the dore is changed. trys|wins/loss 10|5/5 50|25/25 500|244/256 1000|490/510 1500|737/763 2000|1000/1000 But short run its even 50/50 I thought it was not going to turn out even like that but It is. So if dore is changed it don't matter.
Wow, that´s a good combination! You´re smart AND beautiful! I´m not familiar with the show since I don´t live in the US but... what the hell, great explanation!
That's right. If Monty sticks you with your bad choice, your probability of winning is zero.
The probability on the left side of the page is the probability that each of those situations will occur, not the probability that you'll win if it happens. You have a 1/3 chance of getting stuck with your wrong answer, in which case you always lose.
Yes, if the doors were made of clear glass, but the contestant was BLIND. And Monty said "Ok, I just opened one of the doors (but Monty doesn't say WHICH DOOR he opened) Then you are back to the original problem ===> Thus "ALWAYS SWITCH" because it is a 2/3 chance to YOUR ADVANTAGE.
So this blind guy now wins a car that he can drive home. Yeah, that'll work.
But, for argument's sake, what if we were to raise that cash amount to increments of sixths of the car's value? 1/6, 1/3, 1/2 to compensate for the chances. That way, we could modify the win/lose situation into something more dependent on actual value. What do you think? (2/2)
Hmm. I think Monty did that sort of thing, too, but it's been a long time since I watched the show.
To turn the decision into a coin flip, Monty would have to offer 1/3 of the price of the car in cash. Then if p is the price of the car, your expected earnings would be (2/3)p if you switched and (1/3)p + cash if you stayed.
I don't know how it is in your country, but in the German version of the game show, the host sometimes offers cash to influence a candidate's decision. Either to stay or switch. Compared to a car, those amounts are minute. (1/2)
Not relevant to the problem itself, but...when did "Marilyn Vos Savant" write about this? I heard this problem several years ago from Tom and Ray Magliozzi, aka Click and Clack, on the radio show "Car Talk." It's also in their book "A haircut in horse town."
According to Wikipedia, the MHP appeared in _Parade_ in 1990 and on _Car Talk_ in 1998. The problem itself is older than that, but MvS's column was the first to lead to a national kerfluffle.
Hm, there always seems to be one Monty Hall/contestant strategy in this problem. It can be nice in order to explore strategy and incomplete knowledge, but it's unfortunately often used to hit people over the head with probability theory. Anyway, nice work. Good to see another interpretation that doesn't follow the norm.
It's funny, I actually just heard about this problem for the first time recently in a book called "Chance" by Amir Aczel. It's a pretty casual read, mostly about Subjective Probability and how you can apply it to life (stock market, gambling, love, etc). Great video, by the way!
I don't believe it. You made me watch a <12 min video about statistics and I actually enjoyed every minute of it. This can't be right. Speak, what eldritch power do you hold over me, woman?
The power is not my own, but that of MATHEMATICS, which captivates all within range with its rigor and beauty. Either that or you were hypnotized by the background.
P.S. You taught me a new word. I had to go look up "eldritch" -- I'd heard it before but had no idea what it meant.
THis is great! 3 different perspectives about the M.Hall problem! This is the beauty of youtube - it's an epicenter of learning and sharing knowledge.
I'd say that the problem is as simple as MVS presents it, given that the preconditions she assumes can be established empirically (or at least, all contrary theories have been rejected). It's also interesting that LMAD provides empirical evidence of Bayes' theorem, since people who switch actually do win about twice as often. I never quite believed in subjective probability until I heard the empirical evidence.
The version that appeared in her column, I think, did not refer to LMAD specifically, but to a similar but hypothetical game.
The Wikipedia article seems to say that the "Monty Hall Problem" version of the game was never played on LMAD.
"The problem is actually an extrapolation from the game show; Monty Hall did open a wrong door to build excitement, but did not allow players to change their choice."
I'm so old I actually watched LMAD but too old (or too young) to trust my memory in the face of a counterclaim. My memory is that he did let people switch. It's possible the procedure was changed at some point, or that he wasn't consistent. I've also read (don't remember where) that switchers actually won twice as often as non-switchers (which would imply switching was allowed). In any case that outcome (though not, of course, the original conditions) has been verified in simulations.
Haha. I remember watching it when I was very young, but all I remember are the zany costumes, so I have no idea whether you're right about the switching.
But yeah, people have definitely run simulations of the problem under Marilyn's assumptions (and probably in a few other scenarios, too).
Interestingly, classical statistics (AFAIK) can't help you decide which door to choose. Suppose (WLOG) you choose door 1 and door 2 gets eliminated: objectively, the prize is either behind door 1 with probability 1 or behind door 3 with probability 1. You just don't know which hypothesis is correct, and there is no basis for rejecting either hypothesis. But clearly one choice is better. This example calls into question the classical approach used to evaluate scientific research.
I'm not sure you can draw that parallel. (I also don't know what you mean by "classical statistics.")
This is a hypothetical game, which means that we know the entire situation beforehand, including all the probabilities. We know, for instance, that the prize is initially equally likely to be behind each of the three doors, because we've defined the problem that way.
