>This "problem" reminds me of a rant with my math teacher, back in school, where she just wouldn't agree that a coin could land on the edge. But this is not the point. You can't apply calculations to a chaotic system and expect predictable results.
Hmm, I guess it would depend on the type of coin as well though? The assumption I made is that the coin was thrown like you would in a coin toss, that is it would be rotating quite fast. I agree that if you just chuck coins in a random fashion that some of them will end up landing on the edge. However I don't see how it can happen if the coin is rotating fast, there simply would not be enough time for the friction forces to stabilize it on the edge before it falls over. Do you recall what type of coin/surface this happened on?
>>6586381 another example of the value of computer literacy if kids were taught basic programming skills in school they'd be able to determine the correct answer convincingly and quickly with a simple monte carlo algorithm, even if they're absolutely terrible at math and critical thinking
All the PHd mathematicians in the 90s couldn't even get it, lol.
>Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D. George Mason University
>You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida
>Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem. Barry Pasternack, Ph.D. California Faculty Association
>>6588203 Three ( or N ) eggs are in the bowl. Only one of them is hard boiled. You select one egg, put it on the table. The chance that the table egg is hard boiled is 1/3 ( or 1/N ). The chance that the bowl has the hard boiled egg is 2/3 ( or (N-1)/N ). The show host breaks one egg ( or N-2 eggs ) from the bowl. The chance that the bowl has the hard boiled egg is STILL 2/3 ( or (N-1)/N ).
1) The host does NOT open a random door, the opened door always reveals a goat.
2) If the problem had 10 doors instead of 3, after you pick a door, the host would open 8 doors instead of only 1 door.
This thread just reeks of condescending. Hate to break it to you guys, but the result is not intuitive. The only reason all of you claim it is so simple is because you have seen it 50 fucking times, probably on this board alone.
>>6586381 for fuck's sake, why can't people write scripts to check it themselves?
It's as if someone claimed that oil and water mix, and then everyone got their heads up their asses and started arguing with each other, instead of just putting oil and water into a container and seeing what happens.
I remember reading somewhere that in the real Let's Make a Deal Monty could choose whether or not to let you switch, and he could psychologically manipulate you into switching or staying. Like, if you knew it was better to switch, he would only offer you the chance to switch if it would make you lose.
>>6588469 >>6588369 >Since you made your choice with no knowledge you still have a 99% chance of having a goat right? Right.
See, that's the part of the argument where I call bullshit. What happened in the past doesn't effect the probability of this new choice. As far as I'm concerned there's two doors and one of 'em has a car behind it. Both doors have a 50% chance of being correct in this situation, changing doors will make no difference on the outcome.
>>6588453 >>6588489 >>6588498 Just write a simulation in your programming language of choice. The more doors you have, the less trials it will take to make it obvious that you should always switch assuming it's a fair game.
>>6588498 >>Black or white fallacy Yes, I was rephrasing your point to show how ridiculous it was. Why would the door you pick suddenly jump from 1% likely to be the car door to 50% likely to be the car door once 98 other doors were revealed?
>>6588498 I'll try to help. Think back to the three doors. How many different ways can you group what's behind them into groups of two? Goat-goat, goat-car, goat-car right? So when you choose a door, you are leaving two doors unchosen. The chances that the unchosen group of two doors contains a car logically is 2/3. This does not change with the revealing of the goat.
>>6588498 It's like this: You have a 2/3s chance of picking the wrong door at the beginning, and if you did then the door the host doesn't open is always correct. It's very simple when you visualize each step separately.
still going to run a 50 door simulation tomorrow but I understand that every time a for it removes it ups the chance of the 'other' door but not the original (because the original cannot be opened by the host)
>>6588507 The thing that makes it "different" than that other door is this: you are right, in the beginning it is the same. When you choose a door even, nothing changes with the percents. The door that contains the car even has a 1% chance of having it as far as you know. It's when the host starts opening doors that things change, as the first door opens to reveal a goat, the chance that the car is behind the remaining 98 goes to 1.01% each, then 1.02% each as the next door is opened.
