Talk:Monty Hall problem

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Are the odds ever 50-50 ?[edit]

It's been established that the contestant and Monty have produced a pair of doors containing a car and a goat that do not have the same odds of producing a goat. Yet, on Marilyn vos Savant's website where she discusses this teaser, she perhaps yields too much ground to the academic furor that confronted her. She made this concession:

"Suppose we pause at that point [when two doors remain], and a UFO settles down onto the stage. A little green woman emerges, and the host asks her to point to one of the two unopened doors. The chances that she’ll randomly choose the one with the prize are 1/2, all right. But that’s because she lacks the advantage the original contestant had—the help of the host." [1]

But are the chances 50%? Probabilities don't care much for who does the choosing, and neither the contestant nor the green woman has insider information about the whereabouts of the car behind the doors. The contestant can know that the odds of finding a car behind the switched door are 2/3, but the odds don't change just because someone doesn't know the odds. If I know that four sides of a die are red and two are blue before I paint over the sides, the odds of someone who has never seen the die rolling red are not 1/2 due to her unawareness.

If the odds of randomly selecting a car among the two blind choices are 50-50 for anyone other than the contestant, then they must be 50-50 for everyone. We know that they are not, so the green woman approaches a stacked deck, so to speak. Otherwise, we end up saying that all odds between situations with two outcomes are 50-50 so long as we know nothing about the underlying conditions. That's not correct.

Vos Savant refers to the help of the host as being a missing ingredient, but that help actually settled the odds prior to his final selection, and it must've done so for anyone choosing between the two doors. We are now convinced that this problem is a matter of frequency of appearance of the car behind particular doors after particular actions have settled the odds, so vos Savant needn't have made any concessions to the contrary.

Thoughts? — Preceding unsigned comment added by Summers999 (talkcontribs) 14:24, 25 April 2015 (UTC)

The question is what odds are you talking about? If you pick randomly between two choices the odds of your choice being the correct one are 50-50. Note how I worded this - the odds we're talking about are the odds of "your choice". If we roll your red/blue die the odds are 4/6 that it ends up red and 2/6 that it ends up blue. If you roll it 100 times and I randomly guess red or blue, about 50 times I'll guess red and 50 times I'll guess blue. Of the 50 times I guess red I'll be right about 4/6 of the time, so about 33 times. Of the 50 times I guess blue I'll be right about 2/6 of the time, so about 17 times. Altogether I'm right about 50 times out of my 100 guesses, i.e. 50-50. If I don't know 4 sides are red and 2 are blue, my odds of correctly guessing are 50-50 whatever the "actual" odds may be because I have no choice but to randomly guess. If I always guess red (because it's my favorite color), I'll be right about 4/6 of the time, but now we're not talking about the odds of a random guess but the odds that the die ends up red (which is a different question).
If you want to talk about this further let's move the discussion to the Talk:Monty Hall problem/Arguments page. -- Rick Block (talk) 16:40, 25 April 2015 (UTC)
I'm only referring to a single selection of unequal odds. Namely, if the contestant or a green alien chose one of the remaining doors, it would still be better to choose a particular door. And this is true whether or not someone asked to select knows of the contestant's original choice. Even two of three random selections will yield a car from the alternative door, just as blind rolls of the die I described will yield red twice as often as blue. Summers999 (talk) 21:32, 25 April 2015 (UTC) user:Summers999
Like I said - if you want to talk about this further let's move it to Talk:Monty Hall problem/Arguments. -- Rick Block (talk) 04:09, 26 April 2015 (UTC)
It entirely depends on your information, that's all odds are.

The car is behind a specific door. Stick or switch are each either 1 or 0 probability of getting the car. The host knows the car is fixed so for the host choosing stick or switch the odds are 0 or 1 The contestant doesn't know where the car is but he knows the host could have opened door 2 and didn't the odds are 0.33 0.67 stick and switch. The alien doesn't know which door the host chose not to open and so the odds with that information are 50/50 SPACKlick (talk) 09:42, 1 May 2015 (UTC)

Thank you for stating the truth: Odds truly only do exist on the information level. Without information, odds cannot be calculated. But on the extant level, the level of what actually is, the distribution rate of cars to doors is indeed 1/2 after a door is removed. In other words, it's the information about the removed door which informs the choice to switch, not the odds of where the car is. We are not in fact calculating the odds of where the car is. Rather, we are calculating the odds of how effectively we'll find it. And it's that distinction, a distinction which even most probability experts fail to clarify, which muddies the water regarding this brain teaser. 98.118.62.140 (talk) 05:56, 14 October 2015 (UTC)
That is the normal (Bayesian) meaning of the words 'probability' or 'odds'. Martin Hogbin (talk) 00:19, 10 November 2015 (UTC)


The odds will be 50/50 if and only if the host were to randomly (mindlessly) open a door and this door happens to not be the prize, then your odds will instantly change form .3333 to .5 The main difference in the actual problem is that the host does not mindlessly open a door, he specifically opens the one without the prize, which in effect adds value to the one he did not open--Mapsfly (talk) 04:46, 2 December 2015 (UTC)

This important point is made in the article. Martin Hogbin (talk) 09:55, 2 December 2015 (UTC)

Most statements of the problem, notably the one in Parade Magazine, do not match the rules of the actual game show?[edit]

I do not think this is correct. Monty Hall made clear that nothing like the Monty Hall Problem, as it is widely understood, could ever have happened on the game show. Martin Hogbin (talk) 14:34, 29 December 2015 (UTC)