In science, we don't know the original probabilities. We can make some assumptions, but the problem is much fuzzier.
LMAD was an actual game, not hypothetical, and MH could have given people a choice, whether or not he actually did (& I don't trust Wiki on that). I see the scientific community as a contestant on a game show hosted by Mother Nature. The contestant has some set of prior probabilities, which are subjective but obviously relevant to interpreting new data. If the contestant only believes in objective (classical) probabilities, he will make non-optimal decisions.
Imagine a shrink treating depressed patients with St.John's Wort. He thinks based on experience there is a good chance it is effective. Then he hears that a recent study "failed to find evidence of effectiveness." If he believes only in objective probabilities, he'll change his opinion. If he believes in subjective probabilities, he'll look at the study. If it shows statistically insignificant evidence of effectiveness (ignored in the press release), it might strengthen his opinion.
Note that, in the original version of the last comment, I used feminine pronouns. But "she" has one more letter than "he", and YouTube rejected my comment. I think it's time for a feminist protest against comment limits ;-)
LMAD is an actual game, but the MHP is a hypothetical mathematical game. It is well-defined (assuming we can all agree on the assumptions we want to make), and we know the prior probabilities.
This might be a result of my not understanding the difference between subjective and classical probability (I didn't know there was a distinction until today), but I don't think classical probability would give you a 50/50 split between the two remaining doors.
Hmm, I was going to type more, but rereading your comments, I think I see what your point is. I'm not sure whether it can play nicely with my point or not. Blargh. Perhaps I shouldn't post comments at *:** in the morning. =)
Okay, now that I'm awake, here's the particular bit I don't agree with:
"...objectively, the prize is either behind door 1 with probability 1 or behind door 3 with probability 1. ...there is no basis for rejecting either hypothesis."
There is a basis for choosing to switch. I guess you could call it subjective because the contestant, Monty, and a person who walks in after door 2 is opened w/o knowing what has happened would all assign different sets of probabilities.
But this is probably not what subjective probability really is, because if it were, then all probability (with the possible exception of quantum physics) would be subjective. If we weren't always working with incomplete knowledge, then every probability would be either 0 or 1. Classical probability must allow values between 0 and 1, otherwise why would anyone study it?
Classical statistics is used to study nondeterministic processes. You make the valid point that such processes don't really exist (except at the quantum level). But at least there are processes (e.g. a coin toss, considered before the fact) we can reasonably pretend are nondeterministic. But when the process (e.g. placement of a prize behind a door) has already taken place, it's hard to pretend that the outcome has not already been determined.
To me the difference between a the "deterministicness" of a coin flip and of prizes behind doors seems to be only a matter of degree. We can come up with a useful strategy only by pretending that the outcome has not been determined (up to the point we start opening doors, anyway). I see no reason not to pretend.
But you don't pretend that the outcome has not been determined; you acknowledge (critically so) that Monty knows which door the prize is behind and acts accordingly. And even as Monty is acting, you think in terms of probabilities.
Yeah, exactly. That's different than saying that it's either behind door 1 or door 3 with probability 1, so we have no reason to prefer one or the other.
That's what I thought you were saying initially, anyway. Maybe I misunderstood.
I said there was no basis for rejecting either hypothesis. Classical statistics treats probabilities as facts about the world (e.g. a fair coin has a 50% probability of coming up heads). In the LMAD example you need to use probabilities as representations of states of knowledge, which is different.
Mkay, I think I see your point now. To me there's still no difference (except one of degree) between not knowing whether the coin you're about to flip will come up heads, and not knowing which door the prize is behind. I guess it's all in how you interpret the "meaning" of probability, which is what the whole subjective/classical split is about in the first place. I think.
I think there is a qualitative difference, because the solution to the LMAD problem depends on the premise that the objective reality is predetermined. (One particular door has the prize behind it, and Monty knows which door that is, and you know that he won't open that door, which is a critical assumption in the logic of why you should switch -- in the original formulation, anyhow.) With a coin, the objective reality might as well be truly random.
In practical applications it makes a difference, because much decision making is based on assumptions about objective reality, so it often ignores uncertainty unless that uncertainty can be considered objective and therefore built into the assumptions. For example, global warming didn't become a big issue until scientists were convinced of the theory's correctness. In a world of subjective probability it should have been an issue as soon as the theory became "possibly correct."
I'm with you on the practical implications. People ought to take probabilities into account, of course. To what degree they accurately assess those probabilities...I don't know.
I trust that scientists do a pretty good job of it. I think policymakers, voters, etc. sometimes misunderstand what it means for something to be "uncertain" or "a theory," and with something like global warming, that can get us into a whole mess of trouble.
I see the difference now. The "random" part (assigning the prize to a door) takes place before the problem begins.
What, then, of an game in which you flip a coin with your eyes closed? The coin is either heads or tails with probability 1, but you don't know which. Your friend, whose eyes are open, does. In this case your friend's knowledge doesn't give you any information -- is that still subjective?
I'd say you can still treat the coin probability as objective, provided that your friend's knowledge is irrelevant. From your point of view, it's exactly as if the probability were truly objective (as if the outcome depended on a quantum event).