Probability Concentration isn't real. Proof: A1/3 ... B1/3 ... C1/3 = A1/3...BC2/3 - B1/3 = A1/3... C1/3 I don't care if who accepts or rejects it, but it is what it is. Mathematical Conflation stop existing the second a necessary component is removed.
>>6588538 After the original l pick the host opens one of the other n-1 doors to reveal a goat. This action increases the chances of the group you pick but NOT the original pick because the original pick us exempt from the sheep culling process.
>>6586381 "I DISAGREE. In the game, you are effectively given TWO chances to choose your "winning door". Choice 1 is between 1, 2 and 3 and you have a 1/3 chance of picking the correct door. So you pick door 1 with a 1/3 chance of winning. You are then asked to choose again, after Monty opens door 2, and you have to choose door 1 or 3 and you make this choice by either staying with door number 1 or switching to door number 3. So you switch, or stick, but the odds remain at 50% chance of door 1 or door 3. The odds of 1/3 are now irrelevant now you know that door 2 is not a winner. The odds of picking the correct door on the second choice are ALWAYS 50% or 1/2, EVEN if you had a million doors, and Monty opened 999,998 of the other doors, the second choice is the same risk. UNLESS you are assuming that these doors are all analogous to Schrodinger's cat, where the car AND the zonk are both behind ALL doors - until you open it, when it is forced to choose and present itself as containing either the car, or the zonk." OH GOOD NONEXISTANT GOD!
Here's another way of seeing it. If you were given the choice to either open one or two doors you would always go with two for a 2/3 chance of winning opposed to 1/3. You would also know that one out of the two doors you chose will have a goat. So the reveal of one goat doesn't convey any new information. Switching doors in the original problem is equivalent to picking two doors resulting in 2/3 chance.
So many snot-nosed kids here in need of some education. So let's find a general solution to the Monty Hall problem...
Let p be the probability that Monty reveals a goat, given that the prize is not behind your first-choice door. Let q be the probability that you switch doors, given that Monty reveals a goat.
Note that when p=1, we have traditional Monty Hall. When p=1/2, we have random Monty. When p=0, we have Evil Monty. The value q describes your strategy, with q=0 and q=1 in particular being the "never switch doors" and "always switch doors" strategies, respectively.
(1) Find the probability P of your winning, as a function of p and q.
>>6588717 Fixed the image. Basically after the first choice pathways 2 and 3 are the same. As a circuit this could be optimized by eliminating option 3 (which the host graciously does for us). So for practical purposes, your first choice is always 50% probability of a goat or a car regardless of redundancy in the initial question.
Monty Haul isn't even a question if it's written optimally. There are two doors, one has a goat, the other has a car. You pick one. It is either a car or a goat and you are given the option to switch. So throughout you have a 50% chance of getting either regardless of switching.
Either way, goats and cars are pretty awesome. 100% chance of winning something cool.
>>6588507 >I fail to see what makes it different from the door I originally chose. Oh Lord.... It's different because Monty CHOSE that door based on his knowledge of what's behind each door. Put yourself in Monty's shoes: the contestant (most likely) picks the wrong door. You now open all the doors that don't have a car. The contestant should switch. In the less likely scenario, the contestant picks the right door, and you open all doors but one, any one. In the more likely scenario, the contestant is better off switching, in the less likely scenario the contestant is better off sticking. Which scenario we're in doesn't change after the contestant picks the first door.
So here is the original statement: >Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? Note that it says "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat".
It does not say, "the host, who knows what’s behind the doors, chooses another door which he knows to have a goat behind it..." nor does it say, "the host, who will do this regardless of what's behind the door you've chosen...".
The explanation of the "answer" changes the scenario.
It's a riddle, not a problem of math or logic. In problems, the answer follows from the question, in riddles, you can justify the answer in a way that makes it seem as if it is the best response, but if you don't know the answer beforehand, you're guessing.
Riddles are a classic way to make people feel or look stupid when they haven't committed any actual errors. Marilyn vos Savant a shit.
