text:
Talk:Blackjack

== Informal Motion to Remove All References Placed by Objective3000 in Blackjack, Card counting, and Shuffle track and Wherever They May Also Appear in Wikipedia Articles to His Self-published Commercial Websites qfit and blackjackincolor ==

Informal Motion to Remove All References Placed by Objective3000 in Blackjack, Card counting, and Shuffle track and Wherever They May Also Appear in Wikipedia Articles to His Self-published Commercial Websites qfit and blackjackincolor

1. Qfit and blackjack in color are self-published websites (henceforth “Websites”) created by Objective3000.

2. The Websites contain much alleged original research by Objective3000.

3. The Websites contain large banner advertisements for Casino Verite software created by Objective3000, as well as links including instructions for purchase with prices.

4. Citations to the Webpages have been found on Blackjack, Card counting, Hole carding, Martingale (betting system), and Shuffle track (henceforth “the Articles”) either currently or in the past. See Exhibit A for evidence.

5. Objective3000 began working on Wikipedia on 8/31/2007.

6. Before that date, no citations to any page of his two Websites existed on any of the Articles, as evidenced by their wikipedia history.

7. Beginning on 11/15/2007 through 3/2/2008 Objective3000 placed eight citations to his self-published Websites in the Articles (Exhibit A).

8. None of Objective3000’s works in the gambling field have been published by a third party. They are all self-published. Active book publishers have published numerous gambling books, including Cardoza (Las Vegas) and Huntington Press (Las Vegas) and Random House.

9. On December 23, 2010, user QFIT deleted the two citations to the self-published websites inserted by Objective3000 in the article Hole carding. On December 23, 2010, Objective3000 reversed it. On December 24, 2010, user QFIT again deleted the two citations placed by Objective3000 on Hole carding with the comment, “Removed spam links.” On December 24, 2010, Objective3000 reversed the deletion, with the note rvt edit identified as vandalism by user barred for WP:U violation. Objective3000 had entered a complaint for vandalism against the user QFIT, and the user was banned for life on December 24, 2010 (Exhibit: 02:26, 24 December 2010 Orangemike talk contribs blocked QFIT talk contribs with an expiration time of indefinite). On December 24, 2010, a user identified by his computer ID deleted a reference inserted by Objective3000 with the note: Removed self linking spam to co. On December 25, 2010, Objective3000 reversed it. On December 27, 2010, the ID’d user deleted the references by Objective3000 with the note “Removed spam links. Objective3000 is linking to his own commercial site as a reference.”

10. On December 27, 2010, in discussing the issue of the repeated deletions of citations noted in paragraph 8 above at the article Hole carding,  TransporterMan on the talk page of Hole carding wrote, “links [to the citations]. . . appear to me to be very iffy as reliable sources,” and cited violation of WP:SPS and WP:Sources. TransporterMan suggested posting an inquiry at the Reliable Sources Noticeboard. Objective3000 let the issue die, with the citations having been removed by the user noted in paragraph 8 above. Daily average pageviews for Hole carding is currently about 55; it is rarely viewed. Daily average pageviews for Blackjack is about 1500. Daily average pageviews for Card counting about 800. The citations to the Webpages remain in Blackjack and Card counting, among others.

11. On 19 June 2021 Objective3000 posted a message asking that Blackjack and Card counting be given protected status (Special:Contributions/Objective3000: 14:20, 19 June 2021 diff hist  +317  Wikipedia:Requests for page protection). The action of protected status is taken to cease inappropriate editing on controversial articles, articles about celebrities and political figures, and the such, not to ensure that Objective3000’s citations to his self-published webpages with commercial content be preserved. Both Blackjack and Card counting have the lowest ranking of completed articles, C-class, the editing needs of which are described as “Considerable editing is needed to close gaps in content and solve cleanup problems.” Yet, Objective3000 wanted both protected.

Wherefore, we pray that the appropriate administrators provide the following relief:

1. Find that Objective3000 is in violation of WP:SPS, WP:SOURCES, WP:PROMO.

2. Find that Objective3000 silences those who attempt to remove the citations to his Webpages by filing inappropriate vandalism or other charges against them, and seeks inappropriate protected status for articles.

3. Order that all citations to Objective3000’s Webpages are allowed to be removed by the judging administrator or any other editor without retribution from any source, including the filing by Objective3000 of charges of vandalism or other charges.

4. Other remedies found appropriate.

Exhibit A.  Evidence Objective3000 (now also using O3000 and O3000, Ret.) began at Wikipedia 08/31/2007. Here are ten times he inserted his self-published webpages with commercial content as references into multiple articles in his first few months on Wikipedia.

1. 11/15/2007 inserted into Blackjack first of his qfit references, with banner ads at top and bottom

Over 100 variations exist.100+ Blackjack variations

2. 12/24/2007 inserted into Hole carding at 23:13 http://www.qfit.com/blackjack-odds-calculator.htm

3. 12/24/2007 inserted into Hole carding at 16:49 The advantage can vary substantially depending on the rules, the percentage of cards seen, and+ the strategies used. http://www.qfit.com/blackjackholecarding.htm

4. 1/19/2008 inserted into Card counting

The following table illustrates various ranking systems for card counting.Card Counting Strategies

5. 1/26/2008 inserted into Card counting

Another interesting aspect of the probability of card counting is the fact that, at higher counts, the player's probability of winning a hand is only slightly changed and still below 50%. The

6. 1/26/2008 inserted into Card counting

Blackjack played with a perfect basic strategy typically. . . 10%-30% of the time depending on rules, penetration and strategy. BlackjackinColor.com True Count Frequencies

7. 1/28/2008 inserted into Blackjack

Techniques other than card counting can swing the advantage. . . since the shuffle tracker could be, at times, betting and/or playing opposite to how a straightforward card counter would.Shuffle Tracking Counts

8. 3/2/2008 inserted into Martingale (betting system)

As with any betting system,. . . of how many previous losses.http://www.blackjackincolor.com/useless4.htm Martingale Long Term vs. Short Term Charts.

On a whim I also examine Shuffle track. Sure enough, the self-published banner ad-full citations were inserted by Objective3000. 9. 12/29/2008 inserted into Shuffle track

Shuffle tracking is an advanced form of card counting. There exist many types of shuffle tracking.http://www.blackjackincolor.com/Shuffletracking1.htm Blackjack Shuffle Tracking Charts

10. 1/28/2009 inserted into Shuffle track

Blackjack Shuffle Trackers Cookbook: How Players Win (And Why They Lose) With Shuffle Tracking] http://www.qfit.com/blackjackshuffletracking.htm "Blackjack Shuffle-Tracking Treatise".

Aabcxyz (talk) 22:11, 12 July 2021 (UTC)Aabcxyz
 * Are there any diffs to support your claim in #1? How do you know the editor named Objective3000 owns or created those websites? Schazjmd   (talk)  22:25, 12 July 2021 (UTC)

 * Thank you for your interest, Schazjmd. If you go to any of the qfit and blackjackincolor webpages and scroll to the bottom you will see the name of the person who owns the site.  It is probably a violation of some Wikipedia rule to publish names and I want to avoid falling into a trap where I will be suspended, so I respectfully will not produce that name here.  The identify of Objective3000 and that person is well-known, and can be verified, for example, by user Rray.

 * Furthermore, this man has self-published a book, and is available at amazon.com

 * https://www.amazon.com/gp/product/B0044KMPMS/ref=dbs_a_def_rwt_hsch_vapi_taft_p1_i0

 * If you go to that page you will find this description:

 * Highly detailed information on casino Blackjack as played worldwide, including over 100 variations, modern basic strategy, modern card counting systems, casino heat, current casino conditions, strategy comparisons, scams and myths, casino comportment and stories from the road. See the preview at www.qfit.com/book. . ..

 * That establishes the identity of Objective3000 (aka O3000 and O3000, Ret.) and the author of that book. To summarize,

 * 1)  qfit and blackjackincolor webpages provide the real name of the author
 * 2)  amazon.com page establishes the identity of the book author and the webpage author.

 * Aabcxyz (talk) 23:13, 12 July 2021 (UTC)Aabcxyz
 * I don't see anything at any of those links that say that person is Objective3000 (or any other account name) on Wikipedia. Schazjmd   (talk)  23:17, 12 July 2021 (UTC)

 * (I guess the colons establish a continuation?) This is not a court of law, Schazjmd.  Please reread my paragraphs 5, 6, 7, 9, 10.  The connection is clear.  Furthermore, if you read the longer of the two Cites discussion at Hole carding you will see Objective3000 referring to Don Schlesinger, and the amazon.com page noted above similarly refers to Don Schlesinger.  IF you "look inside" his Modern Blackjack Edition II you will see in the front matter the word QFIT in large font.  The author of Modern Blackjack is clearly the author of QFIT.

BUT THIS IS BESIDES THE POINT. Let us call that person, Mr. W. The creator of qfit and blackjackincolor is advertising Casino Verite software. https://qfit.com/ provides the name of the author as Mr. W. That software is prominently posted at the pages TO WHICH Objective3000 has placed links and which he protects by reversing attempts at deletion. The burden falls on Mr. W to establish expertise via WP:SPS and WP:SOURCE. He is reading these posts. He tried to establish expertise at Hole carding and you can read that discussion at the talk page of Hole carding, courtesy of TransporterMan. In summary,

1. Whoever Objective3000 is, he has placed repeated citations to self-published webpages.

2. Whoever Objective3000 is, those webpages have commercial content.

3. Whoever Objective3000 is, he has failed to establish expertise by the criterion of publication by a third-party.

4. None of my allegations above provided the actual name of Mr. W.  That is irrelevant. Points 1, 2, and 3 establish the basis for removal of the citations.