I don't trust that scientists (at least in "objective" sciences like climatology and physiology) do a good job of assessing subjective probabilities. (Economists do a better job because they're used to thinking in terms of subjectivity.) A given scientific model may allow for a range of outcomes depending on uncertain events, but you seldom see a scientist who disagrees with a given theory saying that we should nonetheless take action because it might be true.
I take issue with the last bit -- what does it mean for a scientist to "disagree" with a given theory? If he thinks the theory is ridiculously unlikely, then I'd say he's justified in not saying we should take action on it.
Just because economists might do a better job of assessing subjective probabilities (an assertion I haven't the slightest idea how to attack or defend), scientists don't necessarily do a poor job of it.
Especially when it comes to error analysis, scientists are very aware of what they know and don't know, how well they know what they know, and how that affects the subjective probability of such-and-such being objectively true.
A scientist faced with a data point suspiciously far from its expected value can assign a specific probability to that data point's being a statistical fluke or evidence of a new phenomenon, even though only one of those is objectively true. If this isn't the definition of subjective probability, then I misunderstand that term.
What you describe in the last reply is certainly subjective probability, but I don't think it is what most scientists do. Usually, they look at the hypotheses that there is or is not a new phenomenon, each imagined in turn to be objectively true, and consider the likelihood of the new data point under each hypothesis. I imagine that in some fields Bayesian techniques using subjective probability have become common, but they certainly are not standard procedure for science in general.
...in part because they're very difficult to use in an academic context, since you have to look at a variety of assumptions about what a reader's subjective beliefs were to begin with. In fact, I don't like reading papers that use these techniques because they're too damn complicated. But the Monte Hall Paradox makes me think they might be worth the trouble, because it shows an example where classical statistical hypothesis testing methods can't give you the right answer.
Suppose "disagree" means "believe the case is not yet convincing." This is the position taken, e.g., by scientists skeptical about global warming. Why has nobody said, "The case is not yet convincing, but the [subjective] risks are so high that we should act on it anyway"? (Even if the probability is only 20%, the probability-weighted costs of waiting are high.) This leads me to assign a low subjective probability to the belief that most scientists believe in subjective probability.
Nobody has said that? I haven't been following the debate especially closely, but if that's true, it surprises me. I can see why a scientist wouldn't say something like that to a general audience, but to a scientific audience...surely they would, wouldn't they?
I haven't been following it closely either, so I could be wrong, but I haven't heard anyone (except a few economists) say that, and I've heard plenty of statements taking "yes" or "no" positions on global warming (where "no" means, "Since I don't yet find the case convincing, I'm not going to consider the implications of the possibility that it's right").
Isn't the general audience exactly who needs to hear it? It's not hard to put: "I'm not convinced, but a lot of people I respect disagree, and I could be wrong. If I'm wrong, the dangers are quite high, so it's prudent to plan for the possibility that I'm wrong." I don't think they would say it to a scientific audience, though, because scientists are interested in the science itself rather than the policy implications, and they would be expected to draw their own conclusions.
cool
JosiasCavalcante 9 months ago
girls shouldn't do math
go do ballet
coooldude777 1 year ago
OK. If you stick, you're not going to win. We know that much. If you change, you have a 2/3 chance of winning, not a 1/2. You would think it was 50/50, right? It's not. If there are 3 doors and you've already opened one of them, that's 1/3 of the doors opened. There are 2 doors remaining. That leaves you with 2/3.
MissDelphilia 1 year ago
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Gremel 1 year ago
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Gremel 1 year ago
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gothicsolace 1 year ago
in future videos please stop clicking your tongue. i just couldnt finish watching it because of that. just a helpful tip. good stuff though.
Nesnahed 1 year ago
The problem with ALL of this, is that you're adding more and more complexities that weren't part of the original problem. You can't *assume* that these conditions are present. For example, what if the producers wanted to keep the car, and so they moved the car no matter what door you eventually chose to an unchosen door. Your probability just dropped to zero since there is always a door that is not chosen, and thats where they will put the car if you choose correctly. Original problem is fine.
LesHut 2 years ago
For everyone saying that it's 1/2 - READ:
This of it in the concept of ownership. The host OWNS 2 of the doors (probability the correct door is behind his 2 doors-2/3). You OWN 1 door (probability your door is correct-1/3). When he eliminates one of this OWNED wrong doors, the door remaining retains the 2/3 probability, while yours retains the 1/3 probability. Therefore, switching to the still 2/3 probable door is the RIGHT choice.
Goldiney 2 years ago
In the classical Monty Hall problem, where the car is behind a random door, and Monty Hall knows where the car is and always reveals a goat to the player (picking a door at random if the player picks the car right away), then the chance to win if the player switches is 2/3 and the chance to loose is 1/3.
mrKirosana 3 years ago
ok. dont travel back and fowrd in time. is because you dont know that you calculate in the 1st place.3 doors to begin is concensual 1/3,ok.ok now imagine YOU choose twice, so if you dont get to see door n1 is a simple sequence of 2 like the coins. if you put in a breaking event, 1 door revelead, you have to refigure, not sequence now just single shot 50/50. what happens is pre test , post test and dependent event (sequence)are diferent concepts to really reajust your odds in dinamic situations
giovea 3 years ago
The likelihood of 1/3 changes to 1/2 when you do the choosing both times. The continuance of the 1/3 predicate is based on the person showing you the cups knowing what cup holds what.