>>6588900 It says "He opens another door, which has a goat". He WILL ALWAYS choose a goat based on the original wording. It doesn't say maybe has goat, or could have goat, it say he picks a door which has a goat, excluding any possibility of choosing a door which has the car. The only thing that doesn't matter here is the number of the door, which why it says "say #3".
>>6588929 >It says "He opens another door, which has a goat". He WILL ALWAYS choose a goat based on the original wording. No, the original wording doesn't specify what "WILL ALWAYS" happen all, it just asks you what to do if this happens.
You're interpreting it through what you already know of the solution. Read the original wording neutrally.
There's no explanation of the host's reason for opening the door, no statement that he always does so after the player makes his initial choice, no claim that this is even a regular feature on the show.
We know he knows what's behind the doors. His motivation or criteria for opening a door isn't given.
He might only open a door, show you a goat, and offer to let you change your choice if you've already picked the car.
This way, switching is 0%. You can't possibly win if you're going to take an offer to switch. If you steadfastly refuse to switch, you have 1/3 odds, which can't be improved.
Or he might have a goat all dressed up funny he wants to show the audience. Let's say the showgoat is behind door A, a less interesting goat is behind door B, and the car is behind door C.
If you pick door A, he says, "You win a goat!" game show over. If you initially pick door B, he opens door A "Hey, look at this goat everybody! Do you want to stick with your choice or switch to door C?" switching wins, staying loses If you initially pick door C, he opens door A etc., staying wins, switching loses
This way, there's no way to improve your odds. It's completely random, regardless of your strategy.
Or he might want you to win, because audiences prefer a happy ending. If you pick the car on your first prize, he shows one goat... but doesn't offer to let you change, tension mounts... he has a dramatic pause opens the other door with a goat behind it... then the big reveal of the car you won. If you pick a goat, he reveals a goat, and then offers to let you change.
This way, switching isn't just 2/3, it's 100%. You can win every time by switching if he offers. It's completely non-random, if you know what he's doing.
>>6588959 Well yeah if you arbitrarily change the situation so that now he may not let you switch at all despite that never being a part of the original question, then yeah things will be different. I have no idea why you bring up completely irrelevant things though.
Everytime the host opens a door the chances for the closed doors being right increases. People just don't realize that he doesn't open your door too >example with 3 doors >Monty opens one >now you have 50/50 chance to win if you choose a door >but you have already chosen a door with 50% chance (the first one) >changing your choice doesn't make sense
>>6588968 >if you arbitrarily change the situation so that now he may not let you switch at all despite that never being a part of the original question In the original question, you're not given his motivation for offering to let you switch, or any set of rules by which he chose to make that offer. You're only given one situation which arises after you've chosen a particular door.
I've explained why that matters. If you don't understand, go back and read it again, and think harder about it until you do.
>>6589065 How is it stupid? That's the whole point to make it intuitive (I use this for 12-13 year olds).
When it's just "98 of the other doors without the prize open" the kids find it harder because their intuition doesn't like raw numbers without the human element .
The host's motivation makes no difference, it could be a random number generator. As long as the contestant knows none of the doors opened had the prize, it's still a 99% chance the other door has the prize.
>>6589086 If it isn't clear "a human being is trying to help you out because they win too" helps people grasp the statistics better than just "98 of the other doors accidently open and reveal none of them had the prize"
im late but: http://pastebin.com/6MFKCFHW from 100000tests: >>> win by not swapping 16.86% win by swapping 33.41% lost by not swapping 33.17% lost by swapping 16.55% first picked door win 33.42% second picked door win 66.58%
>>6589100 >"98 of the other doors accidently open and reveal none of them had the prize" This isn't the same situation at all. If it's accidental, and they didn't open specifically because there's no prize behind them, then there's no reason to switch.
Look at it this way: if you pick a door, and 99% of the time you're wrong, then the host specifically picks the one with the prize behind it, and opens all the others, 99% of the time, the host is showing you where the prize is.
