Wikipedia:Articles for deletion/Three cards and a top hat

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result of the debate was keep. Johnleemk | Talk 08:27, 14 January 2006 (UTC)

[edit] Three cards and a top hat

I couldn't decide whether to categorize this or nominate it for deletion, so I've done both. I guess it's, what... original research? Melchoir 00:43, 8 January 2006 (UTC)

• Delete- this is a riddle, not an encyclopedia entry. Seems to be the Monty Hall problem in disguise. Reyk 00:50, 8 January 2006 (UTC)
• It would probably be classed under original research, but 'unoriginal riddle' would be more fitting. Delete. --It's-is-not-a-genitive 00:50, 8 January 2006 (UTC)]]
• Comment. I've heard this before, it may be reasonably well known. I found one site which had a description of the puzzle and added the link to the article. But obviously it is no great tragedy if this is deleted since the article is quite short and doesn't establish context, source or notability. - Haukur 00:54, 8 January 2006 (UTC)

  Keep. Now that Heraclesprogeny has made a great article out of this we're of course keeping it somewhere :) Maybe somewhere on Wikibooks would ultimately be the best place? But if no-one can find the perfect home for it elsewhere then let's just keep it here. - Haukur 15:45, 8 January 2006 (UTC)

  Guess I was a bit too hasty. Having now actually read through it I have to say that I'm not convinced that it's quite correct :) The point of the example is that the scam artist can always offer you the same bet regardless of the colour of the card he flips up. But he'll offer you a win in the cases where the two-coloured card is the one selected. Since the odds are 2/3 that the card is actually single-coloured you only have a 1/3 chance of winning. I think :) - Haukur 20:01, 9 January 2006 (UTC)

• Delete as per Reyk DrIdiot 00:57, 8 January 2006 (UTC)
• Comment: I don't see an obvious isomorphism to Monty Hall, although judging from the discussion Haukur found, the logical traps are similar. I considered a redirect, but it just seemed dishonest. Melchoir 01:12, 8 January 2006 (UTC)
• MergeThis is a fairly standard example used in probability theory to demonstrate some fundamental concepts, like a riddle because of its relatively unintuitive results, but not quite a riddle. I have spend a couple of hours revising it and think it would make a great example in the section on probability axioms or probability theory.Heraclesprogeny 15:20, 8 January 2006 (UTC)

  Wow, this changes everything. Heraclesprogeny, I've only skimmed the new article, but it looks like great writing! Not encyclopedic style, but that might be fixable. Did you draw on any references for the article? Melchoir 10:14, 9 January 2006 (UTC)

*Keep Great improvement. Well done Heraclesprogeny! Though the prose may be original, neither the question, nor the logic meet the meaning of original research. Obina 12:19, 9 January 2006 (UTC)

• Weak delete. It's a nice example, but I'm afraid it's not encyclopaedic enough. I'm all in favour of short examples to explain key concepts, but this is a bit too long and more text book material. By the way, I didn't read and think it over carefully but it seems to me the conclusion is wrong. I think that if a card is chosen at random, and then either side is also chosen at random, and this side turns out to be green, then the probability of the chosen card to be the doubly-green one is 2/3, but the article says it's 1/2. -- Jitse Niesen (talk) 13:11, 9 January 2006 (UTC)

  Changed vote from weak delete to delete because it has no references, making it original research, as pointed out by Melchoir. -- Jitse Niesen (talk) 12:36, 10 January 2006 (UTC)

  Abstain. Changing again as the article is still being edited and some clues to references have been found (see talk page). I still think that it is not encyclopaedic enough, but it's approaching the gray area so I don't feel comfortable deleting it while it is being worked on. -- Jitse Niesen (talk) 10:19, 12 January 2006 (UTC)

• Delete as original research (not to mention wrong). Sorry, Heraclesprogeny, but I've read it through and I can't imagine that you found a reference that would make the claim "Thus, there are only two possible cards, double green-faced or purple/green-faced, and each has an equally likely probability of being the one you chose". The whole point of the example is that this argument doesn't work. Melchoir 19:49, 9 January 2006 (UTC)
• Comment Hmm Haukur suggests the artle (newly written) is now incorrect. Perhaps he is right. But this seems a discussion for the talk page, and helpful to get right. This seems a basis to improve and fix the article, and not a basis to delete. And meanwhile, I shall not bet my salary! Don't know who is right. But I remain in the 'keep' camp.Obina 00:12, 10 January 2006 (UTC)

  I would agree with fixing the article, except that we are not in the business of doing our own mathematics around here. Ideally someone would come up with a reference, but pending that, it's all just original research. I feel justified in beating this dead horse not just because it's policy, but because the current article is a cautionary example of what can happen when even well-meaning, intelligent, and thoughtful contributors ignore that policy. Melchoir 04:09, 10 January 2006 (UTC)