SomethingSeaVlog 3 years ago
it's one more different way to say it's the same. if you realise is a double negative meaning "switch and win"= "stay and loose"="inicial pick goat"=2/3.
We already know that from the start in a sequence of games. and getting it the same reversed only proves there's actually no advantage in switching in a certain game. is reduntant...
giovea 3 years ago
IOkay, so it's a 2/3 shot you got it wrong on your first shot and chose a goat. Then they show you a goat and offer a switch. Since all that is left is the car and a goat and that two out of three times you have chosen wrong on the first guess and given that the other door is the car, switch and your odds are increased. Granted you man be screwing yourself...but the odds are with you to switch. I don't get the argument.
jediforcecny 2 years ago
well the argument is that you are chaining 2 events and what yu get in the end is the same partition you had in the start 1/3 vs 2/3. it's an ilusion to think there's an advantage of switching as what you get is dependent of your inicial pick in reverse- the "switch" matter. it is simply semantic and not probability, you are still refering to first event. god please get it!
giovea 2 years ago
In fact the second step beeing inocuous (meaning no advantage cause you can't tell what your pick was) leaves you with the inicial oods, presented in reversed as to "switch", instead of "2n pick". Obviously semantic isuae because if it was a "2nd pick" you wouldn't doubt to call it 50/50, now would you?
giovea 2 years ago
The two events ARE chained, because you are makeing TWO choices! If something is done in series the past effects the future. I flip a coin twice, each flip is a 50/50 as to heads or tail, but .the odds of me getting heads both times is 1/4 right? Because the previous event has influence. Otherwise I'd be an idiot and say it was 50/50. and (before I get any kind of hate filled response) I'm in no way calling you and idiot, but you ARE dead wrong this time.
jediforcecny 2 years ago
Ok you call them chained and you exemplify with the coins. well as with the coins the are INDEPENDENt events, one does not influeence the other's oods. In fact it could if the first pick was disclosed, but it NEVER IS so you cant call it an event, and you only make one choise in the end, otherwise ....yes :). so your second pick is as good as the first. and swicthing back would be the same!!! try it!cheers
giovea 2 years ago
Okay, as far the coin flipping problem each flip is indepedent, however if asked about a coin being tossed x amount of times in y order...each flip is independent but the chance of a certain outcome or winning outcome depends on the previous cases. You ask me to try it....have you? Your numbers are ass backwards, you just don't want to admit it.. Infact, if you honestly believe your odds to be true...I have a poker game every Tuesday. Your MORE than welcome to come.
jediforcecny 2 years ago
as to pocker if someone flashes a joker on you your oods remain the same. .. but you know what they say "players win and winners play".have a lucky day!
giovea 2 years ago
huh?! IF I'm reading this right I'd argue that first, any respectable game of poker will never use a joker. But more importantly, if you're flashed any card, joker, ace, seven, or anything really....that card being flashed should effect decision. There is a reason people try to hide their cards you know. Whether spades, nines or whatever you are drawing out of a defined set. So what you know showing can not be drawn again. Like this Monty problem, the past events should effect future choices.
jediforcecny 2 years ago
The odds of getting heads 2 times in a row is 1/3. The chance of getting 2 heads in a row is 1/4. Its confusing i know. There are never good sources to learn about words or math. Good thing i could help out :D.
adamjcc 2 years ago
no mather what your name or alledged I.q. is , it's wrong.breaks rules of statistic. pre-test and post test recalculation of probabilities enters altering events and not solutions, that circles it. it's amazing how such illusion can crack people. best pre and post test or "event" probabilitie calculation e.g would be a couple of coin trous. 2 equal at start would be 0.25. 1 equal afterthe first would be 0.5. the "head or tails" result is irrelevant (always0.5) get it??? ok rest is romance
giovea 3 years ago
What if Monty randomly opens one of the doors that you did not choose? Whould you switch or not if he opens an empty door?
srki22 3 years ago
what do u mean by 'empty door'? the problem only works if monty knows what is behind the doors and he chooses a goat
duckey6161 3 years ago
but what if monty doesn't know where is the car and randomly opens a door? if it opens a door and you see that there is the price then there is nothing you can do, but what if you see a goat and you know that monty did not know if there was a goat? does it make any difference if you change the door when that goat is revealed? i think that it does not make any difference.
srki22 3 years ago
aslong as monty opens a door with a goat, it is always your best option to switch, it does not matter if he knew where the prizes were or not. However, if he doesn't know where the prizes are placed and he opens a door with a car you're screwed.
duckey6161 3 years ago
it does matter if monty knew where the prize was. if he opens a door with a car you're screwed, i agree to that, but if he opens a door with a goat then it doesn't matter if you switch or not. I know that it looks strange but trust me that this is true. I made a program simulating this. You don't have any advantage (or disadvantage) if you switch in this case.
srki22 3 years ago
Really?? That's so confusing lol...damnit...just when i thought i had this paradox figured out lol.
duckey6161 3 years ago
A lot gets lost in type, but I'm going to believe in humanity and say that was sarcasm....right?!! Please say yes.
jediforcecny 2 years ago
hahahah yes it was
duckey6161 2 years ago
No, because you cannot measure human behavior with probability. In other words, there is NOT a 50% chance the player will switch.
