Talk:Monty Hall problem

Any real mathematicians ?

This article is lovely insofar as it illustrates so well confusion. It should be listed under "Magical Thinking", or "Cognitive bias", and probably "Vain attempts". I will not even begin to correct it, nor explain (I know my WP); just let possible startled readers know that yes, it is a lot of gobbledigook, some of it by people who are perfectly aware and enjoy it.Environnement2100 (talk) 10:55, 8 April 2023 (UTC)

Do you know your WP enough to know that there are at least 2 articles with Argument pages? This article is one of them. You may have been referring to something other than WP:RS, but my understanding is that on the arguments page, WP:RS only comes in if the conversation-starter brings up changing the article, rather than to shut down other conversations. JumpDiscont (talk) 22:46, 13 April 2023 (UTC)

Genuinely curious what another article with an Argument page is, can't find any info on Google. 174.44.112.170 (talk) 07:25, 21 March 2024 (UTC)

I know of Talk:Cantor's diagonal argument/Arguments. - Jochen Burghardt (talk) 12:27, 21 March 2024 (UTC)

You can search intitle:"Arguments" on Wikipedia and then filter by the talk namespace.

• Talk:0.999.../Arguments
• Talk:Gödel's incompleteness theorems/Arguments
• Talk:Two envelopes problem/Arguments
• Talk:Cantor's diagonal argument/Arguments
• Talk:Jyllands-Posten Muhammad cartoons controversy/Arguments
• Talk:Azerbaijanis/Arguments
• Talk:Electron/Arguments
• Talk:Armenian genocide/Arguments

Avessa (talk) 12:31, 21 March 2024 (UTC)

for anyone who's more curious ​ ^_^ : ​ ​ ​ The 0.999... Arguments page is the one - other than _this_ page - that I knew about before I saw Jochen's reply. ​ ​ ​ ​ ​ ​ ​ JumpDiscont (talk) 07:28, 17 April 2024 (UTC)

What on earth are any of you talking about? What, concretely, is wrong with the article? Brusquedandelion (talk) 07:37, 21 March 2024 (UTC)

50/50

Monty Hall

Prize behind door 1.

Choose door 1. Shown door 2. Swap Result lose.

Chose door 1. Shown door 3. Swap Result lose.

Choose door 1. Shown door 2. No swap. Result win.

Choose door 1. Shown door 3. No swap. Result win.

2 wins and 2 losses from 4 possibilities when you choose the correct door.

Choose door 2. Shown door 3. Swap. Result win.

Choose door 2. Shown door 3. No swap. Result lose.

1 win and 1 loss from 2 possibilities when you choose the wrong door.

50/50 chance. 213.128.242.112 (talk) 18:59, 1 July 2023 (UTC)

Amazing, that table recapitulates the subject to the point. All difficult aspects of the matter are summarized on a small plot. In a fantastic way, you present complex issues clearly.

Though your result is only possible under special conditions concerning the host's behavior e.g. the "lazy host" who stands next to the object of attention and only wants to open door 3 if possible to avoid long distances. In that case, among many, there is indeed a 50/50 chance to win the trophy.

When we follow all the standard assumptions which are listed in the article and additionally assume that we are dealing with a "balanced" host that means the host's intention to open the one or the other door is completely random (50/50), then the following table would apply.

I added the host's intention to the table: "as wanted" means that the host opens the door he originally wanted to, "door x wanted" means that the host actually wanted to open door x. If he can decide between two "goat doors" he is free to choose one of them and does so randomly with a probability of 50%. If there is the "prize door" and a "goat door" left and he actually wanted to open the "goat door" he must open it, which coincides his intention. If there is the "prize door" and a "goat door" left and he actually wanted to open the "prize door" he must open the "goat door" nevertheless.

But these are two seperate cases that need to be taken into account and this fact affects the probability values of our overall calculation.

Monty Hall

Prize behind door 1.

Choose door 1. Shown door 2 (as wanted). No swap. Result win.

Choose door 3. Shown door 2 (as wanted). No swap. Result lose.

Choose door 3. Shown door 2 (door 1 wanted). No swap. Result lose.

Choose door 1. Shown door 3 (as wanted). No swap. Result win.

Choose door 2. Shown door 3 (as wanted). No swap. Result lose.

Choose door 2. Shown door 3 (door 1 wanted). No swap. Result lose.

2 wins and 4 losses from 6 possibilities.

33.33 chance to win if player decides not to swap.

Choose door 1. Shown door 2 (as wanted). Swap. Result lose.

Choose door 3. Shown door 2 (as wanted). Swap. Result win.

Choose door 3. Shown door 2 (door 1 wanted). Swap. Result win.

Choose door 1. Shown door 3 (as wanted). Swap. Result lose.

Choose door 2. Shown door 3 (as wanted). Swap. Result win.

Choose door 2. Shown door 3 (door 1 wanted). Swap. Result win.

4 wins and 2 losses from 6 possibilities.

66.66 chance to win if player decides to swap. 188.106.91.33 (talk) 10:25, 16 July 2023 (UTC)

Savant's opinion on the readers' understanding of the problem

She said: "Very few raised questions about ambiguity, and the letters actually published in the column were not among those few."

But not questioning the ambiguity does not mean that the readers understood the assumptions the same way as what she meant. Khamphatg (talk) 21:39, 8 August 2023 (UTC)

If she based on the above to conclude that "Virtually all of my critics understood the intended scenario." then I think it is a problem. Khamphatg (talk) 22:03, 8 August 2023 (UTC)

reminder about the Arguments page

Since I had forgotten - which is why I initially replied here - and RK20030 might've missed it, I'm pointing out that "discussions on the underlying mathematical issues" should go "on the Arguments page." ​ The section RK20030 created was moved there yesterday. ​ ​ ​ JumpDiscont (talk) 07:23, 9 December 2023 (UTC)