If you pick a door, and 99% of the time you're wrong, then 98 doors open at random, 98% of the time, one of those doors is going to show the prize. The 2% of the times that the doors don't reveal a prize include the 1% chance that you got the door right, and the 1% chance that you got the door wrong and all of these randomly opening doors failed to show the prize. It's a 50% chance whether you switch or not.
>98% of the time, one of those doors is going to show the prize
>"98 of the other doors accidently open and reveal NONE OF THEM HAD THE PRIZE"
It's just stats. I flip two coins, one of them is heads, that means there's a 1/3 chance the other is heads. I pick a door, 98 of other doors open, none of them have the prize, 99% certainty it's behind the door you didn't pick. Doesn't matter why those 98 doors open.
For the coins, 3 possibilities, 2 of which have a tails.
For the doors, 100 possibilities, 99 of which have the prize behind the door the contestant didn't pick.
>>6589124 'kay You don't initialyze all variables on one line, it is messy and hard to read. You're using list when they are not needed, only because you are too tied to the mechanics of the game : we don't care to know where there's nothing/a goat, you shouldn't stock. A simple variable or a dictionnary would have been more efficient. Plus the way you construct your list is messy : two variables to change to increase the number of doors is too much. his may sound ridicule in something as little as this, but it will be important on bigger projects. Why is swap a number where it could have been a boolean. "pick" is not a clear name for a variable. win_noswap, win_swap, lose_swap, lose_noswap are irrelevant for the experience. And your commentaries are stupid.
>>6589160 >You don't initialyze all variables on one line Might be hard to read for some people, but its faster to understand what the variables are intended for and it doesnt wastes lines for nothing >using list when they are not needed >dictionnary would have been more efficient they function the same in this problem >A simple variable how? >two variables to change to increase the number of doors is too much Im not increasing the size, it is initialized as a 3element long list. Too much? Should i put it in a single line? >it will be important on bigger projects Havent have problems sofar. >"pick" is not a clear name for a variable. Yet you understood what it does. >Why is swap a number Was easier to randomize, but 0 and 1 translates to bool to be frank >... are irrelevant for the experience You meant experiment? Nothing is irrelevant, its just less irrelevant, it just shows how the probabilities work out. >And your commentaries are stupid. I agree, but "on bigger projects" the work like a charm to understand whats going on.
>It's just stats. I flip two coins, one of them is heads, that means there's a 1/3 chance the other is heads. You've understood this puzzle very badly. It only works in a contrived situation where you somehow get the exact amount of information, "at least one of them is heads", and you would get that information every time it was true.
If you flip two coins, and look at one of them, and it's heads, that means there's a 1/2 chance the other is heads, just like if you flipped one coin, got heads, and then flipped it again. The one doesn't affect the other.
Even in the case where you flip two coins, and someone looks at both and says, "At least one is heads", you have to know why he's doing so, and what he would do in other cases. For instance, what is he going to say when two tails come up? Does say, "Neither one is heads."? Or does he say, "At least one is tails." If he can say, "At least one is tails." which does he pick when it comes up one heads and one tails? Does he reflip the coins if they both come up tails?
This all matters. If he only says "At least one is heads." when both are heads, then it's not a 1/3 chance the other is heads, but a 100% chance. You need to know the full scenario.
>I pick a door, 98 of other doors open, none of them have the prize, 99% certainty it's behind the door you didn't pick. Doesn't matter why those 98 doors open. This is completely wrong.
If 98 doors are opened, chosen at random from among those you don't pick, it works out this way: 1% of the time, the correct door is the one you chose 1% of the time, the correct door is the unopened one you didn't choose 98% of the time, the correct door is opened randomly
The 2% of cases in which the opened doors don't reveal the prize are distributed equally between you having chosen the correct door, and you having not chosen the correct door, on your first guess.
>>6589141 >As long as the door revealed has a goat behind it, it's 2/3 chance the other unpicked door has the car. How can you think this?
It matters what his rules are for deciding whether to open a door, and which door to open: >>6588959
Given the original wording of the question, it isn't specified whether or not he only opens a door and offers to let you change when you've picked the car on your first guess.
Nor is it specified that he, despite knowing where the car is, specifically chooses to open a door with a goat behind it, rather than picking at random.