Besides, we're looking at the problem from the player's perspective anyway.
shadyparadox 3 years ago
While you can measure human behavior with probability, the probability in this case is NOT 1/2.
SomethingSeaVlog 3 years ago
If Monty picks at random, (the assumption that he does not know where the car is), the chances of success in switching returns to 50% or 1/2. When he is forced to reveal the goat, 2 out of the six possibilities are eliminated, because he cannot reveal the car. Taking this into account, her conclusion is correct, that you have two-thirds a chance of winning the car, if you switch, when in the beginning you have two-thirds of a chance to pick a goat. Clear as mud??
jblow00 3 years ago
Most of her explanation is correct, except when, at 2:22, she states the premises by which the monty hall paradox is predicated. She states that this problem must be predicated on two premises: 1) Monty Hall picks at random the door to reveal after you make your choice, and 2) He offers you the option to switch. She got the first premise wrong. In fact, this problem only works when Monty knows what is behind each door and deliberately picks a door with the goat.
jblow00 3 years ago
she has to stop the clicking sound with her tongue. once that is accomplished, we have a well done vid here. ha ha
acool76 3 years ago
You're cute. You have a 66% chance of going on a date with me. so gimme an email. Are you part Irish and part cute? Yhat's a 66% probability that you qualify for a date. This means you have a good chance that we are compatible. I can even do math with you in spare time.
romansura 3 years ago
This has been flagged as spam show
U suck bitch.
cfhasib 4 years ago
Its not simple at all if the host selectively offers swaps or follows a pattern of which of two loss doors to open. If events are NOT random, statistics become worthless or even less than worthless.
jdohe 4 years ago
Well for me this is math and basically it is just about itself. It's fun being able to go through the possibilities - but they are just that: possibilities. In reality the gameshow host - if possible - uses reverse and multiple-reverse psychology. But of course the contestant figures that out, so a mind game is the result. This scenario is a little hard to break down to hard data. So you have a strong point here. Still these problems are fun seen as pure math: they keep our brains active.
aihoschema 3 years ago
The big issue is how to value statistics. Statistics require RANDOM samples. Getting random data is extremely difficult. For instance in polls, you are never random because certain groups of people would be more willing to participate in a poll than others.
jdohe 4 years ago
Same in physics (=applied math): is an experiment representative? Most of the time not; so you have to make more experiments and include as many parameters as possible. To fully understand any process we need an infinite number of experiments and include the full analysis of an infinite number of parameters in each. Meaning: we will never fully understand anything, including my post ;-)
aihoschema 3 years ago
This is pretty simple problem. I am taking an intro statistcs class at UCSB and this would have been about as hard as the simplest problem on our first test. I dont understand why this is difficult for people to understand.
kauffman88 4 years ago
One word....... HUH?
cloud9srainbow 4 years ago
Absolutely. It took me quite some time to go through this problem step by step (some of the most complex added-on scenarios still have me lost). If one sees this vid without knowing and understanding the others, it's a big: Huh???
aihoschema 3 years ago
I suspect people also get duped by thinking you have three doors to choose from. Well, you dont...you have just TWO doors to pick from because Monty eliminates one...ALWAYS!
izeman458 4 years ago
you are tard math wins. learn what probability is dumb ass. you have a 2/3 or 1/3 (depending on switching or not) chance of winning cause it starts with 3 doors. they even draw pictures and explain the probability yet you still dont get it. let me guess you are bad at math?
cruxbucket 4 years ago
Let me guess, you didn't realize that this post of mine was 28 days old? Its counter intuitive so many people think its 50-50 until they replay the scenario in their own head.
izeman458 4 years ago
He Crux, why don't you take a chill pill.
From you excitement of calling people names, it is so obvious you are not very smart.
Get a Life !!!
Velvet4U 4 years ago
I don't buy it! The two doors that are left both have an equal chance of holding the car. That equal chance used to be 33% versus 33% and after eliminating the third door that equal chance has now become 50% versus 50%. I know people say its just intuition but its intuition + logic as I just explained.
izeman458 4 years ago
kcdclan 4 years ago
huh??? you are dumb. 1/6 + 1/6 = 2/6 = 1/3
KarrotKun1 4 years ago
LOL you dont get it that is the odds of him not changing.
man stuped people..anyways i'ma respond my research.
kcdclan 4 years ago
Wow, that´s a good combination! You´re smart AND beautiful! I´m not familiar with the show since I don´t live in the US but... what the hell, great explanation!
