Talk:Law of averages

Comment

The gambler in the illustrations really does demonstrate poor logic if his estimated probability of a coin flip showing 'heads' is often greater than 1. I assume someone mistook the odds (e.g. 4:1) for the probability? --Msr657 20:00, 11 July 2006 (UTC)

Yeah, having a probability over 1 is not possible; there's an error there. GlassOnion 21:17, 6 February 2007 (UTC)

If no one's going to fix that, I might remove it someday. It's more confusing than explanatory, and it's not really about the law of averages. Msr657 09:17, 14 April 2007 (UTC)

Vandalism

in examples section that contradicts the first part of the article —Preceding unsigned comment added by 129.116.18.104 (talk) 19:54, 9 November 2008 (UTC)

Murphy's Law vs. Law of Averages

I have heard of a saying, somewhat of "If we have lots of little problems along the way, this will satisfy the problem gods and we won't have a big problem opening night [for a show]." Is this part of Murphy's law or the law of averages? Dachshund2k3 00:36, 10 April 2007 (UTC)

Sounds to me like wishful thinking. Murphy's Law is usually stated as "whatever can go wrong, will", which is quite the opposite sentiment, and the Law of Averages doesn't have much to say about the probability of a particular outcome for a single event. It's repetition that brings the law into play. Msr657 09:17, 14 April 2007 (UTC)

It sounds a bit like the law of averages. To assume that a sequence of problem nights will mean that it is less likely a problem will occur on the next night, is just like assuming that a sequence of "heads" results on a coin mean it is less likely the next coin toss will be "heads". 210.84.17.12 (talk) 06:31, 17 May 2009 (UTC)

Tyranny of averages

I've created an article that is the converse of this, and welcome any comments/contributions. I've not yet x-ref'd it, in case people feel it ought to simply be merged and a redirect placed in its stead. --Belg4mit 20:11, 31 July 2007 (UTC)

Page Edited

I have taken the liberty to fix this page up to include properly lexed math formulas. I also redid a couple of sentences. I hope you all enjoy it. mikecucuk 18:46, 26 March 2008 (UTC)

I gotta say, I didn't like the math section. This article is just about the lay term. We don't need a proof of the LLN here. Shivan Bird (talk) 22:09, 13 May 2008 (UTC)

Test Case

Like many before, I also had that itch at the back of my brain saying that black were to show up 5 times in a row red would be more likely the next time. So, I took a test case of 500 rolls on a 2 sided die and calculated the result. 5 number in a row showed up 18 times and 8 times the 6th number was the same and 8 times the 6th number was different. Which the chances of it actually being 50% 50% aren't that high for such a small test case but they were. I mean it does make sense that a 50% chance is a 50% chance regardless of what happened before. Adding a mental note to the back of my brain. —Preceding unsigned comment added by Gernapious (talk • contribs) 02:38, 13 January 2009 (UTC)

Good illustration and testing method 210.84.17.12 (talk) 06:18, 17 May 2009 (UTC)

what is law of averages?please explain?

The is no 'law' of averages! There is the hope that a mathematical probability will occur. — Preceding unsigned comment added by 92.30.29.66 (talk) 15:42, 18 July 2011 (UTC)

Wrong theorem

I get it. This is not a mathematical article. However, "a real theorem that a random variable will reflect its underlying probability over a very large sample" can only mean the convergence of the empirical distribution to the theoretical one as the sample size goes to infinity. This has nothing to do with the law of large numbers, which says that under some assumption, the sample mean converges to the theoretical mean. The two theorems are "related", which I will not elaborate here, but they aren't the same.