And how does this conflict with "most statements of the problem do not match the rules of the actual game show" (which, BTW, is sourced)? -- Rick Block (talk) 17:35, 31 December 2015 (UTC)
By starting with, 'Most statements of the problem..', the wording suggests that there was a real game that was similar to the MHP. We know from Monty Hall's words that nothing like the well known problem could have happened on the TV show. Martin Hogbin (talk) 16:09, 1 January 2016 (UTC)

Is this *problem* a "stupid filter"?[edit]

Correct?[edit]

It is a matter of discussion whether vos Savant's response was correct. Even under the standard conditions several authors consider vos Savant's reasoning not correct, although the actual advice of switching is right. Nijdam (talk) 19:46, 10 January 2016 (UTC)

Quite a lot of disussion if I remember correctly. Martin Hogbin (talk) 22:04, 10 January 2016 (UTC)
Actually, I do not see an issue with using 'correct' here. We had, 'Vos Savant's correct response was that the contestant should switch to the other door.' The correct response, as defined in this sentence was that the contestant should switch, which we all agree is correct. The Engish here does not imply that her entire response was correct, only that the advice to switch was correct. Martin Hogbin (talk) 22:09, 10 January 2016 (UTC)
Here is Monty Hall Problem simulator I made. This simulator removes the win-by-stay/win-by-switch choice and assumes the only method is winning-by-staying (the simulator always stays with the first choice). 1/2 of the wins get the Car, 1/4 of the wins get one goat, and 1/4 of the wins get the other goat. It clearly shows that there is a 50% chance of winning the car by staying and that there is no advantage by switching, so Vos Savant was incorrect. 24.205.110.111 (talk) 00:41, 11 January 2016 (UTC)
@24.205.110.111: Please take this up on the /Arguments page as I suggested. Suffice it to say that you're wrong, but this is not the place to argue about it. -- Rick Block (talk) 04:55, 11 January 2016 (UTC)
@Martin Hogbin: Adding "correct" implies Wikipedia is taking a stance here. This is not appropriate, and is in fact counter to a fundamental Wikipedia policy, which is that Wikipedia is neutral with respect to all sources - please see WP:NPOV. What is unambiguously true is that vos Savant's response was that the contestant should switch. Wikipedia certainly can and should say this. Adding "correct" is saying that Wikipedia agrees. Wikipedia does not agree. Nor does Wikipedia disagree. Wikipedia could say "most reliable sources agree" - but Wikipedia cannot, by fundamental policy, say vos Savant's answer is "correct". -- Rick Block (talk) 04:55, 11 January 2016 (UTC)
This is a question about the meaning of English. I am not trying to restart old disputes. My understanding of the sentence, 'Vos Savant's correct response was that the contestant should switch to the other door.' is just that that her words 'you should switch' were correct, it does not imply that her entire response and method of solution (which is not stated here) is correct. Do you understand the English that way?
If you do not understand the sentence that way I would be perfectly happy to make it clearer (so long as we did not use an awkward or hard-to-understand construction or something that implies some sort of mysterty, later to be revealed).
I think it is accepted by all sources that, given any resonable intepretation of the problem, it is to your advantage to switch. I think it would be fair to say that this fact could be considered the result of a routine calculation and part of mainstream maths and science. It is a generally accepted fact that vos Savant was correct in saying that you should switch. Martin Hogbin (talk) 10:32, 11 January 2016 (UTC)
I am not aware of any good quality reliable sources that say you should not switch. It is widely, in fact I would say universally, accepted that vS was correct in advising players to switch. I do know that the rest of her analysis is debated by some but please let us keep clear of that discussion. Martin Hogbin (talk) 10:32, 11 January 2016 (UTC)
Can somebody else chime in here? I do not agree, but I am not going to argue with Martin. -- Rick Block (talk) 12:52, 11 January 2016 (UTC)
Yes please. It seems very simple to me. Vos Savant was correct when she said that you should switch. Nobody disputes this fact. Martin Hogbin (talk) 22:44, 11 January 2016 (UTC)
Well, who's there to decide? Certainly not Wikipedia. Nijdam (talk) 10:53, 12 January 2016 (UTC)
I have no problem with WP using "correct" with vS's interpretation. There were certainly a lot of people who said that she was wrong, and most of those people were confused/wrong rather than delving into subtle issues about the problem statement. Glrx (talk) 20:58, 14 January 2016 (UTC)
Nice to know. Nijdam (talk) 09:28, 15 January 2016 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I have no problem referring to the conclusion that "player should switch" as the correct solution. However referring to VS's response as correct probably shouldn't be in WP's voice as it is disputed by some experts. The sentence refers to VS's response as correct rather than, as I would prefer "Correct conclusion". SPACKlick (talk) 12:30, 15 January 2016 (UTC)

The disputed text is, 'Vos Savant's response was that the contestant should switch to the other door'. So what 'her response' was is defined immediately afterwords to be 'that the player should switch doors'. It is purely a matter of English ther is no dispute about the maths.
If sombody wants to change the wording to make it absolutely clear that WP is saying only that the specific response/answer/solution/advice 'you should switch doors' is correct that would be fine with me. This is what most readers are interested in. I assume that everyone agree that switching doors is the correct thing to do? Martin Hogbin (talk) 12:47, 15 January 2016 (UTC)