Minhiris 4 years ago
You are awesome.
stretchsje 4 years ago
That's right. If Monty sticks you with your bad choice, your probability of winning is zero.
The probability on the left side of the page is the probability that each of those situations will occur, not the probability that you'll win if it happens. You have a 1/3 chance of getting stuck with your wrong answer, in which case you always lose.
Prepoceros 5 years ago
Yes, if the doors were made of clear glass, but the contestant was BLIND. And Monty said "Ok, I just opened one of the doors (but Monty doesn't say WHICH DOOR he opened) Then you are back to the original problem ===> Thus "ALWAYS SWITCH" because it is a 2/3 chance to YOUR ADVANTAGE.
So this blind guy now wins a car that he can drive home. Yeah, that'll work.
Velvet4U 4 years ago
1/3 and 3/9 are equal to each other.
Prepoceros 5 years ago
YOU > laws of the universe
SonofNewo 5 years ago
Enthusiasm amplifies beauty.
AericWinter 5 years ago
a true and brilliant statement.
OC5 4 years ago
But, for argument's sake, what if we were to raise that cash amount to increments of sixths of the car's value? 1/6, 1/3, 1/2 to compensate for the chances. That way, we could modify the win/lose situation into something more dependent on actual value. What do you think? (2/2)
AericWinter 5 years ago
Hmm. I think Monty did that sort of thing, too, but it's been a long time since I watched the show.
To turn the decision into a coin flip, Monty would have to offer 1/3 of the price of the car in cash. Then if p is the price of the car, your expected earnings would be (2/3)p if you switched and (1/3)p + cash if you stayed.
Prepoceros 5 years ago
Here's food for thought:
I don't know how it is in your country, but in the German version of the game show, the host sometimes offers cash to influence a candidate's decision. Either to stay or switch. Compared to a car, those amounts are minute. (1/2)
AericWinter 5 years ago
Not relevant to the problem itself, but...when did "Marilyn Vos Savant" write about this? I heard this problem several years ago from Tom and Ray Magliozzi, aka Click and Clack, on the radio show "Car Talk." It's also in their book "A haircut in horse town."
scott97 5 years ago
According to Wikipedia, the MHP appeared in _Parade_ in 1990 and on _Car Talk_ in 1998. The problem itself is older than that, but MvS's column was the first to lead to a national kerfluffle.
Prepoceros 5 years ago
You're so cute that it was hard for me to focus on the problem.
dexarouskies 5 years ago
Hm, there always seems to be one Monty Hall/contestant strategy in this problem. It can be nice in order to explore strategy and incomplete knowledge, but it's unfortunately often used to hit people over the head with probability theory. Anyway, nice work. Good to see another interpretation that doesn't follow the norm.
trondreitan 5 years ago
It's funny, I actually just heard about this problem for the first time recently in a book called "Chance" by Amir Aczel. It's a pretty casual read, mostly about Subjective Probability and how you can apply it to life (stock market, gambling, love, etc). Great video, by the way!
jonwedd 5 years ago
I don't believe it. You made me watch a <12 min video about statistics and I actually enjoyed every minute of it. This can't be right. Speak, what eldritch power do you hold over me, woman?
GaeriSummer 5 years ago
The power is not my own, but that of MATHEMATICS, which captivates all within range with its rigor and beauty. Either that or you were hypnotized by the background.
P.S. You taught me a new word. I had to go look up "eldritch" -- I'd heard it before but had no idea what it meant.
Prepoceros 5 years ago
THis is great! 3 different perspectives about the M.Hall problem! This is the beauty of youtube - it's an epicenter of learning and sharing knowledge.
Thanks tons. Great interpretation. Yay math!
clockworkhorrorshow 5 years ago
Awesome. If you don't play poker, you should.
OC5 5 years ago
I'd say that the problem is as simple as MVS presents it, given that the preconditions she assumes can be established empirically (or at least, all contrary theories have been rejected). It's also interesting that LMAD provides empirical evidence of Bayes' theorem, since people who switch actually do win about twice as often. I never quite believed in subjective probability until I heard the empirical evidence.
DClaudeKatz 5 years ago
The version that appeared in her column, I think, did not refer to LMAD specifically, but to a similar but hypothetical game.
The Wikipedia article seems to say that the "Monty Hall Problem" version of the game was never played on LMAD.
"The problem is actually an extrapolation from the game show; Monty Hall did open a wrong door to build excitement, but did not allow players to change their choice."
Have you seen empirical evidence somewhere else?
Prepoceros 5 years ago
I'm so old I actually watched LMAD but too old (or too young) to trust my memory in the face of a counterclaim. My memory is that he did let people switch. It's possible the procedure was changed at some point, or that he wasn't consistent. I've also read (don't remember where) that switchers actually won twice as often as non-switchers (which would imply switching was allowed). In any case that outcome (though not, of course, the original conditions) has been verified in simulations.
DClaudeKatz 5 years ago
Haha. I remember watching it when I was very young, but all I remember are the zany costumes, so I have no idea whether you're right about the switching.
But yeah, people have definitely run simulations of the problem under Marilyn's assumptions (and probably in a few other scenarios, too).
