Talk:Monty Hall problem

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Former featured article Monty Hall problem is a former featured article. Please see the links under Article milestones below for its original nomination page (for older articles, check the nomination archive) and why it was removed.
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To what "standard" do we refer?[edit]

The article currently has a section named "standard assumptions". That's a misnomer; no standards body promulgates a list of statements whose truth can be assumed when analyzing mathematical problems.

This quirky bit of lingo seems to be a sneaky way of excusing people who omit important parts of the problem statement. Marilyn Vos Savant made this error in her initial description of the problem; she described the host opening a non-winning door, but failed, crucially, to state that the host always does this. A reader new to the problem can be forgiven for failing to guess at this rule which, after all, the real Monty Hall did not follow.

This section should be named something more like "stipulations", and shouldn't try to do double duty by both stating the stipulations and subtly claiming that their statement shouldn't be necessary. TypoBoy (talk) 03:10, 15 March 2016 (UTC)

Per the sources in the standard version of this problem all of these are usually assumed even if not stated, you can see from MSV's answer that she assumed the host always opened the door even though she didn't state it. Relation to the original show is irrelevant as the problem isn't based on the show. SPACKlick (talk) 14:49, 15 March 2016 (UTC)
What's not clear is whether she realized at the time that the assumption mattered. (She clearly knew that by the time of the second column, but at the time of the first column, I don't see any evidence beyond her later say-so.) --Trovatore (talk) 17:39, 15 March 2016 (UTC)
All of that may seem correct, but take a closer look. She did not just say that "the host opens just one of the two other doors", but (let's forget about the door #numbers) she wrote indeed: "...and the host, who knows what’s behind the doors, opens another door which has a goat. So IMO indeed it's necessary to take a closer look. Kind regards, Gerhardvalentin (talk) 12:19, 2 May 2016 (UTC)

This section is problematic. The MHP can be solved without the assumption that the host always reveals a goat. For example, the host may sometimes reveal a goat and sometimes not; we are presented with a game in which he does. Is he doing so to help us win the car as we chose a goat first (the Angelic Monty variant), or to discourage us from winning it as we chose the car first (Monty from Hell)? In the absence of any other information, the principle of indifference suggests we have equal chance of either, supporting the 2/3 solution. Anyway, surely the key assumption is that a car is more advantageous than a goat, without which the solution cannot be verified.Freddie Orrell 20:54, 14 June 2016 (UTC) — Preceding unsigned comment added by Freddie Orrell (talkcontribs)

You are wrong. If the host doesn't specifically show a goat, the chance to win by switching to the second closed door is not 2/3. Have a look to university of California, San Diego: "Monty Does Not Know Version", and the "Explanation of the game". If the host did show a goat just by chance, the winning rate is not 2/3, but only 1/2. Gerhardvalentin (talk) 10:48, 21 June 2016 (UTC)
Since I said 'we are presented with a game in which he does', I was not discussing the probabilities associated with not showing a goat. The MHP contains the phrase 'and the host, who knows what's behind the doors', which would be superfluous were he to show a goat just by chance; we may therefore assume he is acting deliberately.Freddie Orrell 09:56, 22 June 2016 (UTC) — Preceding unsigned comment added by Freddie Orrell (talkcontribs)

The article currently claims that "Krauss and Wang (2003:10) conjecture that people make the standard assumptions even if they are not explicitly stated." I can't speak for everyone, but I assumed that the host was trying to win against the guest. So if the host knew what was behind each door, and the host hadn't picked the car in the first round, then the host would pick the car before the second round. And if the host did not know, then the host would choose at random. Each of these interpretations is at odds with the "standard assumptions" and each changes the odds and the best strategy for the guest. They obviously can't be talking about all people, since some of us don't make the "standard assumptions," so which people? (talk) 21:36, 2 January 2017 (UTC)

The probability is 2/3. Where is the trick?[edit]

Non-editorial exchange moved to /Arguments subpage. --Trovatore (talk) 20:46, 10 August 2016 (UTC)

I realized that the odds of winning pass to 2/3 changing the initial choice and I realized my mistake. I explain it because it could help somebody. What the host do opening a door and showing a goat is, in fact, to give to the player the possibility of inverting his initial choice (if he found a goat he’ll get a car and vice versa). For a better explanation I use an extreme version of the game where the initial choice is made between 100 doors with 1 car e 99 goats. If the host asked to the player “Do you want invert the result of your initial choice?” it’s easy to realize that changing is convenient. Coming back to the game with 3 doors, the opening of a door with the goat from the host, even though has the effect of giving to the host the possibility of invert his choice, it’s confused with the random opening of a door behind wich there is a goat. It’s this the event that leads to 50-50 odds (but that clearly is a different game because the host has 1/3 of chance of opening a door with the car and this is impossible in the original game). Alessmaga (talk) 09:29, 11 August 2016 (UTC)

Example door numbers should be removed from the quoted letter at the beginning of the page as they just confuse you[edit]

Example door numbers should be removed from the quoted letter at the beginning of the page as they just confuse you. If we are specifying that the player choose door 1 and the host opened 3 and it contained a goat, there is no advantage in switching. both switching and stay give a 50% chance of winning (because if the host opened door n3, it means the car could not have been there in the first place, in this case, so only two possibilities are left). You should just explain that the player picks a door and the host opens another one with a goat and he ask the player if he wants to switch to the remaining door. It is the sum of all the cases together that gives you an advantage by switching. — Preceding unsigned comment added by 2001:b07:644c:a33:70f1:7f9b:d96d:4295 (talkcontribs) 23:21, 26 August 2016 (UTC)

If it's not verbatim, it's not a quote. I think that failing to quote exactly what the question actually said can only increase confusion and doubt about what it means. As vos Savant herself has said, "anything else is a different question". ~ Ningauble (talk) 16:15, 3 September 2016 (UTC)

whats wrong with this?[edit]

We have this:

[If]f the contestant picks a goat (2 of 3 doors) the contestant will win the car by switching as the other goat can no longer be picked, while if the contestant picks the car (1 of 3 doors) the contestant will not win the car by switching The fact that the host subsequently reveals a goat in one of the unchosen doors changes nothing about the initial probability.

and an editor (not me) wanted to add this:

[I]n 2 out of 3 chances, the contestants first guess will be wrong. If the first guess is wrong, and the host shows the other wrong choice, then the remaining door must be the winner. Thus, in 2 out of 3 chances, switching will win.

and has been reverted. But the first passage is poor. "the contestant will win the car by switching" is not true. She might win the car by switching. She will increase her odds by switching. But there's guarantee that she's getting a car. "the other goat can no longer be picked" is not true either. The "other" goat -- by which I assume is meant the non-revealed goat -- is certainly a possibility to be picked. If is meant "the revealed goat" then it should say so.

The second passage seems a lot more easy to understand than the first, although it's not perfect. It's also true, unlike the first passage. But editors are resisting this. Why? Editors are invited to explain. Herostratus (talk) 20:47, 26 September 2016 (UTC)

You have misread the current version. If the contestant picks a goat then they will always win by switching because the other door is necessarily a car. The "Other goat" referred to is the goat Other than the one they previously picked and which was an object earlier in the sentence and as such is the revealed goat. There would be nothing wrong with clarifying by adding "because monty has already revealed it" to that sentence. SPACKlick (talk) 21:03, 26 September 2016 (UTC)