Respectfully, Aabcxyz (talk) 23:44, 12 July 2021 (UTC)Aabcxyz
 * Not a court of law, yet you word this as an "informal motion" and include ridiculous legalese such as Wherefore, we pray.... You based your whole tirade on your accusations against Objective3000, yet fail to show that Objective3000 and anyone associated with those websites are the same person.You've gone about this all wrong. You should have put together your arguments about qfit and blackjackincolor not being reliable sources and simply focused the discussion on that issue. If you have evidence to support that Objection3000 had an undeclared conflict of interest, that's a task for the conflict of interest board (although it's meaningless to start anything as the editor is retired).   Schazjmd   (talk)  23:55, 12 July 2021 (UTC)

 * Dear Schazjmd, I'm new here and greatly appreciate your guidance.  But to clarify, first the editor is not retired.  When I deleted the  citations to his self-published commercial webpages at qfit and blackjackincolor, he posted a vandalism notice, as is his practice (please see commentary at talk page of El C).  Second, he still sells the software as you can verify by calling the phone number at the qfit and blackjackincolor webpages. Despite any retirement status, the existence of those citations in Wikipedia to his commercial webpages remain.

Third, here's the smoking gun. If you go to

https://en.wikipedia.org/w/index.php?title=User:Objective3000&diff=404456459&oldid=169284509

you will see that Objective3000 is the author of the Casino Verite software in question to which his self-published website refer. He is without doubt Mr. W. That establishes the COI to which you refer.

User:Objective3000: Difference between revisions From Wikipedia, the free encyclopedia Jump to navigationJump to search Browse history interactively Revision as of 01:41, 5 November 2007 (edit) UnqstnableTruth (talk | contribs) (wrong user) ← Previous edit Revision as of 13:15, 27 December 2010 (edit) (undo) (thank) Objective3000 (talk | contribs) Next edit →

Line 1:	Line 1: +	'''Author Casino Vérité and some other stuff. Editor here since 2007, if my ancient mind recalls correctly.''' (bold mine) ________________________________________ Revision as of 13:15, 27 December 2010 Author Casino Vérité and some other stuff. Editor here since 2007, if my ancient mind recalls correctly. Languages •	This page was last edited on 27 December 2010, at 13:15.

In case someone decides to edit that page, I have taken a photograph of it. I hope you and those reading this will go to it to verify the statement "Author Casino Vérité and some other stuff." Aabcxyz (talk) 00:06, 13 July 2021 (UTC)Aabcxyz

 * It's helpful to discuss content on article talk pages. It's not helpful to discuss editors on an article talk page. As far as I know, Wikipedia doesn't hold "trials" and enforce "orders." Even if it did, the article talk page wouldn't be the appropriate venue.

 * Regarding the content, specifically, the references in question: If better quality references can replace the references in question, then, of course, they should be replaced. The fact that external sites display banner ads and/or are commercial sites is irrelevant; almost all the websites being used as references on Wikipedia are commercial sites and carry advertising -- including The New York Times. Rray (talk) 00:31, 13 July 2021 (UTC)

One of the issues is self-published webpages used as references. As TransporterMan pointed out in the discussion at Hole carding, you have to have established expertise by publicatioon by a third party. That's the test that Objection3000 fails. Aabcxyz (talk) 00:49, 13 July 2021 (UTC)Aabcxyz

 * Rray, you gave me good advice to carry the discussion at the talk area rather than in edit post comments, and Schazjmd directed me to make sure that Objective3000 is the exact same person as Mr. W. who is the author of Modern Blackjack and the qfit and blackjackincolor webpages that Objective3000 links to. We have established that identity, and I am grateful to Schazjmd for pointing out the need for establishing that identity.  Now I need more advice.  There are three issues identified by TransporterMan, Schazjmd, and I think Orangemike or QFIT.  How long is the protocol to let the talk continue here before I post to noticeboards or ask for third party or in general to proceed to the next step?  Your guidance would be much appreciated; I do NOT want to be banned for inadvertently violating some guideline of which I am not aware.  Thanks in advance.  On your NYT comment, I come to wikipedia to get references for my research.  They are 100% scholarly articles and have not a tidbit of advertising.  I have NEVER run across a reference that contains an ad, overtly or covertly.  In contrast, qit and blackjackincolor have OVERT BANNER ADS as well as links to purchase prices!  So your comment that "almost all the websites being used as references on Wikipedia are commercial sites" does not stand up to at least my extensive scrutiny.  As obviously a veteran user who has read many, many articles and contributed greatly, can you provide me ONE citation other than qfit and blackjackincolor in which a banner ad is placed?  And besides, "two wrongs don't make a right"; that is, in the equivalent statement quoted from the web: "the fact that someone has done something unjust or dishonest is no justification for acting in a similar way." N'est ce pas?  To be careful, I am not implying the citations in question are "unjust or dishonest"; those are words taken directly from the web.

Other issues you brought up. It's not a question of "better" references. Many articles have NO references. For example, Hole carding. And much of the material to which qfit and blackjackincolor citations are added do not require references. In addition, in my looking at the edits on Card counting and Blackjack I found that Objective3000 removed dozens of references when they displaced ONE of his, and he removed another excellent reference with the comment to the effect "two references aren't needed," but of course he retained the one to qfit.

RE trials and orders, you said the talk area is not the proper venue for trials and orders. Again, can you suggest what are the proper venues, in particular for the issues being discussed here? I really look forward to continued input from you and Schazjmd and others who find these issues important. Aabcxyz (talk) 01:27, 13 July 2021 (UTC)Aabcxyz

 * If you feel like you need to go through the dispute resolution process, you can learn more about that here: https://en.wikipedia.org/wiki/Wikipedia:Dispute_resolution_requests.

 * You might also find https://en.wikipedia.org/wiki/Wikipedia:Citing_sources helpful. Newspapers and websites are both listed as examples of possible references.

 * Look at the other references in this article for yourself rather than asking me to look them up for you. At least 6 or 7 of them are for other commercial websites, including one newspaper site. The fact that you're only concerned about websites owned by one individual makes it look like you're on a crusade against a specific individual rather than trying to improve the article. Stop discussing what a retired editor added to or deleted from an article. This isn't the place for you to try to "build a case" against another editor. Please, focus on doing something to improve the content. Reading https://en.wikipedia.org/wiki/Wikipedia:Drop_the_stick_and_back_slowly_away_from_the_horse_carcass might also serve you well. Rray (talk) 02:52, 13 July 2021 (UTC)

 * Thanks, as always, for the advice, Rray. Re improving the article, my only experience with Blackjack other than those deleted citations was an improvement (as an multiple-award winning essayist) to I think the first sentence and you yourself reversed it, so I basically said forget it. Re retirement.  He's not retired.  He posted the protection request for Blackjack and Card counting as a means of preventing deletion of his citations, and that to C-class articles which you spent much-appreciated time in trying to remediate.  Re crusades.  I couldn't care less about the individual; I do care about violations of COIN and SPS and SOURCE and PROMO.  There's a reason such prohibitions exist.  It is clear that only experts can refer to self-published webpages and just because a few friends of his refer to Casino Verit software doesn't make him an expert.  I won't comment on the content of his qfit and blackjackincolor pages other to say there's a reason he had to self-publish his book.  Two publishers specialize in gambling books, Cardoza and Huntington, so they are out there.  As you suggested, I will look at citations at Blackjack to look for banner ads. Thanks again for all your time.  I'm trying desperately to avoid falling into a trap to allow me to get banned, but there's a lot of mudslides and tar pits in all the wikipedia rules and that's why I so greatly appreciate your advice.

Aabcxyz (talk) 03:39, 13 July 2021 (UTC)Aabcxyz

 * Rray, I looked at the Blackjack references as you suggested. There are 29.  There are 11 from books, government posts, gambling magazine, or newspapers, lacking ads.  There are 6, numbers 4 through 9, which have page citations, so are books.  Three are citations inserted to his webpage by Objective3000, possessing banner ads.  Four are to the wizard of odds.  That leaves 5 webpages.  #11 has no ad.  #16 has no ad, just a link to gambling addiction services.  #19 has no ads, just lengthy tables of numbers.  #27 has links to gambling casinos, but no ads.  I assume the casinos pay for advertising space which would I guess cover part of the web hosting charges of the website owner.  The wizard pages have links to casinos as does #27.  No banner ads appear for products developed by the website owners on either the webpages of the wizard or those of the other five.

Because they are four in number, I should address the four wizard of odds posts. 1. The wiz’s ads, as noted, are for third party casinos. 2. The wiz and #27 earn no money other than toward the web hosting fee. 3. The wiz, according to his Wikipedia page, is in fact the renowned Michael Shackleford. His credentials are vast. His book Blackjack102 was published by a third-paper publisher, the distinguished gambling publishing house Huntington Press. He is a professor of mathematics at the University of Nevada, Las Vegas, a licensed actuary, a frequent consultant to casinos, and his wizard of odds webpage was purchased from him for well over $2 MILLION. So he doesn’t even earn money for the ads! He has appeared before the Nevada Gaming Board and consults in various capacities, e.g. to game developers. By all criteria, he is a bonafide expert. 4. The 10 citations I noted to Objective3000’s qfit and blackjackincolor were made by Objective3000, including all that were made in the first 6 months of his editing. None were inserted into Blackjack by others before he began editing or during this 6 month period. In contrast, none of the citations to the wizard of odds were inserted by Michael Shackleford. In other words, there is very little in common between the citations of the two. For your benefit as well as to answer the concern of Schazjmd, here is the direct and intimate connection. Objective3000 is Mr. W (not his name, as I don’t want to run afoul of some Wikipedia rule), as shown on his talk page as the author of Casino Verit software. Qfit and blackjackincolor have banner ads and price lists for Casino Verit software, and those webpages note Mr. W as the owner of the webpages. The only citations (that I found) to those webpages came from Objective3000. Most of those who, like myself, found those citations troublesome as new users and deleted them were banned upon action by Objective3000 on claims of vandalism and Objective3000 reversed the deletions. Thank you for your consideration of my Informal Motion. Please let me know if any of my comments here are in violation of Wikipedia rules and I will eliminate them. I try to present only objective, verifiable facts. By the way, my name turns up in RED, and yours turns up in BLUE. Do I have to have a certain number of posts before my name shows up in BLUE? Thanks. Aabcxyz (talk) 16:27, 13 July 2021 (UTC)Aabcxyz

 * @Aabcxyz, is there any reason you didn't just go add to the assertions in question? Did someone object to you doing that somewhere? Sorry if you explained that in the above, too long, didn't read. —valereee (talk) 15:02, 14 July 2021 (UTC)
 * Oh, and to make your name show up in blue, you just have to go create your user page. If you have trouble, someone will be happy to do that for you, but it's not considered polite to just make the assumption someone wants that. —valereee (talk) 15:04, 14 July 2021 (UTC)