Prepoceros 5 years ago
Interestingly, classical statistics (AFAIK) can't help you decide which door to choose. Suppose (WLOG) you choose door 1 and door 2 gets eliminated: objectively, the prize is either behind door 1 with probability 1 or behind door 3 with probability 1. You just don't know which hypothesis is correct, and there is no basis for rejecting either hypothesis. But clearly one choice is better. This example calls into question the classical approach used to evaluate scientific research.
DClaudeKatz 5 years ago
I'm not sure you can draw that parallel. (I also don't know what you mean by "classical statistics.")
This is a hypothetical game, which means that we know the entire situation beforehand, including all the probabilities. We know, for instance, that the prize is initially equally likely to be behind each of the three doors, because we've defined the problem that way.
In science, we don't know the original probabilities. We can make some assumptions, but the problem is much fuzzier.
Prepoceros 5 years ago
LMAD was an actual game, not hypothetical, and MH could have given people a choice, whether or not he actually did (& I don't trust Wiki on that). I see the scientific community as a contestant on a game show hosted by Mother Nature. The contestant has some set of prior probabilities, which are subjective but obviously relevant to interpreting new data. If the contestant only believes in objective (classical) probabilities, he will make non-optimal decisions.
DClaudeKatz 5 years ago
Imagine a shrink treating depressed patients with St.John's Wort. He thinks based on experience there is a good chance it is effective. Then he hears that a recent study "failed to find evidence of effectiveness." If he believes only in objective probabilities, he'll change his opinion. If he believes in subjective probabilities, he'll look at the study. If it shows statistically insignificant evidence of effectiveness (ignored in the press release), it might strengthen his opinion.
DClaudeKatz 5 years ago
Note that, in the original version of the last comment, I used feminine pronouns. But "she" has one more letter than "he", and YouTube rejected my comment. I think it's time for a feminist protest against comment limits ;-)
DClaudeKatz 5 years ago
LMAD is an actual game, but the MHP is a hypothetical mathematical game. It is well-defined (assuming we can all agree on the assumptions we want to make), and we know the prior probabilities.
This might be a result of my not understanding the difference between subjective and classical probability (I didn't know there was a distinction until today), but I don't think classical probability would give you a 50/50 split between the two remaining doors.
Prepoceros 5 years ago
Hmm, I was going to type more, but rereading your comments, I think I see what your point is. I'm not sure whether it can play nicely with my point or not. Blargh. Perhaps I shouldn't post comments at *:** in the morning. =)
Prepoceros 5 years ago
So what is the probability of going out with me? 1/3 or 2/3
Velvet4U 4 years ago 2
-27/3
DrRetardette 4 years ago
Okay, now that I'm awake, here's the particular bit I don't agree with:
"...objectively, the prize is either behind door 1 with probability 1 or behind door 3 with probability 1. ...there is no basis for rejecting either hypothesis."
There is a basis for choosing to switch. I guess you could call it subjective because the contestant, Monty, and a person who walks in after door 2 is opened w/o knowing what has happened would all assign different sets of probabilities.
Prepoceros 5 years ago
But this is probably not what subjective probability really is, because if it were, then all probability (with the possible exception of quantum physics) would be subjective. If we weren't always working with incomplete knowledge, then every probability would be either 0 or 1. Classical probability must allow values between 0 and 1, otherwise why would anyone study it?
Prepoceros 5 years ago
Classical statistics is used to study nondeterministic processes. You make the valid point that such processes don't really exist (except at the quantum level). But at least there are processes (e.g. a coin toss, considered before the fact) we can reasonably pretend are nondeterministic. But when the process (e.g. placement of a prize behind a door) has already taken place, it's hard to pretend that the outcome has not already been determined.
DClaudeKatz 5 years ago
To me the difference between a the "deterministicness" of a coin flip and of prizes behind doors seems to be only a matter of degree. We can come up with a useful strategy only by pretending that the outcome has not been determined (up to the point we start opening doors, anyway). I see no reason not to pretend.
Prepoceros 5 years ago
But you don't pretend that the outcome has not been determined; you acknowledge (critically so) that Monty knows which door the prize is behind and acts accordingly. And even as Monty is acting, you think in terms of probabilities.
DClaudeKatz 5 years ago
Yeah, exactly. That's different than saying that it's either behind door 1 or door 3 with probability 1, so we have no reason to prefer one or the other.
That's what I thought you were saying initially, anyway. Maybe I misunderstood.
Prepoceros 5 years ago
I said there was no basis for rejecting either hypothesis. Classical statistics treats probabilities as facts about the world (e.g. a fair coin has a 50% probability of coming up heads). In the LMAD example you need to use probabilities as representations of states of knowledge, which is different.
DClaudeKatz 5 years ago
Mkay, I think I see your point now. To me there's still no difference (except one of degree) between not knowing whether the coin you're about to flip will come up heads, and not knowing which door the prize is behind. I guess it's all in how you interpret the "meaning" of probability, which is what the whole subjective/classical split is about in the first place. I think.