  You all make valid points. When writing, I was afraid it was lengthy and a bit too "text book", and I didn't include any refs. because, at the time of writing, I wasn't using any. This is all learnt material and not original in any way, but I couldn't produce any references pertaining to the exact question. Any first-year text would do as reference for the rest. I thought this to be a good example because it illustrates so many fundamental and often overlooked points. Incidentally, I have attached a short paragraph at the bottom of the article for those who still have questions about the answer. I will try to dig up some references soon, but understand if it must be deleted. Thank you for your patience as this is my first effort at contributing to this valuable resource. Heraclesprogeny 12:09, 11 January 2006 (UTC)

  Well, it was still quite the entrance! Happy editing! Melchoir 19:29, 11 January 2006 (UTC)

• Delete. I'm sorry to change my vote. WP:NOR makes the right thing to do clear, whatever we all think of the new version.Obina 12:19, 11 January 2006 (UTC)
• Comment. It's been stated the article is wrong, but it's better to say it's ambiguous. No mention is made of whether the person will offer the same bet if another color shows. If the same bet is made irregardless of color (then modulo other possible ambiguities), then obviously the bet is not 50/50 as stated, since 2/3 of the time you will get a card with both sides the same color. This is similar to the "What are the odds that the other child is also a boy" question (or whatever that is called). That one is much more famous by the way, having been popularized by Martin Gardner, Marilyn Vos Savant, etc, with plenty of literature and references. --Chan-Ho (Talk) 17:13, 11 January 2006 (UTC)

  What the host would have done if the other color had shown is an interesting thought experiment, but it doesn't affect the answer to the question, which is quite unambiguous. Melchoir 19:23, 11 January 2006 (UTC)

Sure it does. If the host offers the bet only when one color shows, then it's 50/50, but if the host offers the bet always, then you should bet the other side is the same color. The situation is ambiguous precisely because we are not told the host's intentions. And the intentions do make a big difference. If for some reason, you don't believe me, you can try repeated trials yourself and see: draw a card out and then guess the opposite color shown. Do this, say, 25 times. Now try this again (same number of times) but always guess the same color as shown. Now finally, start over again but every time you draw a card and see purple, put it back in the hat, shake it up, and try it again until you see green. Then guess your color (it doesn't matter, since now it is even odds). --Chan-Ho (Talk) 21:02, 11 January 2006 (UTC)

If you weren't a mathematician I would just give up right now, but perhaps there is hope. Forget about the host. We draw from the hat a large number of times. True or false: of the draws when we see red, 2/3 of the time, the other side is red. Melchoir 21:19, 11 January 2006 (UTC)

Uh, you mean green or purple, right? Your true false question shows that you're not getting the point of my comments - that it's important to state the host's intentions. This is quite standard fare. --Chan-Ho (Talk) 21:33, 11 January 2006 (UTC)

I am intentionally asking a different question. Melchoir 21:36, 11 January 2006 (UTC)

Ah, I think I see what you're saying now. In my previous response, I somehow assumed that when drawing a green/purple card, you would draaw it showing green. So your point is that when the host only offers the bet when green is shown, 2/3 of the time the other side is green. Well, ok. I withdraw my previous responses. --Chan-Ho (Talk) 22:06, 11 January 2006 (UTC)

Um... something like that, yes. Sure! Melchoir 22:25, 11 January 2006 (UTC)

• Keep (possibly including Rename and Improve.) It's similar to the Monty Hall problem, but not identical, and is in the probabilitic literature. Arthur Rubin | (talk) 23:18, 11 January 2006 (UTC)

  If you have a reference, by all means go nuts! I would love to see an article here. However, I suspect you'll have to start from scratch, no offense to anyone. Melchoir 23:26, 11 January 2006 (UTC)

• Okay, I'm again moving into keep now that the article has been vastly improved. The external links help too. - Haukur 00:27, 12 January 2006 (UTC)

  And who would have thought that this near-speediable little text dump would prove so fertile? :) - Haukur 00:31, 12 January 2006 (UTC)

• Weak keep per Arthur Rubin's pledge to continue improving. It's got a long way to go all around, but this is the right direction. Melchoir 07:36, 12 January 2006 (UTC)
• Keep. Yes I'm changing my vote again, too. Shows the process works. The version as of now, with input form several editors, has clear references, and we don't need to debate 1/2 versus 2/3 as editors. The references quoted are clear that the answer is 2/3. We are quoting their answer, not our opinions, per WP:NOR.Any editor with a different view will need to provide references to justify including this view. And yes there is an active talk on the discussion page - let's take "improving it" discussions there.Obina 11:46, 12 January 2006 (UTC)
• Keep, as a vastly improved article. Similarly to the Monty Hall problem, 2/3 is correct. It seems illogical at first, but is true. Ral315 (talk) 13:00, 12 January 2006 (UTC)
• Keep an excellent article and an asset to Wikipedia ➥the Epopt 15:34, 12 January 2006 (UTC)
• Comment Thanks for the corrections. Must say I'm a little embarrassed that I made such an obvious mistake. When I saw the question and saw it was up for deletion I felt it would be a shame to lose such a nice example, at least I was right on that! By the way, I changed the colours from the original "white and red faces" because some people read much more into these things than they should. Cheers. Heraclesprogeny 01:45, 13 January 2006 (UTC)
• Weak keep based upon the upcoming improvements. Themusicking 01:54, 13 January 2006 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.