 * “Just when I thought I was out, they pull me back in.” The majority of the WP:SPA’s posts here are false and littered with WP:AGF and WP:PA violations, in particular the IP edit summaries (oddly with no notice of these attacks). And they go back 14 years to try to make some sort of case. I’m certainly not about bore everyone with point-by-point refutations of these screeds. But, I will make one comment because it is an example of irony – and I adore irony. The editor, in eight (8) sentences, writes about how much they respect Mike Shackleford‘s knowledge and how he is an acceptable source in this field. Well, Shackleford references the work of “Mr. W” on many pages of his sites. (A few:, , , )  Indeed, trusting Mr. W’s results over his own. So, Aabcxyz thinks Shackleford is an acceptable source – but as unacceptable a source who Shackleford has gone to for answers. O3000, Ret. (talk) 15:45, 14 July 2021 (UTC)
 * This is a bit tldr for me, but qfit seems questionable to be used as a WP:RS here. OhNo itsJamie Talk 21:27, 10 August 2021 (UTC)
 * @Ohnoitsjamie "A bit"? Ya think? :D The editor hasn't come back, despite being pinged. @Objective3000, WP has changed a lot over the time since these sources were added, but it might not be a bad idea for you to go through and insert bsn tags yourself. —valereee (talk) 22:09, 10 August 2021 (UTC)
 * @Ohnoitsjamie A few points: 1. I did not add most of these cites. I did suggest them. I also added cites to many other sources. 2. "Mr. W" is cited by many of the other sources on these articles and is mentioned in about 30 books on the subject, as well as being a nominee for the Blackjack_Hall_of_Fame 4. Aabcxyz is one of the numerous socks of this farm.[]. 5. Anyone is welcome to replace these cites in the unlikely chance that they can find better sources. Makes no difference to me and I reverted none of these recent deletions. I would be happy to discuss this further via email as I was the target of serious harassment by telephone and other means by the sock and do not wish another year of such. Regards, O3000, Ret. (talk)
 * I don't see anything actionable here. Aabcxyz, it's unlikely that anyone is going to be interested in reading that wall of text. I don't think Wikipedia is the courtroom you're seeking. If you're interested in building an encyclopedia, feel free to make suggestions for improvement to this article (e.g., "change X to Y").  OhNo itsJamie  Talk 22:59, 10 August 2021 (UTC)
 * This is quite funny. As you know, he just requested qfit be put on the spam blacklist at WP:SBL and mentioned that a table was added and that I deleted it. The table he speaks of was cited by the article. He deleted the cite and copied the table from qfit using another sock. So, he's saying the source is no good for cites and yet took the material wholesale from qfit. I removed it as it was a copyright violation, even though he doctored it up to remove all its cites to authors replacing them with online casino portals. Then, he oddly claimed "Mr. W" deleted the author refs that "Mr. W" added (and still exist at qfit) when he himself deleted then. This decade long retribution for the fact that I participated in one of the multiple AfDs removing articles that he and his over dozen socks added to WP praising himself, and my refusal (on a phone call) to help him get a publishing deal for a book he hadn't written by supporting such articles is getting quite weird. I explained to him a decade ago that you do not put an article in WP to give yourself notability -- you get an article because you have notability. That hasn't stopped him from adding them to the ES version of WP and other wikis. Personally, I stand by what I said a decade ago. If someone creates an article about me; I will be the first to AfD it. O3000, Ret. (talk) 11:04, 11 August 2021 (UTC)
 * Sounds like he's suggesting poorly sourced material with a possible WP:COI behind it be removed from the article. That would appear to be a perfectly "actionable" instruction. Likewise, also just personally attacked the user by revealing real-world interactions I suppose might be perceived as embarrassing. Whether the above constitutes "outing," I don't know, but O3000 also just acknowledged that there is a possible COI here. Wikieditor19920 (talk) 16:43, 31 August 2021 (UTC)
 * You have attempted to get me (and others) sanctioned on multiple occasions related to the topic area from which you are now indef TBanned. I am retired and no longer have any interest. I realize that you have posted that all admins are corrupt, but suggest you take the advice of El C and JzG on your talk page. As I don't believe you have ever edited any article in the arena of this, and have a history with me, you might also read WP:HOUND to avoid starting upon a new, rocky path. O3000, Ret. (talk) 17:27, 31 August 2021 (UTC)
 * Is that your defense for advocating inclusion of, or adding yourself, sources that you bear a personal connection to or created yourself? Too bad. You cannot argue for the reliability of a source you were involved in creating. WP:COI. The same applies when someone attempts to create a Wikipedia page for you assuming it meets WP:NOTABLE. Wikieditor19920 (talk) 18:12, 31 August 2021 (UTC)
 * Actually, you are quite wrong on the first two points, and the third is not relevant. It was the OP that attempted to add several pages talking about himself to EN WP, his name to this article, and an article about himself to the Spanish version of WP. I said I would AfD any article added about me. And, avocation is encouraged. But, I'm not going to get into another one of the endless arguments for which you are known at ANI. As an editor, I was interested in building an encyclopedia, and only 0.023% of my edits were to this article. If you have become interested in this article, find some better sources. The sources here were restored by two other editors and have been stable for many years. This was once a featured article. It lost that before I became an editor on review due to having too few sources. You are welcome to improve the article. O3000, Ret. (talk) 18:38, 31 August 2021 (UTC)
 * This is all sidestepping the relevant part of this discussion. The fundamental point is that a self-published website selling commercial, blackjack-related products is not a reliable secondary source. Given that multiple users have raised this concern, I've removed the QFIT citations from the article, which seem to provide mostly basic information. Secondarily, if you have any personal or financial connection to these sources (QFIT or related, self-published books/products), you should allow other editors to weigh in and avoid mounting a defense of them yourself, per COI. (Amazingly, you suggest that my points are "quite wrong," but you have made on-Wiki posts describing yourself as the author of this website, and earlier said you did suggest these sources for the article.) [ Wikieditor19920 (talk) 20:01, 31 August 2021 (UTC)
 * Again, you are wrong on the guidelines. And, I removed that personal info after severe harassment by the OP. An admin at the time suggested I have it redacted. I declined as I wanted the evidence to remain. You are here only to take some sort of retribution against a former editor with whom you have had many arguments. As for the removals, I have repeatedly said that I don't care. Sorry to disappoint you. BUT, the removal should have been a replacement. You have harmed the article by removing perfectly acceptable cites in an article with too few cites. I hope someone who actually cares about the article edits it in good faith. But I'm retired as I'm sick of the atmosphere brought here by some editors. O3000, Ret. (talk) 20:16, 31 August 2021 (UTC)
 * You spend as much time complaining about PA's as you do making them. Ditto for a bad "atmosphere."
 * I hope someone who actually cares about the article edits it in good faith.
 * You are here only to take some sort of retribution against a former editor with whom you have had many arguments.
 * I'm not going to get into another one of the endless arguments for which you are known
 * COI is absolutely an issue if you are either proposing or adding yourself a website as a citation in which you have a commercial interest. You are entitled to your privacy but you are also required to disclose your connection to a source if you openly advocate for it, even in underhanded ways like "Gee, you're really harming the article by removing this website, I hope someone restores it." Enjoy your retirement.
 * Separately, Blackjackincolor seems to present some helpful graphs, but again, it's a self-published source. I for one would like to see some secondary sources covering "shuffle tracking." Wikieditor19920 (talk) 21:01, 31 August 2021 (UTC)
 * , This really does look like you're importing a personal dispute. Feel free to replace these citations with better ones, but simply removing them and making personal attacks on this talk page is not helpful. Also, COI editors are perfectly welcome on talk pages, and may discuss issues they are conflicted about, that is what we want them to be doing. MrOllie (talk) 21:20, 31 August 2021 (UTC)
 * No, I suggest you read the exchanges above, or at least try to represent them accurately. These:
 * I hope someone who actually cares about the article edits it in good faith.
 * You are here only to take some sort of retribution against a former editor with whom you have had many arguments.
 * I'm not going to get into another one of the endless arguments for which you are known
 * are personal attacks and presumptions of bad faith. My questioning the propriety of a source is not a "personal attack." COI editors are encouraged to disclose their connections to a source, which Objective3000 didn't do until another editor pointed out their prior admissions. That's not compliant with guidelines. I have no "dispute" with Objective3000, other than the way that this user addresses others.
 * To your point, I see you just restored the sources despite multiple editors in this thread questioning whether Qfit is reliable. Perhaps you should gather consensus before adding sources back into an article, which seem largely redundant with secondary sources already present. Wikieditor19920 (talk) Wikieditor19920 (talk) 21:29, 31 August 2021 (UTC)
 * , I assure you, I have read this whole talk page. I doubt that uninvolved editors would read this situation in the way you are presenting it. But by all means, let us leave the article 'status quo ante' and see if other opinions come in. MrOllie (talk) 21:49, 31 August 2021 (UTC)
 * , your comment irresponsibly & unfairly mischaracterizes the interactions above. I'm sure there are plenty of "friendly" editors who would happily pile on and agree with you, but that doesn't change the facts that 1) nowhere did I make a "personal attack" and 2) most of what Objective3000's posts above are just personal attacks and accusations of bad faith. If you are interested in helping facilitate a more productive conversation, perhaps you should avoid such one-sided weigh-ins.
 * There is no compelling reason to maintain the "status quo" and prevent removal of an unreliable source. I see you've made edits to this page in the past to remove references to questionable sites; what is the holdup with this one? Wikieditor19920 (talk) 22:04, 31 August 2021 (UTC)
 * You should know by now that something that has been in an article for years has implicit consensus. The onus is on those wishing to make a removal. O3000, Ret. (talk) 22:52, 31 August 2021 (UTC)
 * Wrong again. WP:IMPLICITCONSENSUS applies unless it is disputed or reverted.. I think the optics of you aggressively pushing to keep your website as a citation for extraordinarily niche information would be a WP:COI. Wikieditor19920 (talk) 23:52, 31 August 2021 (UTC)
 * Would you fully read guidelines? You are referring to a bold edit, not edits that have lasted for years. And, I have repeatedly stated that I don't care and that you are welcome to replace. You are now reverting to your well known aggressive tactics that resulted in your current indef TBan and several blocks in your short period here some of which relate to me. Further, "niche" is a part of an encyclopedia. Just because you don't care or know anything about a subject area that is extremely important to readers of this article does not make it unimportant. This article is about BJ. The info relates to casinos in Australia, an English speaking country and this is EN WP. And, one of the common tags is that articles are US oriented. To claim we shouldn't doc things that are "niche" is.... O3000, Ret. (talk) 00:11, 1 September 2021 (UTC)
 * Three editors in this discussion have questioned the propriety of using your website: myself, the original opener of this thread, and an admin who commented on it.
 * Under what conception of COI is you leaving your "retirement" to aggressively advocate using your website as a cite in an article not problematic? Surely it would have something to do with the fact that Wikipedia gets a lot of page views, and some of those views will ultimately be redirected to your website by virtue of it being cited here.
 * And here we go again -- you're attacking me personally and bringing up things that are totally irrelevant here, something I'm sure will surely be concerned about, rather than addressing the issue at hand. Sorry, I'm not taking the bait.
 * The "percent edge" against the house gained by a particular strategy, and which QFit is used to cite, is too much detail and the type of information that will lose a general audience. WP:TOOMUCH. WP:NOTGUIDE. That is in addition to concerns about using a self-published source. The term you claim you "coined," which I'm presuming is the "Original Bets Only," is not one I can find having any mainstream usage. In any normal scenario, this would be quickly removed pending further discussion. Wikieditor19920 (talk) 00:22, 1 September 2021 (UTC)
 * is too much detail and the type of information” Which is exactly why it is in a cite instead of the article. which I'm presuming is the "Original Bets Only," You presume incorrectly. And if you cannot find it, where did you look? Why would you remove non-US rules in EN WP? Why dumb down an article? It is not in the article – but should be in cites. Can't believe I fell into arguing with you again. Say what you wish. You have never understood the purpose of WP. O3000, Ret. (talk) 00:35, 1 September 2021 (UTC)
 * The "Original Bets Only" section only cites your website. The "house edge" advantage down to a percentage - <1 and of two decimal points -- is in the body of the article. Wikieditor19920 (talk) 00:41, 1 September 2021 (UTC)
 * The "Original Bets Only" section only cites your website. Yes, there is a dearth of info in the article about non-US casinos which must be increased, not decreased. The "house edge" advantage down to a percentage - <1 and of two decimal points -- is in the body of the article. Only on a few rules. The cite adds many more. Continue to dumb down the article. Many folks have had these endless arguments with you at ANI. You never convince. O3000, Ret. (talk) 00:54, 1 September 2021 (UTC)
 * Unfortunately, the article does not benefit from sources which are not usable under the WP:SELFPUBLISHED guidelines. I'll repost them here in full, with the especially relevant sections bolded:
 * Anyone can create a personal web page, self-publish a book, or claim to be an expert. That is why self-published material such as books, patents, newsletters, personal websites, open wikis, personal or group blogs (as distinguished from newsblogs, above), content farms, Internet forum postings, and social media postings are largely not acceptable as sources. Self-published expert sources may be considered reliable when produced by an established subject-matter expert, whose work in the relevant field has previously been published by reliable, independent publications. Exercise caution when using such sources: if the information in question is suitable for inclusion, someone else will probably have published it in independent reliable sources. Never use self-published sources as third-party sources about living people, even if the author is an expert, well-known professional researcher, or writer.
 * Unusable sources are just that -- unusable. If this results in some indiscriminate detail lacking any other independent sources, than it probably shouldn't have been in the article to begin with. Your opinions about me are irrelevant. Wikieditor19920 (talk) 01:05, 1 September 2021 (UTC)
 * And to the contrary, I see exactly what's going on here. It's totally inappropriate for you to be this involved in preserving these citations to your website and going to the lengths you are here. If the merits are correct, other editors will recognize it and keep the citations. Wikieditor19920 (talk) 00:42, 1 September 2021 (UTC)
 * Ahh yes, you see all. This is a comment about the conduct you are repeating here that led to your sanctions: I have no problem with consensus. But, I see you are now vandalizing other articles in retribution, calling consensus "vandalism". Careful. I know you posted that admins are all corrupt. But, you are going too far again. We have procedures. O3000, Ret. (talk) 01:11, 1 September 2021 (UTC)
 * Is the author of these sites an "established subject-matter expert whose work in the field has been previously published by reliable, independent publications?" If the answer is no, then the sources are not usable under WP:RS. Vague threats don't change that. Sorry. Nor is removing such content "vandalism," even if you don't like the changes. Wikieditor19920 (talk) 01:26, 1 September 2021 (UTC)
 * Absolutely. O3000, Ret. (talk) 11:13, 1 September 2021 (UTC)
 * @Objective3000 Where has this author had independently published works? Wikieditor19920 (talk) 19:04, 1 September 2021 (UTC)
 * The Wizard of Odds, beatingbonuses.com, The Gambling Times Guide to Blackjack, and BlackjackReview are also included self-published sources. Why didn't you bring them up? Veritop doesn't even exist. You seem to have a singular focus here instead of something against self-published sources. This is your COI. And everything has ads. CNN and the New York Times have dozens on their main pages alone. QFIT and blackjackincolor don't. And, read the guidelines. You are allowed to propose. O3000, Ret. (talk) 21:22, 31 August 2021 (UTC)
 * This is your COI. I'm not the one pushing a website that I authored. I agree that some of these other sources are sub-par, but there's a problem with wholesale removing all of the sources in a page, as I'm sure you'd agree. Before you go on another rant about how I have a "COI" against your sources, note that I did not remove "Blackjack in Color," another affiliate of the above-mentioned website, because I believe it provided helpful info. The cites to CV provided extraordinarily basic information that seemed redundant with other sources already provided; in other words, the added cite was not necessary. Wikieditor19920 (talk) 21:32, 31 August 2021 (UTC)
 * I didn't say they were subpar. Self-published does not mean subpar. And there is nothing basic about 113 variations many with effects on edge. As for blackjackincolor, most of the info doesn't exist anywhere else. And, it was edited by the same person who edited a large number of the famous texts on the subject. He also edited the free book you removed a cite to. O3000, Ret. (talk) 21:47, 31 August 2021 (UTC)
 * COI covers personal and financial interests. I didn't remove blackjackincolor precisely because the information wasn't readily available in another source. The QFIt citations were next to information supported by already-cited secondary sources. Wikieditor19920 (talk) 22:06, 31 August 2021 (UTC)
 * Actually, one of the terms in the removed cite, now in common use, was coined by me. O3000, Ret. (talk) 22:12, 31 August 2021 (UTC)
 * Which term was that? Both cites were restored, FWIW. Wikieditor19920 (talk) 22:28, 31 August 2021 (UTC)
 * And is there a source (not by you) that backs up this claim? Wikieditor19920 (talk) 23:53, 31 August 2021 (UTC)
 * And is there a source (not by you) that backs up this claim? Wikieditor19920 (talk) 23:53, 31 August 2021 (UTC)