Prepoceros 5 years ago
I think there is a qualitative difference, because the solution to the LMAD problem depends on the premise that the objective reality is predetermined. (One particular door has the prize behind it, and Monty knows which door that is, and you know that he won't open that door, which is a critical assumption in the logic of why you should switch -- in the original formulation, anyhow.) With a coin, the objective reality might as well be truly random.
DClaudeKatz 5 years ago
In practical applications it makes a difference, because much decision making is based on assumptions about objective reality, so it often ignores uncertainty unless that uncertainty can be considered objective and therefore built into the assumptions. For example, global warming didn't become a big issue until scientists were convinced of the theory's correctness. In a world of subjective probability it should have been an issue as soon as the theory became "possibly correct."
DClaudeKatz 5 years ago
I'm with you on the practical implications. People ought to take probabilities into account, of course. To what degree they accurately assess those probabilities...I don't know.
I trust that scientists do a pretty good job of it. I think policymakers, voters, etc. sometimes misunderstand what it means for something to be "uncertain" or "a theory," and with something like global warming, that can get us into a whole mess of trouble.
Prepoceros 5 years ago
I see the difference now. The "random" part (assigning the prize to a door) takes place before the problem begins.
What, then, of an game in which you flip a coin with your eyes closed? The coin is either heads or tails with probability 1, but you don't know which. Your friend, whose eyes are open, does. In this case your friend's knowledge doesn't give you any information -- is that still subjective?
Prepoceros 5 years ago
I'd say you can still treat the coin probability as objective, provided that your friend's knowledge is irrelevant. From your point of view, it's exactly as if the probability were truly objective (as if the outcome depended on a quantum event).
DClaudeKatz 5 years ago
I don't trust that scientists (at least in "objective" sciences like climatology and physiology) do a good job of assessing subjective probabilities. (Economists do a better job because they're used to thinking in terms of subjectivity.) A given scientific model may allow for a range of outcomes depending on uncertain events, but you seldom see a scientist who disagrees with a given theory saying that we should nonetheless take action because it might be true.
DClaudeKatz 5 years ago
I take issue with the last bit -- what does it mean for a scientist to "disagree" with a given theory? If he thinks the theory is ridiculously unlikely, then I'd say he's justified in not saying we should take action on it.
Prepoceros 5 years ago
Just because economists might do a better job of assessing subjective probabilities (an assertion I haven't the slightest idea how to attack or defend), scientists don't necessarily do a poor job of it.
Especially when it comes to error analysis, scientists are very aware of what they know and don't know, how well they know what they know, and how that affects the subjective probability of such-and-such being objectively true.
Prepoceros 5 years ago
A scientist faced with a data point suspiciously far from its expected value can assign a specific probability to that data point's being a statistical fluke or evidence of a new phenomenon, even though only one of those is objectively true. If this isn't the definition of subjective probability, then I misunderstand that term.
Prepoceros 5 years ago
What you describe in the last reply is certainly subjective probability, but I don't think it is what most scientists do. Usually, they look at the hypotheses that there is or is not a new phenomenon, each imagined in turn to be objectively true, and consider the likelihood of the new data point under each hypothesis. I imagine that in some fields Bayesian techniques using subjective probability have become common, but they certainly are not standard procedure for science in general.
DClaudeKatz 5 years ago
...in part because they're very difficult to use in an academic context, since you have to look at a variety of assumptions about what a reader's subjective beliefs were to begin with. In fact, I don't like reading papers that use these techniques because they're too damn complicated. But the Monte Hall Paradox makes me think they might be worth the trouble, because it shows an example where classical statistical hypothesis testing methods can't give you the right answer.
DClaudeKatz 5 years ago
Suppose "disagree" means "believe the case is not yet convincing." This is the position taken, e.g., by scientists skeptical about global warming. Why has nobody said, "The case is not yet convincing, but the [subjective] risks are so high that we should act on it anyway"? (Even if the probability is only 20%, the probability-weighted costs of waiting are high.) This leads me to assign a low subjective probability to the belief that most scientists believe in subjective probability.
DClaudeKatz 5 years ago
Nobody has said that? I haven't been following the debate especially closely, but if that's true, it surprises me. I can see why a scientist wouldn't say something like that to a general audience, but to a scientific audience...surely they would, wouldn't they?
Prepoceros 5 years ago
I haven't been following it closely either, so I could be wrong, but I haven't heard anyone (except a few economists) say that, and I've heard plenty of statements taking "yes" or "no" positions on global warming (where "no" means, "Since I don't yet find the case convincing, I'm not going to consider the implications of the possibility that it's right").
DClaudeKatz 5 years ago
Isn't the general audience exactly who needs to hear it? It's not hard to put: "I'm not convinced, but a lot of people I respect disagree, and I could be wrong. If I'm wrong, the dangers are quite high, so it's prudent to plan for the possibility that I'm wrong." I don't think they would say it to a scientific audience, though, because scientists are interested in the science itself rather than the policy implications, and they would be expected to draw their own conclusions.
DClaudeKatz 5 years ago
Very nice!! For some reason, I hadn't thought of combining the two. Anyhow, great post! :)
websnarf 5 years ago