All we are told is that, in this specific case, he has happened to open a door which has a goat behind it. Without knowing the decision-making process which led to this action, this tells us nothing about whether we should switch.
>>6589188 >Might be hard to read for some people, but its faster to understand what the variables are intended for and it doesnt wastes lines for nothing YOU. NEVER. WASTE. LINES. Whatever you'll do. There will always be enough lines. And more lines = more space = easier to read. >they function the same in this problem No. They seem to but if you take 1000 doors, you'll have 999 doors that will mean literally nothing. But in a dictionnary you'll always have two keys : userChoice and treasureDoor. >how? treasureDoor = <nbOfTheTreasureDoor>. You will only have to compare it with the <nbOfUserChoice> to see if it is the same. >Im not increasing the size, it is initialized as a 3element long list. Too much? Should i put it in a single line? You have to think about modulability. To make the problem clearer lots af poeple have talked about increasing the number of doors to 100 or 1000. It should be more easy, just stock it in a nbDoors variable. >Havent have problems sofar. Then you'll have some later >Yet you understood what it does Think about everyone else being stupid >0 and 1 translates to bool to be frank Not in an interpreted language. You have to make some optimizations a compiler would make by yourself. >You meant experiment? Forgive my French. >I agree, but "on bigger projects" the work like a charm to understand whats going on. Wouldn't do it with my coworkers, but well if you didn't had any problems by now, you'll have some later.
>>6589242 If you have to scroll while reading a function, your function is definitely too long. Also >you are a horrible programmer >i haven't ever read a single mine of your code and >i can't code properly >but i can judge other people's code I hope next time you'll get some advices you won't try to shit on the face of the person who's trying to help you.
>>6586411 Well sometimes you don't have a desk, so you catch the coin an place it on your hand. Earlier today I flipped a coin, caught it between my fingers, so it was on its side, and then placed it on my hand. It was on its side.
>>6589251 >one-size-fits-all thinking about things where flexibility is more practical >dogmatism toward trivial things like whether to put more than one variable on a line Confirmed for horrible programmer, accomplishes nothing on own aside from following texbook examples, negative productivity when placed on team.
>>6589251 >If you have to scroll while reading a function, your function is definitely too long. not the person you replied to, but have you ever done any real programming? Or do you just make nifty little python scripts and call it "muh programming"
>>6589324 Everybody fucking laughing about the people who "got it wrong".
Nobody paying attention to the fact that the way it was originally explained, there wasn't sufficient information to justify Marilyn's answer.
Original question: >Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
>the host, who knows what’s behind the doors, opens another door, say #3, which has a goat
Original answer: >Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
>the host, who knows what’s behind the doors and will always avoid the one with the prize >will always
It's the "will always" that makes her answer work. The "will always" isn't in the question. That's something she made up, not as the person posing the problem, but as the person proposing an answer.
It's an unjustified assumption. That's what all of those PhDs wrote in to correct her about. She snipped down their letters, removing their explanations, to make them look foolish.
In the original question, we don't know whether the host "will always" avoid the one with the prize. We don't know whether he'll always offer to let you change. All we know is that this one case, he chose to open a door, and it happened to reveal a goat. He may only choose to do the reveal and make the offer if you've chosen the right one.
>>6589353 In the Monty Hall problem the host will always pick a goat. While this may not have technically been stated originally it was what was intended, and is what people mean when they say "Monty hall problem".
>>6589357 >>the host, who knows what’s behind the doors, opens another door, say #3, which has a goat >If there wasn't a second comma, after "#3", you'd be right This doesn't matter at all. He knows what's behind the doors. He opens another door. The door has a goat.
Not "regardless of what you choose, he will always open a door which has a goat". Not "he will always" anything. It's just a statement of what he has done in this particular case. There's nothing to firmly establish that he's following a fixed procedure.
>>6589363 >In the Monty Hall problem the host will always pick a goat. ...and always offer the choice. Sure. As long as it's stated that way.