 * This is unfortunate. Wikieditor has just deleted a cite to one of the most important papers ever written about shuffle tracking. (second link) just because it is on QFIT -- even though it is not linked to on any page in QFIT, has no links itself at all, no ads of any kind, and no mention of QFIT. This is a long standing addition that has implied consensus, but was deleted without any discussion or attempt to qualify the link. This is pure vandalism. He's also deleting other links on other pages referring to them as vandalism -- which is a sanctionable act. There are ways of handling this. This ain't one. O3000, Ret. (talk) 01:32, 1 September 2021 (UTC)
 * This looks to be a long and detailed document, but this website is quite literally the only location online where I could find it. We have no way of verifying the authenticity of it. It is not published in any second-hand source that I can find. I see it has been referenced it some books, which is useful, but again, how can we confirm that this is the original/intended work?
 * Second, I did not remove such cites on the premise they were "vandalism." I removed them, per the description, because it was a WP:SELFPUBLISHED piece, and I also cited my reasoning above in the edit summary. Wikieditor19920 (talk) 01:42, 1 September 2021 (UTC)
 * Bull. You removed it because it was on QFIT, even though it does not benefit QFIT in any conceivable manner. This is a well known, breakthrough document that means nothing to you. But it was lost for a time. Any number of experts can verify its authenticity. But, you wouldn't believe them either. Realize that the most important books on BJ, Snyder's Blackbelt, Grosjean's CAA (currently for sale on eBay for $8,800), Wong's Professional BJ, many, many more are ALL self-published. That is the nature of the field. Yet you continue to ignore all the other self-published sources here, and go after a perceived enemy of yours in a very different topic area where you are TBanned, even going to other articles with the same purpose. This is understood in the RS guidelines, if you would just read all of the text instead of cherry-picking. You are walking into articles that you have never edited and removing consensus material with zero discussion. Again, please reread the advice admin's gave you on your talk page. Your combative nature has never served you well. Look at your block log. Also, read WP:HOUND as it is now obviously on point and sanctionable. Also, see Law_of_holes. O3000, Ret. (talk) 01:59, 1 September 2021 (UTC)
 * Snyder's Blackbelt is published by Cardoza. Grosjean's CAA is published and has an assigned ISBN number. Wong's Professional Blackjack is published by Pi Yee Press and, again, has an ISBN number. All of these works are available on multiple platforms. Conversely, this other document, is not available on any other site and apparently has not been published by any major publisher. It's just not true that the only works available in this field are self published. The site itself raises possible permissions issues with regard to this work. I asked, on the relevant talk page, if we should include this link notwithstanding the 1) permissions issues and 2) authenticity/confirmation issues. Wikieditor19920 (talk) 02:13, 1 September 2021 (UTC)
 * Synder’s Blackbelt was self-published and only purchased by Cardoza many, many years later to reprint. His newest book released last month, Radical Blackjack, is published by Huntington Press. You will find me in the index on pages 116-121,153-158, 297, and in the acknowledgements. Wong is the sole owner of Pi Yee Press which has only published one other book not by Wong, no longer in print. It is self-published. Grosjean’s CAA was self-published by he and Mankodi. Yes it has an ISBN. So does Modern Blackjack, to which you deleted a cite. Modern Blackjack is also available at Amazon, Barnes & Noble, and dozens of other platforms. (I just looked and found out Walmart sells it. I had no idea.) Seriously, you know not of what you speak. O3000, Ret. (talk) 02:27, 1 September 2021 (UTC)
 * I did not remove a cite to Modern Blackjack. This was my only edit to the other page. Based on the information you provided, Snyder's Blackbelt is not self-published. Wong and Grosjean are both established experts in the field. The reason I referenced an ISBN, however, is to stress the point that I can find their works on various platforms, unlike the Shuffle treatise from Qfit. Again, QFit itself raised possible permissions issue, and it's not available elsewhere. I raised these issues on the relevant talk page. Wikieditor19920 (talk) 02:36, 1 September 2021 (UTC)
 * Yes, you deleted a cite to Modern Blackjack. This is pointless. O3000, Ret. (talk) 02:48, 1 September 2021 (UTC)
 * My mistake. I did. Restored, pending discussion. Wikieditor19920 (talk) 02:52, 1 September 2021 (UTC)