As people who come to read this article could care less about Theory of Probability, perhaps this need not be a part of the article. However, either correct the link to the right theorem or simply state that the term may be deemed imprecise/confusing/... by specialists. 18.83.1.20 (talk) 19:16, 20 May 2009 (UTC)

Merge suggestion

It has been suggested at the Wikipedia:Proposed mergers page, that Law of averages be merged with Law of large numbers (LLN). Please state your comments regarding this action. --TitanOne (talk) 20:59, 3 March 2010 (UTC)

Disagree.... Looking through "google books" and the web, the term "Law of averages" refers to either law of large numbers (ratio of heads to tails approaches 1, which is true), or gambler's fallacy (a run of heads is compensated by a run of tails, so difference between heads and tails approaches 0, which is false). The way it's presented here now is gambler's fallacy. And gambler's fallacy seems somewhat more common online, but I didn't look enough to be sure. Therefore my initial impression is that this page should be a disambiguation or short article sending interested readers to learn more at either law of large numbers or gambler's fallacy. What do other people think? --Steve (talk) 22:53, 3 March 2010 (UTC)

NOTE: The template describing the proposed merge links to the "Law of large numbers" talk page. Please discuss the merge there. (I have copied Steve's comment over to that page.) Thank you! -- Firefeather (talk) 21:48, 26 March 2010 (UTC)

Delete this article, with redirect to LLN. The cited source uses the term “law of averages” as a synonym for LLN, and does not provide the interpretation given in this article. The examples section looks like WP:OR. The first one describes the gambler's fallacy, for which we already have a fairly developed article; the second example should be dubbed “idiot’s fallacy” or something like that — really, is there a person who would think that out of 99 coin tosses, exactly 49.5 of them should be heads?; the third example is just a corollary from the strong law of large numbers, or from the second Borel-Cantelli lemma; the last example is not even funny — people don't think that in the longrun a good team and a bad team would perform equally, that would contradict the mere notion of “skill”.  // stpasha »  22:18, 1 June 2010 (UTC)

I have copied the above comment to "Law of large numbers" talk page which, as noted by Firefeather immediately above, is where discussion is ongoing. Melcombe (talk) 09:46, 4 June 2010 (UTC)

Example 4 deleted

The example bullet point "regardless of the actual scenario", which was criticised by "Stpasha" above, has survived for some time. It was apparently backed-up by an in-line citation (which was added rather later) to Grinstead & Snell, but that text says nothing like it, as far as I can see. I have therefore deleted the bullet point. Melcombe (talk) 10:06, 4 June 2010 (UTC)

Note, I have not checked that Grinstead & Snell include material related to the other supposed examples, but it seems doubtful that there is any close similarity. Otherwise we need some page numbers for the citations, or other sources. Melcombe (talk) 10:15, 4 June 2010 (UTC)

Problem with the first example.

"if the wheel has landed on red in ten consecutive spins, that is strong evidence that the wheel is not fair - that it is biased toward red. Thus, the wise course on the eleventh spin would be to bet on red, not on black: exactly the opposite of the layman's analysis."

This is wrong. It implicitly assumes memory in the wheel in the form of bias towards red. Let the probability of landing on red be 50%, then ten consequtive reds in a row is (1/2)^10 = 1/1024. While this one in a thousand chance seems small it will inevitably happen given enough spins. Considering that most roulette tables are placed in casinos and that those casinos have many tables which are constantly spinning, you may not have to wait very long at all to see this situation happen. You may even consider that records based on random events are roughly logarithmic. — Preceding unsigned comment added by 165.214.14.21 (talk) 19:28, 21 October 2011 (UTC)

I agree; in fact, the article seems to be invoking the law of averages in determining that the wheel is not fair! — Preceding unsigned comment added by 76.180.35.223 (talk) 03:31, 11 November 2012 (UTC)

Why does this page exist?

It doesn't describe any well-defined topic other than "people are bad at statistics and probability," which is better covered elsewhere. It's poorly sourced and hinges on a very particular definition of "law of averages" as a fallacious belief, that isn't supported by any evidence.

This page should redirect to Law of large numbers. TiC ^(talk) 11:07, 17 August 2014 (UTC)

When I say "Law of averages" I mean the same thing as "law of large numbers". It's easier to say. Equilibrium007 (talk) 01:47, 28 September 2014 (UTC)