But if you fuck up the definition of the problem, you don't get to mock people for getting the "wrong" answer. And if someone only asks you a question that sounds *mostly* like the Monty Hall problem, but changes or leaves out key details, then giving the answer to the Monty Hall problem is just wrong, as Marilyn was.
lol. Think of the coin example again. AT LEAST ONE vs THIS ONE. 1/3 vs 1/2. Two very different pieces of info.
Say it's A B C behind the doors.
A random host reveals B, then it's 1/2 you've got A in your door.
A random host reveals not-A (but doesn't reveal if it's B or C), then it's 1/3 you've got A in your door.
Not-A is interchangeable, B is not. The host picks B, knowledge or no, it means it's favored A and C statistically, even if A was the only thing the host wouldn't pick or if it was a random choice. Hence equal odds. The host picking not-A means it's favored A but hasn't favored B or C, so A becomes weighted. Since you know the range of possibilities falls under "98 non-A doors you didn't pick are randomly opened" when you see no A behind the doors, you also know only your door can't be opened in any of those possibilities, so only the other door left unopened receives the favor towards A. Hence it becomes 99/100 if you do the math.
ANN NAN NNA all x2 does not mean ANN vs NNA if the non-A picking host reveals the middle door to be N (otherwise it's 1/2 which you rejected). The door position doesn't matter, because N's are interchangeable (so 98% 1% 1% is bullshit, and the whole reason this is the go-to unintuitive problem in the first place).
Now I'm going back to a forum where people understand this shit.
>>6589390 >hurf durf he's right I'm wrong I'm embarassed >better call him an "autist"
>>6586381 >https://www.youtube.com/watch?v=4Lb-6rxZxx0 This annoys the fuck out of me, because she heavily implies that this is how Let's Make A Deal actually worked. It's not. I used to watch Let's Make A Deal when I was a kid. This is a made-up problem.
I'm not sure Monty Hall ever acted out "the Monty Hall problem". His name was just used to make a scenario: http://www.jstor.org/discover/10.2307/2683689?uid=2&uid=4&sid=21104146785477
It's pretty annoying, because she actually comes out and says that people watched the show for years, and saw this problem acted out time after time, and thought there was no strategy (i.e. all of these slack-jawed yokels didn't notice that the people who switched won twice as often as the people who didn't). So isn't it special and clever that mathematicians found the answer?
Well no, this was never a real life problem, it was originally a riddle posed by a mathematician (a professor of biostatistics), and in quite a different form. The contestant asks to switch doors (boxes), without being being offered the choice. Monty's (Monte's) response is "That's weird!" It's not clear he's going to be allowed to change his choice.
In this version, you're not asked to assume that Monty's either ignorantly or deliberately making the game easier to win, in ways that will quickly be noticed and become a boring part of the show. He's just trying different things to make the game exciting, and a contestant catches him probably giving away useful information, and tries to take advantage.
>>6588061 I'm pretty sure any mathematician worth his salt already knows the answer to the Monty Hall problem. Marilyn vos Savant probably paid these guys to pretend to be stupid so that she appears even smarter to dumbasses. She's already spent her whole life trying to appear as smart as possible to everyone.
>>6589406 >>6589395 Jesus guys, it's even on the Wikipedia page: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors
>The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door, or always offer a choice to switch, or even never open the door revealing the car. However, vos Savant made it clear in her second follow-up column that the intended host's behavior could only be what led to the 2/3 probability she gave as her original answer.
>Possible host behaviors in unspecified problem >"Monty from Hell":The host offers the option to switch only when the player's initial choice is the winning door. = Switching always yields a goat. >"Angelic Monty": The host offers the option to switch only when the player has chosen incorrectly = Switching always wins the car. >Ignorant Monty": The host does not know what lies behind the doors, and opens one at random that happens not to reveal the car = Switching wins the car half of the time.
>>6589486 >if phrased as intended completely legallistically, people still claim 2/3rds is wrong Sure, some people.
>the criticism of the original description is basically damage control Now this is just bullshit, because the fully-specified scenario is utterly contrived and implausible.