Well, this is getting quite ridiculous. I started editing here as a user 14 years ago yesterday. I have never attempted to add my name to WP and 99.97% of my edits are outside of my field. I do not like talking about myself. But, Wikieditorxxxx is demanding info. So, I’ll provide some. But first, let me clear up the suggestions that I have illegitimately hidden any possible COI. Over a decade ago, I added a COI notice to my user page. It was the only thing on my UP. The OP pointed to it in this discussion. Then came the AfD for an article about the OP. The subject and author of the article started phoning me, sometimes using pseudonyms as he does here. I was quite unnerved by the calls. I was further unnerved when an edit to the AfD pointed out that he had recently been convicted of trespassing related to an obsession with a local official. That edit is still in the AfD archives. So, I removed my personal info. An admin suggested I have it REVDELed. I should have.

Now in answer to the requests demands:
 * Arnold Snyder is acknowledged here as an expert in BJ. I contributed work to his latest book, Radical Blackjack published by Huntington Press. You will find me in the index for pages 116-121,153-158, 297, 301, and in the acknowledgements.
 * Don Schlesinger is widely acknowledged as one of the top BJ experts in the world. In Blackjack Attack, published by Huntington Press, I and my works are indexed for pages: 13, 106, 107, 134, 140-146, 152, 178, 179, 186, 189, 190, 204, 207, 209, 211. Also, the analyses on pages 214-286 and several other spots were created by me.
 * Game theorist Richard A. Epstein authored the text The Theory of Gambling and Statistical Logic, publisher Academic Press Elsevier. I am in the index for pages 140, 158, 239, 283, 416, 436, 437. Only three people are in the acknowledgements: Solomon W. Golomb distinguished prof at USC, Stewart N. Ethier, Professor Emeritus, Mathematics at Utah, and me. He states I “contributed numerical solutions to several problems posed herein – problems that would otherwise have remained wholly intractable.”
 * Speaking of Prof. Ethier, among his publications is Optimal Play Mathematical Studies of Games and Gambling with William R. Eadington Publisher : Institute for the Study of Gambling and Commercial Gaming at the Univ. of Nev. It contains a paper written by Prof. R. Michael Canjar which includes my analysis of Prof. Werthamer’s book on risk. I’m also mentioned in Werthamer’s book.
 * Michael Shackleford, AKA The Wizard of Odds, has been noted in this discussion as an expert. I already pointed out that he has published my work., , ,  These, and others, are studies that he requested I perform.
 * Altogether, I’m mentioned in 28 respected books, and others not so great or I haven’t read. I repeat, I do not want to be in WP and request that this edit be removed once this discussion is archived. O3000, Ret. (talk) 20:33, 1 September 2021 (UTC)

 * I do not think that acknowledgments or cites by peers is independent publication. And COI requires your disclosure. If you want to argue the case for using books that you wrote and self published as citations, as well as to your website, then you have to disclose that conflict per WP:COI. You can't have it both ways. Wikieditor19920 (talk) 23:19, 1 September 2021 (UTC)
 * , It's been disclosed, it's all over this discussion. You obviously know, or you wouldn't be on this page repeating that charge ad nauseum. At any rate, this isn't a venue for complaining about another editor's behavior. Please drop this and stick to content, or take it to an appropriate noticeboard and risk the inevitable WP:BOOMERANG. MrOllie (talk) 23:27, 1 September 2021 (UTC)
 * My reply is about whether the above constitutes "independent publication." As stated I am not clear, and frankly am leaning against, considering acknowledgements or citations to satisfy that standard. This is a content discussion. As for the COI, Objective3000 asked that this conversation be archived/deleted so as to protect their identity. I am all for privacy, but the COI guidelines require disclosure. Noting that in my response is not necessarily a "comment on the behavior" of another editor. Wikieditor19920 (talk) 23:37, 1 September 2021 (UTC)
 * , I believe that reliable sources repeating or republishing the prospective expert's work is exactly what WP:SELFPUB is about. MrOllie (talk) 23:42, 1 September 2021 (UTC)
 * The references carry some meaning, but they aren't "independent publication." SELFPUB asks for subject matter experts whose work in the relevant field has previously been published by reliable, independent publications. It would be helpful to know more about which aspects of the work, or which specific works, were acknowledged. I found the graphs and mathematical data (even if niche) more inclusion-appropriate than the broad overview of different strategies from Qfit, for which we are better off with published, secondary sources. Wikieditor19920 (talk) 23:47, 1 September 2021 (UTC)
 * Of course they are independent. And what do you mean by "independent sources"? Do you believe Elsevier Academic Press, known for publishing scientific articles by Noble Laureates, publishing books with my work is somehow not independent or not acceptable? And these are not just mentions - look at the number of index entries and read the acknowledgements. Did you look at any of the cites? Did you read any of the books? Just how far are you going to move the goalposts? It is clear you are here because you are barred from posting your Trumpian POV on polit articles and coming after an editor on an article where you have never before edited, with whom you have had multiple interactions at ANI before your indef TBan. Be careful. WP:HOUND O3000, Ret. (talk) 00:32, 2 September 2021 (UTC)
 * Misleading. Elsevier Academic Press did not publish your works. A citation or a footnote in someone else's book is not independent publication of your work. The book "Modern Blackjack" was published through Lulu.com, a platform for self publishers. Otherwise, I see no compelling reason to include these cites to Qfit, and especially not where a proper secondary source is available. Wikieditor19920 (talk) 02:43, 2 September 2021 (UTC)
 * These were not "citations" or "footnotes". They were studies I performed at the request of the author specifically for inclusion in the book. I spent a couple months collaborating with the author in a number of areas. Yes, it was my work being published by Elsevier. Consider that there might be some reason that experts come to me for help. As for Lulu, I created a book (now 700 pages) to be available online for free. I have a long history of providing free, online info. No publisher has any interest in publishing a free book. I went to Lulu later only because people were asking for hard copies. And BTW, the cite you just added to the shuffle tracking article is to an author with a bad reputation in the field after pushing a system considered nonsense (to put it politely) by his own partners. You do not "evaluate" a table based on things like the number of cigarette butts in ashtrays. You really need to read something, know something about the source, and not make assumptions before adding a cite. The vast majority of gambling books put out by large publishing houses push fraudulent systems. Large numbers are bought in airports and casino gift shops. They are popular because they are easy to read and promise that you will win with no effort. They all fit under your definition of a usable source, even though they are harmful. O3000, Ret. (talk) 10:30, 2 September 2021 (UTC)
 * This is not a megathread for all related pages. But Jerry Patterson, who by all reliable accounts invented the term shuffle tracking, was not mentioned or cited at all in that article (and whether or not you want to call it "airplane reading," his work is published in an independent secondary source). Curiously, Qfit and blackjackincolor were the first sources cited.
 * Further, it is possible to distinguish between popular sources and specialize sources without abandoning principles of RS. I don't really have much to add to the above. If limited sections of the Qfit author's studies or material is cited or used in a published book or by an expert, that's great. I don't see that as a carte blanche to prefer that author's work and have it prolifically cited in every blackjack page when secondary sources are available to provide the same information. Wikieditor19920 (talk) 21:19, 2 September 2021 (UTC)
 * Patterson has not been respected since the late 1980's and his book talks more about clumping than shuffle tracking. Clumping has no basis in math or probability theory. There are several real sources about ST:
 * Blackjack Blueprint, Rick Blaine, 2006, Chapter 24
 * Ready to Start Shuffle Tracking, Ted Forrester, 2004
 * Shuffle Tracker’s Cookbook, Arnold Snyder, 2003, Compilation of three Blackjack Forum 1994–1995 articles on ST with added updates and commentary.
 * Shuffle Tracking Report, Carl J. Sampson, 2003
 * Shuffle Tracking for Dummies, George C., 1996
 * Shuffle Tracking Treatise, Michael Hall, 1990 (currently found at www.qfit.com/blackjackshuffletracking.htm)
 * Non-Random Shuffling for Multiple Decks, Journal of Applied Probability, Vol. 24, No. 2, Gary Gottlieb, 1987
 * Also, my own book. Only the first is not self-published. Most valuable works in advantage play are self-published, and most are also hard to come by. You simply have not studied this area and have no idea what is and is not a good source. I don't even know why you think the book is related to ST, other than someone mistakenly added it to this article. But, WP is not RS. Having an ISBN number and popular publisher does not make anything reliable. I have never heard of anyone suggesting this Patterson book for anything, much less ST. His work before 1988 was acceptable, albeit outdated. And, the link to QFIT is to one of the most important studies ever performed on ST and the page does not in a way mention me, QFIT, or have any links to anywhere. O3000, Ret. (talk) 22:03, 2 September 2021 (UTC)
 * Even if he was later criticized, the article should not omit his role in the "coining" of this term. Reliable sources attribute it to him. As for the sources above, self published sources are reliable pertaining to facts about the source itself, so it would not be an improper use to say "X has criticized Patterson's methods/theories" and use X's blog or self-published book. That would be appropriate to include if X is an established expert. But it's not appropriate to just link to a self-published review for the statement "Patterson is widely criticized as unscientific by respected experts." This is also an extremely non-neutral way to word a sentence. Wikieditor19920 (talk) 00:07, 3 September 2021 (UTC)
 * As for the "treatise," my issues are outlined here. Wikieditor19920 (talk) 00:08, 3 September 2021 (UTC)
 * No, he was earlier criticized for pushing voodoo to try to make money. Viciously criticized by multiple actual, respected experts some of which were his partners. OK, this is now pure vandalism. Who said JP invented ST? Your cite is to his book. Of course his book said something roughly along those lines, related to his T.A.R.G.E.T. strategy created by Olsen who has since retracted support. Did you read the book? Have you read a single one of the actual sources on the subject? A single one of them? What reliable sources attribute it to him? You provided none. You simply have no idea what you are talking about. Let me remind you of the warning on your indef TBan, WP:IDHT WP:CIR. O3000, Ret. (talk) 00:37, 3 September 2021 (UTC)
 * Your vandalism continues. You now removed from the Patterson article that his TARGET strategy is questioned claiming the source (The Blackjack Encyclopedia) is not RS, when that source is used here. It is extremely well documented that TARGET is a fraud. His own instructors resigned rather then teach it, the developer retracted the strategy. This is like a bull in a china shop. You are turning Wikipedia into a casino fraud pusher. Why? O3000, Ret. (talk) 01:02, 3 September 2021 (UTC)
 * The main article attributed the term to him with citations to him and another source well before I ever touched it. The "Blackjack Encyclopedia" is self-published source and not adequate for the sentence it was cited for ("widely criticized by respected experts), as I noted in my edit summary. It is also a violation of WP:BLP to call someone a "fraud" without providing any sources to back that up. Wikieditor19920 (talk) 08:53, 3 September 2021 (UTC)
 * Two of the cites are to Patterson himself and the third, Gambler's Guide, is Sludikoff, who's reputation was worse. And that guide was also self-published. There exist myriad sources calling it a fraud in no uncertain terms. Snyder, Wong, and Schlesinger are three top sources. Snyder reminds us on page 289 in Radical Blackjack that he blasted Patterson in Blackjack Forum Magazine back in 1983. Wong performed simulations on his system and called it nonsense in his newsletters. Schlesinger publicly broke off his relationship with Patterson when TARGET came out, as did Feldman and Schiff. Eddie Olsen designed the strategy for Patterson, but then withdrew his support for it while Patterson continued to sell it. (Oddly, Olsen is used as a ref in this article with no mention that he withdrew support for the book used a a ref that he co-authored.) Blackjack Encyclopedia is referenced here -- which doesn't seem to bother you. Your focus is singular. O3000, Ret. (talk) 10:40, 3 September 2021 (UTC)
 * Simple solution: Provide those sources in the article. Wikieditor19920 (talk) 13:18, 3 September 2021 (UTC)
 * So, your solution is to have inaccurate info from bad sources followed by good sources negating the info? No. O3000, Ret. (talk) 13:37, 3 September 2021 (UTC)
 * No, the solution is to provide the source for your claims in the article. The attribution of "Shuffle tracking" was already in the article. You're raising the claim that this is a false attribution, but none of the sources by your description say this is a false attribution.
 * The sentence I removed, which referenced a consensus unspecified "respected experts," only provided a cite to a single individual's website. A poorly worded, poorly cited criticism does not belong in a BLP. If you want to add the criticisms of Patterson to either the Patterson or Shuffle Tracking article, then it would seem to make sense to add the sources you cited above. Wikieditor19920 (talk) 13:50, 3 September 2021 (UTC)
 * I am talking about the Shuffle tracking article where you added a sentence stating that Patterson invented shuffle tracking using Patterson as the reference. Obviously Patterson cannot be used as a reference to a major claim like this. O3000, Ret. (talk) 13:57, 3 September 2021 (UTC)
 * Is it actually disputed that he coined the term, outside of our discussion here? Wikieditor19920 (talk) 14:03, 3 September 2021 (UTC)
 * I can't recall ever seeing anyone attach the term to him before reading it in Wikipedia. He did have a chapter on a debunked method of cutting to cause dealer busts. This refers to "card clumping" which is considered nonsense by all the experts. It is not related to what all of the material on shuffle tracking refers. Whoever added the cite may have not known what shuffle tracking is. O3000, Ret. (talk) 14:23, 3 September 2021 (UTC)
 * OK, the addition of Jerry Patterson to this article was made in April 2007 by user LankyLongArm. That user made a total of 73 edits every one of which was related to Patterson projects, and then left the project. You added the text to the shuffle tracking article copying the claim from this article. As I said earlier, Wikipedia is not considered a reliable source by Wikipedia. O3000, Ret. (talk) 14:48, 3 September 2021 (UTC)
 * The claim was from the source, not the article. Wikieditor19920 (talk) 18:18, 3 September 2021 (UTC)
 * Again, the claim about the person is made by the person. The claim is unsupported by a source. The original claim here was made by an WP:SPA who created the shuffle tracking article as a hagiograph, quickly trimmed by RRay, along with additions in other articles making claims about Patterson projects. O3000, Ret. (talk) 19:34, 3 September 2021 (UTC)
 * To repeat: it is the sources in the article that provide the basis for the attribution of "Shuffle tracking" to Jerry Patterson. One is Patterson's book, and the other is a book co-written by Patterson and another. My question to you again is: Do you have a reliable source disputing that he coined the term? Wikieditor19920 (talk) 20:49, 3 September 2021 (UTC)
 * Where do the sources say this? What page numbers? And since when do we state in wikivoice the validity of claims made by people about themselves. As for dispute, I say again, I can't recall anyone ever making this claim. So, why would there be a dispute. That would be like me asking is there is any dispute over my claim that I can fly faster than the speed of light. There isn't source for any such dispute. So, I guess I can. This is just like all the past discussions I've seen involving you. O3000, Ret. (talk) 21:39, 3 September 2021 (UTC)
 * How about the very book that you described as the seminal treatise on shuffle tracking? In "Break the Dealer", Patterson and Olsen published the first book describing shuffle-tracking. The cites in the article are to the 1986 book and Patterson's updated 2001 book. Wikieditor19920 (talk) 22:35, 3 September 2021 (UTC)
 * Well yes, that treatise is accepted by the experts as a seminal work. It was not self-proclaimed as I had nothing to do with it. Do you actually not understand that an encyclopedia does not accept as a source self-proclaimed declarations? Do you actually not understand that these claims were added by an WP:SPA who did nothing but add salesy crap about Patterson? Do you actually have any concept of shuffle tracking and the math behind NRS? Have you read anything at all discussing the history, methodologies, or math behind these concepts? Of course he claimed his book was great. Olsen also said this, and then later totally retracted his support after it was proved to be nonsense. But, go ahead and add claims that strategies debunked decades ago are valid. Casinos love it. I'm tired of your IDHT. O3000, Ret. (talk) 00:34, 4 September 2021 (UTC)
 * If we couldn't find a secondary source to back up Patterson's claim that he coined the term "shuffle tracking," it would need to be qualified with language like "Patterson claims." If someone makes a claim and it is published, it is includable. No such qualifier is necessary because we have a secondary source backing that one up, one that you claimed was so important it was vandalism if it was not cited in the particular place you left it. I also found the page where you echo your claims here about how Jerry Patterson is a fraud. Wikieditor19920 (talk) 01:22, 4 September 2021 (UTC)
 * I already responded to this and have no idea why you are linking to something I put on the web over 20 years ago. I will not play this game of infinite, circular argument with you any more. Please read WP:IDHT as advised by El C in your TBan. O3000, Ret. (talk) 10:46, 4 September 2021 (UTC)
 * Incidentally, since you feel the publisher is of such importance, Gambler's Guide, which you used as an acceptable source, was published by Lyle Stuart, a very small publishing house that published The Turner Diaries and The Anarchist Cookbook, required reading for racist, terrorists. Hope you won't be using them as sources. Just because something has an ISBN number and has the name of a "publisher" inside doesn't mean you should use it as a source without at least reading it first and learning something about the author. O3000, Ret. (talk) 13:07, 3 September 2021 (UTC)
 * "Gamblers' Guide" was already cited as a source in the main Jerry Patterson article, which you previously edited. If "Gambler's Guide" is associated with "frauds, racists, and terrorists," why didn't you remove it then? Not unironically, Lyle Stuart was a prolific gambler/writer himself and his publishing house apparently posted books that are "controversial." He was also apparently a womanizer. Wikieditor19920 (talk) 13:18, 3 September 2021 (UTC)
 * I didn't remove it because I don't remove non-SPAM cites from these articles. Someone else who doesn't personally know most everyone in the field needs to do this. O3000, Ret. (talk) 13:37, 3 September 2021 (UTC)
 * Also, "MrOllie," don't ping me again. Wikieditor19920 (talk) 23:39, 1 September 2021 (UTC)
 * I'll do my best, it is built into the reply-link script which I use for most talk page discussions. - MrOllie (talk) 23:43, 1 September 2021 (UTC)
 * OK no worries. I'm following the discussion. I'll add a please next time. Wikieditor19920 (talk) 23:48, 1 September 2021 (UTC)

Constructionism is an established legal doctrine which restricts interpretations of a statute only to its precise wording. In other words, if the administrators who established WP:RS and WP:SOURCES wanted to include citations of one’s work as a sufficient criterion for expert status, they could have done so. They did not.Aabcxyz (talk) 18:19, 17 September 2021 (UTC)

Reliable source noticeboard now has a discussion as to the lack of expert status of Objective3000, and that therefore the references to the self-published webpages qfit.com, blackjackincolor.com, and blackjack-scams.com are in violation of WP:RS and WP:SOURCES. Reliable_sources/Noticeboard Aabcxyz (talk) 20:50, 17 September 2021 (UTC)
 * This RSN filing by Aabcxyz has been closed. Aabcxyz has been indef blocked by two admins for abusing editing privileges and sockpuppetry. I have made an appointment to get new glasses after reading all of these. O3000, Ret. (talk) 00:37, 23 September 2021 (UTC)