As I pointed out before, if this was actually done, it would become obvious very quickly to people who watched the show that the switchers win twice as often. Realistically, they'd catch that in playtesting, and it would never get aired. It's not an interesting game when the correct strategy is so obvious after watching people play for a while.
If your intuition tells you that a situation should exist, where a game show host repeatedly offers people a choice where one option can be determined to be consistently twice as good as the other by watching it a few times, your intuition sucks.
>>6589435 >i.e. all of these slack-jawed yokels didn't notice that the people who switched won twice as often as the people who didn't
Why would you think they would? Do you think anyone would keep a running tally of all the results? For anyone completely ignorant of the math behind it all it would take quite a few games worth of remembering the results before they clued in.
Fuck, you're acting like the average TV viewer is like that guy who memorized the pattern on Press Your Luck.
>>6589439 vos Savant's article is what popularized the problem. While most mathematicians know about the problem now, they were unlikely to have heard it back then. It's easy to get it wrong unless you are paying attention close to the wording and it is worded correctly to begin with.
>>6589596 When everyone's attention is on this one big decision in the game, and choosing one way wins twice as often as the other, people wouldn't have to keep a tally of the results. They'd just notice.
>>6589648 >How is choosing door one different than sticking with door one? Because if you were wrong originally, of which there is a 2/3 probability, then the host ensured that the remaining door is the right one.
>>6589667 But the friend is missing a key piece of information that you do possess when you're offered the option to switch: the fact that the host opened door 3 *when you chose door 1*. This critical piece of information changes the probabilities involved, which allows you to make a more informed decision than your friend could.
>>6588834 >Yes, but between them they are twice as likely to happen as choice one.
It's just stuffing in an extra option that isn't actually a different option from the two that's there. This is highlighted by the fact that one can add as many extra meaningless doors as one likes and it still comes down to a car or a goat. In game design this would be like advertising a million different endings when 999,999 lead to the same cutscene. Or like having an FPS that touts a million different guns, when 999,999 are shit variations of the same gun or even literally function/look the same.
So yeah, you can artificially weight a scenario like this one with as many false choices as you like. You still only have two endings.
I was a grown ass man when someone first showed me the Monty Hall problem. I swore that they were retarded for thinking it was better to switch. I swore it was 50/50 either way. I wasn't convinced until I wrote a program to play the game a thousand times and saw the probability work out to 2/3. I learned a lesson about being closed minded when something seems non-intuitive.
>>6590309 let the car be behind door 2. scenario 1: you pick door 1. the host opens a goat door, showing a goat. if you switch, you get the car. scenario 2: you picked door 2. the host opens a goat door. if you switch, you get a goat. scenario 3: you picked door 3. the host opens a goat door. if you switch, you get the car.
notice three outcomes, and two of the outcomes leading to a car.
if you pick a choice, and the chance of the choice being a certain outcome was 1/3, if you get to do the opposite of your choice the other outcome is 2/3. picking a car the first time round is the 1/3 chance.
>>6589645 They wouldn't. You'd need to observe and remember many games before the pattern became clear because sometimes people would switch and lose and sometimes people would stay and win. You might be able to pick up on the pattern more quickly if every single participant used one or the other strategy, but with a mix of strategies and results you'd need at least a few dozen before the pattern began to crystallize. And nobody's going to fucking remember dozens of results just by passively watching.
Fucking embarrassing. Mark my words, the transhumans in 200 years will point at the inability of most humans to not understand the simple logic behind the Monty Hall problem why we as a species were doomed to be replaced.
It boils down to thinking it like this. Ignore the whole door opening shit. You have two choices. You pick door A. And you keep with that door. Or you can pick both doors B and C and if you get the wrong choice once, you can ignore it and pick a second time. Because that is what is happening. If you pick two doors to choose from, you get one free get out of the jail card. That skews the probabilities in its favor.
>>6588235 I see the reasoning. But why does the probability stack? Shouldnt it merely revert to 50/50 since the 2/3 probability went out the window when one egg was cracked? And having a 2/3 probability on a set with only 2 options seems counter intuitive
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