OBO rule
On the original bets only rule. This is an important rule in Puerto Rico, Korea, all but the Galaxy casinos in Macao, various casinos in Canada, Europe, Australia, and the UK. This is not an American only encyclopedia. O3000, Ret. (talk) 19:10, 27 September 2021 (UTC)

 * Thanks -- I was going to mention that, but it doesn't seem like my revert has proven contentious yet. Rray (talk) 19:47, 27 September 2021 (UTC)
 * Someone with obviously little knowledge of the subject removing consensus text and then removing it a second time after reversion by someone editing this article since the early days, instead of coming to the talk page. But, it seems discussion is an obsolete concept. Wikieditor* obviously violated guidelines. O3000, Ret. (talk) 21:53, 27 September 2021 (UTC)

the controlling player
what exactly does a controlling player do as it is not made clear from the article ; nor is it made clear what constuties a controlling player although it seems that it is a player whose bet is highest ==BBLLAANNKK TR41N== (talk) 08:45, 16 October 2022 (UTC)

Five card charlie
It redirects to Blackjack, but there's nothing relevant to it in that section. 89.64.70.62 (talk) 22:55, 9 December 2022 (UTC)

 * Unfortunately, this is not a rare occurrence. Sometimes an article is created, goes through AfD, results in redirect, and overtime the target changes to move or even remove the relevant reference. There are others ways this happens too. Solutions might include updating the redirect to a better target on this or another page, updating this page with the content inferred by the redirected page name, or even deletion of the redirect. —¿philoserf? (talk) 00:56, 10 December 2022 (UTC)
 * So, is anyone knowledgeable enough to "update this page with the content inferred by the redirected page name"? 37.47.205.253 (talk) 09:43, 29 December 2022 (UTC)

title: Talk:Blackjack


text:
Naive set theory

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.

Sets are of great importance in mathematics; in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory suffices for many purposes, while also serving as a stepping stone towards more formal treatments.

Method
A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics. As a matter of convenience, use of naive set theory and its formalism prevails even in higher mathematics – including in more formal settings of set theory itself.

The first development of set theory was a naive set theory. It was created at the end of the 19th century by Georg Cantor as part of his study of infinite sets and developed by Gottlob Frege in his Grundgesetze der Arithmetik.

Naive set theory may refer to several very distinct notions. It may refer to
 * Informal presentation of an axiomatic set theory, e.g. as in Naive Set Theory by Paul Halmos.
 * Early or later versions of Georg Cantor's theory and other informal systems.
 * Decidedly inconsistent theories (whether axiomatic or not), such as a theory of Gottlob Frege that yielded Russell's paradox, and theories of Giuseppe Peano and Richard Dedekind.

Paradoxes
The assumption that any property may be used to form a set, without restriction, leads to paradoxes. One common example is Russell's paradox: there is no set consisting of "all sets that do not contain themselves". Thus consistent systems of naive set theory must include some limitations on the principles which can be used to form sets.

Cantor's theory
Some believe that Georg Cantor's set theory was not actually implicated in the set-theoretic paradoxes (see Frápolli 1991). One difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system. By 1899, Cantor was aware of some of the paradoxes following from unrestricted interpretation of his theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory. Cantor's paradox can actually be derived from the above (false) assumption—that any property $P(x)$ may be used to form a set—using for $P(x)$ "$x$ is a cardinal number". Frege explicitly axiomatized a theory in which a formalized version of naive set theory can be interpreted, and it is this formal theory which Bertrand Russell actually addressed when he presented his paradox, not necessarily a theory Cantorwho, as mentioned, was aware of several paradoxespresumably had in mind.

Axiomatic theories
Axiomatic set theory was developed in response to these early attempts to understand sets, with the goal of determining precisely what operations were allowed and when.

Consistency
A naive set theory is not necessarily inconsistent, if it correctly specifies the sets allowed to be considered. This can be done by the means of definitions, which are implicit axioms. It is possible to state all the axioms explicitly, as in the case of Halmos' Naive Set Theory, which is actually an informal presentation of the usual axiomatic Zermelo–Fraenkel set theory. It is "naive" in that the language and notations are those of ordinary informal mathematics, and in that it does not deal with consistency or completeness of the axiom system.

Likewise, an axiomatic set theory is not necessarily consistent: not necessarily free of paradoxes. It follows from Gödel's incompleteness theorems that a sufficiently complicated first order logic system (which includes most common axiomatic set theories) cannot be proved consistent from within the theory itself – even if it actually is consistent. However, the common axiomatic systems are generally believed to be consistent; by their axioms they do exclude some paradoxes, like Russell's paradox. Based on Gödel's theorem, it is just not known – and never can be – if there are no paradoxes at all in these theories or in any first-order set theory.

The term naive set theory is still today also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory.

Utility
The choice between an axiomatic approach and other approaches is largely a matter of convenience. In everyday mathematics the best choice may be informal use of axiomatic set theory. References to particular axioms typically then occur only when demanded by tradition, e.g. the axiom of choice is often mentioned when used. Likewise, formal proofs occur only when warranted by exceptional circumstances. This informal usage of axiomatic set theory can have (depending on notation) precisely the appearance of naive set theory as outlined below. It is considerably easier to read and write (in the formulation of most statements, proofs, and lines of discussion) and is less error-prone than a strictly formal approach.

Sets, membership and equality
In naive set theory, a set is described as a well-defined collection of objects. These objects are called the elements or members of the set. Objects can be anything: numbers, people, other sets, etc. For instance, 4 is a member of the set of all even integers. Clearly, the set of even numbers is infinitely large; there is no requirement that a set be finite.

The definition of sets goes back to Georg Cantor. He wrote in his 1915 article Beiträge zur Begründung der transfiniten Mengenlehre:

"“Unter einer 'Menge' verstehen wir jede Zusammenfassung M von bestimmten wohlunterschiedenen Objekten unserer Anschauung oder unseres Denkens (welche die 'Elemente' von M genannt werden) zu einem Ganzen.” – Georg Cantor" "“A set is a gathering together into a whole of definite, distinct objects of our perception or of our thought—which are called elements of the set.” – Georg Cantor"

Note on consistency
It does not follow from this definition how sets can be formed, and what operations on sets again will produce a set. The term "well-defined" in "well-defined collection of objects" cannot, by itself, guarantee the consistency and unambiguity of what exactly constitutes and what does not constitute a set. Attempting to achieve this would be the realm of axiomatic set theory or of axiomatic class theory.

The problem, in this context, with informally formulated set theories, not derived from (and implying) any particular axiomatic theory, is that there may be several widely differing formalized versions, that have both different sets and different rules for how new sets may be formed, that all conform to the original informal definition. For example, Cantor's verbatim definition allows for considerable freedom in what constitutes a set. On the other hand, it is unlikely that Cantor was particularly interested in sets containing cats and dogs, but rather only in sets containing purely mathematical objects. An example of such a class of sets could be the von Neumann universe. But even when fixing the class of sets under consideration, it is not always clear which rules for set formation are allowed without introducing paradoxes.

For the purpose of fixing the discussion below, the term "well-defined" should instead be interpreted as an intention, with either implicit or explicit rules (axioms or definitions), to rule out inconsistencies. The purpose is to keep the often deep and difficult issues of consistency away from the, usually simpler, context at hand. An explicit ruling out of all conceivable inconsistencies (paradoxes) cannot be achieved for an axiomatic set theory anyway, due to Gödel's second incompleteness theorem, so this does not at all hamper the utility of naive set theory as compared to axiomatic set theory in the simple contexts considered below. It merely simplifies the discussion. Consistency is henceforth taken for granted unless explicitly mentioned.

Membership
If x is a member of a set A, then it is also said that x belongs to A, or that x is in A. This is denoted by x ∈ A. The symbol ∈ is a derivation from the lowercase Greek letter epsilon, "ε", introduced by Giuseppe Peano in 1889 and is the first letter of the word ἐστί (means "is"). The symbol ∉ is often used to write x ∉ A, meaning "x is not in A".

Equality
Two sets A and B are defined to be equal when they have precisely the same elements, that is, if every element of A is an element of B and every element of B is an element of A. (See axiom of extensionality.) Thus a set is completely determined by its elements; the description is immaterial. For example, the set with elements 2, 3, and 5 is equal to the set of all prime numbers less than 6. If the sets A and B are equal, this is denoted symbolically as A = B (as usual).

Empty set
The empty set, denoted as $$\varnothing$$ and sometimes $$\{\}$$, is a set with no members at all. Because a set is determined completely by its elements, there can be only one empty set. (See axiom of empty set.) Although the empty set has no members, it can be a member of other sets. Thus $$\varnothing\neq\{\varnothing\}$$, because the former has no members and the latter has one member.

Specifying sets
The simplest way to describe a set is to list its elements between curly braces (known as defining a set extensionally). Thus $\{1, 2\}$ denotes the set whose only elements are $1$ and $2$. (See axiom of pairing.) Note the following points: (These are consequences of the definition of equality in the previous section.)
 * The order of elements is immaterial; for example, $\{1, 2\} = \{2, 1\}$.
 * Repetition (multiplicity) of elements is irrelevant; for example, $\{1, 2, 2\} = \{1, 1, 1, 2\} = \{1, 2\}$.

This notation can be informally abused by saying something like $\{dogs\}$ to indicate the set of all dogs, but this example would usually be read by mathematicians as "the set containing the single element dogs".

An extreme (but correct) example of this notation is $\{\}$, which denotes the empty set.

The notation $\{x : P(x)\}$, or sometimes $\{x$, is used to denote the set containing all objects for which the condition $P$ holds (known as defining a set intensionally). For example, $\{x$ denotes the set of real numbers, $\{x$ denotes the set of everything with blonde hair.

This notation is called set-builder notation (or "set comprehension", particularly in the context of Functional programming). Some variants of set builder notation are:
 * $\{x ∈ A$ denotes the set of all $x$ that are already members of $A$ such that the condition $P$ holds for $x$. For example, if $Z$ is the set of integers, then $\{x ∈ Z$ is the set of all even integers. (See axiom of specification.)
 * $\{F(x)$ denotes the set of all objects obtained by putting members of the set $A$ into the formula $F$. For example, $\{2x$ is again the set of all even integers. (See axiom of replacement.)
 * $\{F(x)$ is the most general form of set builder notation. For example, $\{x's owner$ is the set of all dog owners.

Subsets
Given two sets A and B, A is a subset of B if every element of A is also an element of B. In particular, each set B is a subset of itself; a subset of B that is not equal to B is called a proper subset.

If A is a subset of B, then one can also say that B is a superset of A, that A is contained in B, or that B contains A. In symbols, $A ⊆ B$ means that A is a subset of B, and $B ⊇ A$ means that B is a superset of A. Some authors use the symbols ⊂ and ⊃ for subsets, and others use these symbols only for proper subsets. For clarity, one can explicitly use the symbols ⊊ and ⊋ to indicate non-equality.

As an illustration, let R be the set of real numbers, let Z be the set of integers, let O be the set of odd integers, and let P be the set of current or former U.S. Presidents. Then O is a subset of Z, Z is a subset of R, and (hence) O is a subset of R, where in all cases subset may even be read as proper subset. Not all sets are comparable in this way. For example, it is not the case either that R is a subset of P nor that P is a subset of R.

It follows immediately from the definition of equality of sets above that, given two sets A and B, $A = B$ if and only if $A ⊆ B$ and $B ⊆ A$. In fact this is often given as the definition of equality. Usually when trying to prove that two sets are equal, one aims to show these two inclusions. The empty set is a subset of every set (the statement that all elements of the empty set are also members of any set A is vacuously true).

The set of all subsets of a given set A is called the power set of A and is denoted by $$2^A$$ or $$P(A)$$; the "$P$" is sometimes in a script font: $\wp(A)$. If the set A has n elements, then $$P(A)$$ will have $$2^n$$ elements.

Universal sets and absolute complements
In certain contexts, one may consider all sets under consideration as being subsets of some given universal set. For instance, when investigating properties of the real numbers R (and subsets of R), R may be taken as the universal set. A true universal set is not included in standard set theory (see Paradoxes below), but is included in some non-standard set theories.

Given a universal set U and a subset A of U, the complement of A (in U) is defined as

In other words, AC ("A-complement"; sometimes simply A, "A-prime" ) is the set of all members of U' which are not members of A. Thus with R, Z and O defined as in the section on subsets, if Z is the universal set, then OC is the set of even integers, while if R is the universal set, then OC is the set of all real numbers that are either even integers or not integers at all.

Unions, intersections, and relative complements
Given two sets A and B, their union is the set consisting of all objects which are elements of A or of B or of both (see axiom of union). It is denoted by $x ∉ A\}$.

The intersection of A and B is the set of all objects which are both in A and in B. It is denoted by $A ∪ B$.

Finally, the relative complement of B relative to A, also known as the set theoretic difference of A and B, is the set of all objects that belong to A but not to B. It is written as $A ∩ B$ or $A \ B$.

Symbolically, these are respectively

The set B doesn't have to be a subset of A for $A − B$ to make sense; this is the difference between the relative complement and the absolute complement ($(x ∈ A) ∨ (x ∈ B)\}$) from the previous section.

To illustrate these ideas, let A be the set of left-handed people, and let B be the set of people with blond hair. Then $(x ∈ A) ∧ (x ∈ B)\} = \{x ∈ A$ is the set of all left-handed blond-haired people, while $(x ∈ A) ∧ ¬ (x ∈ B) \} = \{x ∈ A$ is the set of all people who are left-handed or blond-haired or both. $A \ B$, on the other hand, is the set of all people that are left-handed but not blond-haired, while $A^{C} = U \ A$ is the set of all people who have blond hair but aren't left-handed.

Now let E be the set of all human beings, and let F be the set of all living things over 1000 years old. What is $A ∩ B$ in this case? No living human being is over 1000 years old, so $A ∪ B$ must be the empty set {}.

For any set A, the power set $$P(A)$$ is a Boolean algebra under the operations of union and intersection.

Ordered pairs and Cartesian products
Intuitively, an ordered pair is simply a collection of two objects such that one can be distinguished as the first element and the other as the second element, and having the fundamental property that, two ordered pairs are equal if and only if their first elements are equal and their second elements are equal.

Formally, an ordered pair with first coordinate a, and second coordinate b, usually denoted by (a, b), can be defined as the set $$\{\{a\}, \{a, b\}\}.$$

It follows that, two ordered pairs (a,b) and (c,d) are equal if and only if $A \ B$ and $B \ A$.

Alternatively, an ordered pair can be formally thought of as a set {a,b} with a total order.

(The notation (a, b) is also used to denote an open interval on the real number line, but the context should make it clear which meaning is intended. Otherwise, the notation ]a, b[ may be used to denote the open interval whereas (a, b) is used for the ordered pair).

If A and B are sets, then the Cartesian product (or simply product) is defined to be:

That is, $E ∩ F$ is the set of all ordered pairs whose first coordinate is an element of A and whose second coordinate is an element of B.

This definition may be extended to a set $E ∩ F$ of ordered triples, and more generally to sets of ordered n-tuples for any positive integer n. It is even possible to define infinite Cartesian products, but this requires a more recondite definition of the product.

Cartesian products were first developed by René Descartes in the context of analytic geometry. If R denotes the set of all real numbers, then $a = c$ represents the Euclidean plane and $b = d$ represents three-dimensional Euclidean space.

Some important sets
There are some ubiquitous sets for which the notation is almost universal. Some of these are listed below. In the list, a, b, and c refer to natural numbers, and r and s are real numbers.
 * 1) Natural numbers are used for counting. A blackboard bold capital N ($$\mathbb{N}$$) often represents this set.
 * 2) Integers appear as solutions for x in equations like x + a = b. A blackboard bold capital Z ($$\mathbb{Z}$$) often represents this set (from the German Zahlen, meaning numbers).
 * 3) Rational numbers appear as solutions to equations like a + bx = c. A blackboard bold capital Q ($$\mathbb{Q}$$) often represents this set (for quotient, because R is used for the set of real numbers).
 * 4) Algebraic numbers appear as solutions to polynomial equations (with integer coefficients) and may involve radicals (including $$i=\sqrt{-1\,}$$) and certain other irrational numbers. A Q with an overline ($$\overline{\mathbb{Q}}$$) often represents this set. The overline denotes the operation of algebraic closure.
 * 5) Real numbers represent the "real line" and include all numbers that can be approximated by rationals. These numbers may be rational or algebraic but may also be transcendental numbers, which cannot appear as solutions to polynomial equations with rational coefficients. A blackboard bold capital R ($$\mathbb{R}$$) often represents this set.
 * 6) Complex numbers are sums of a real and an imaginary number: $$r+s\,i$$. Here either $$r$$ or $$s$$ (or both) can be zero; thus, the set of real numbers and the set of strictly imaginary numbers are subsets of the set of complex numbers, which form an algebraic closure for the set of real numbers, meaning that every polynomial with coefficients in $$\mathbb{R}$$ has at least one root in this set. A blackboard bold capital C ($$\mathbb{C}$$) often represents this set. Note that since a number $$r+s\,i$$ can be identified with a point $$(r,s)$$ in the plane, $$\mathbb{C}$$ is basically "the same" as the Cartesian product $$\R\times\R$$ ("the same" meaning that any point in one determines a unique point in the other and for the result of calculations, it doesn't matter which one is used for the calculation, as long as multiplication rule is appropriate for $$\mathbb{C}$$).

Paradoxes in early set theory
The unrestricted formation principle of sets referred to as the axiom schema of unrestricted comprehension,

is the source of several early appearing paradoxes:
 * $a ∈ A and b ∈ B\}.$ led, in the year 1897, to the Burali-Forti paradox, the first published antinomy.
 * $A × B$ produced Cantor's paradox in 1897.
 * $A × B × C$ yielded Cantor's second antinomy in the year 1899. Here the property $P$ is true for all $x$, whatever $x$ may be, so $Y$ would be a universal set, containing everything.
 * $R^{2} := R × R$, i.e. the set of all sets that do not contain themselves as elements, gave Russell's paradox in 1902.

If the axiom schema of unrestricted comprehension is weakened to the axiom schema of specification or axiom schema of separation,

then all the above paradoxes disappear. There is a corollary. With the axiom schema of separation as an axiom of the theory, it follows, as a theorem of the theory:

Or, more spectacularly (Halmos' phrasing): There is no universe. Proof: Suppose that it exists and call it $P$. Now apply the axiom schema of separation with $R^{3} := R × R × R$ and for $P$ use $Y = {x : P(x)}$. This leads to Russell's paradox again. Hence $X$ cannot exist in this theory.

Related to the above constructions is formation of the set

where the statement following the implication certainly is false. It follows, from the definition of $U$, using the usual inference rules (and some afterthought when reading the proof in the linked article below) both that $x is an ordinal\}$ and $x is a cardinal\}$ holds, hence $\{\} = \{\}\}$. This is Curry's paradox.

It is (perhaps surprisingly) not the possibility of $x ∉ x\}$ that is problematic. It is again the axiom schema of unrestricted comprehension allowing $Y = \{x ∈ X : P(x)\}$ for $X = U$. With the axiom schema of specification instead of unrestricted comprehension, the conclusion $P(x)$ does not hold and hence $x ∉ x$ is not a logical consequence.

Nonetheless, the possibility of $(x ∈ x) → \{\} ≠ \{\}\}$ is often removed explicitly or, e.g. in ZFC, implicitly, by demanding the axiom of regularity to hold. One consequence of it is

or, in other words, no set is an element of itself.

The axiom schema of separation is simply too weak (while unrestricted comprehension is a very strong axiom—too strong for set theory) to develop set theory with its usual operations and constructions outlined above. The axiom of regularity is of a restrictive nature as well. Therefore, one is led to the formulation of other axioms to guarantee the existence of enough sets to form a set theory. Some of these have been described informally above and many others are possible. Not all conceivable axioms can be combined freely into consistent theories. For example, the axiom of choice of ZFC is incompatible with the conceivable "every set of reals is Lebesgue measurable". The former implies the latter is false.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Naive set theory