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Archive 1

I think the following link should be added in the External links section: probability.infarom.ro Lottery Mathematics. There are some general formulas covering all numeric lotteries regarding probabilities and number of prizes. —Preceding unsigned comment added by Infarom (talkcontribs) 14:02, 14 March 2009 (UTC)

you added it to the Lottery mathematics article. It isn't needed here too. 2005 (talk) 09:07, 14 June 2009 (UTC)

Lottery Winner's Names

These should be removed. These people are not noteworthy other than being lucky and don't merit inclusion in an encylopedia. Seems like an attempt to enable people to solicit donations from the winner. I know the names are available on other Internet sites, but since Wikipedia comes up first in most Google searches and it's not the people who are important, but rather the event (the biggest winning jackpot) that is important I say remove the names 63.26.103.24 (talk) 03:42, 10 August 2008 (UTC)eric

Canada's two "national lotteries"

Are Canada's two "national lotteries" really "national"? Seems to me they are just run by associations of provincial lotteries, much like the state lottery associations (like Powerball) in the USA. Already the great majority of US population lives in Powerball states—if every state had a Powerball-associated lottery, would Powerball be a national lottery? To me the term "national" implies that is run by the federal government. (Which might be unconstitutional as things stand in the States.) NTK 18:30, 3 Feb 2005 (UTC)

  • A good point; I have changed this to "nation-wide" and also did some minor changes to the prior paragraph about the prior truly national lottery. Beyond this, I have a more major concern that this article focusses only on the official widespread Lotteries with little or no space for lotteries in general, eg, types of lotteries, informal lotteries at the level of communities or service clubs, etc. If I were starting from scratch I'd move this whole article to something like "Current major regional lotteries" and have a more general "Lottery" article...but I don't have the scope to do that myself right now. Sharkford 15:15, 21 October 2005 (UTC)
  • "To me the term 'national' implies that is run by the federal government." I think that's a limiting definition. Lotto 6/49 is played in every jurisdiction in Canada and is administered by a public corporation formed by the lottery commissions of every province and territory (the Interprovincial Lottery Corporation). Typically, governments in Canada form public corporations for these kinds of activities, and federal programs are frequently designed through meetings of the provincial premiers, outside of the federal legislative houses. Your definition might be suitable for most countries but it would make it impossible to describe almost anything in Canada as "national," (including our "national" health care). --Tedd (talk) 17:24, 29 December 2007 (UTC)

Vanishingly small?

Sure, to win a Powerball jackpot. But there other smaller jackpot games with much easier odds, like Cash 5 here in Pennsylvania. The odds are about 1 in 575,595, not good odds, but not "vanishingly small". For that reason I have to put the objectivity of this article in question.

Odds for Cash 5 in Virginia are 1 in 278,256.

While there is some subjectivity in the choice of words to describe the long odds (hence the use of "many", one supposes), it's also important to distinguish the odds of the different prizes. The odds against winning the biggest prizes are indeed huge, but many lotteries, in order to keep players playing, have thousands, even millions, of low-value "prizes" (such as another lottery ticket) so buyers feel like they've won something. I added a note to this effect.
In addition, the length of the odds should be balanced with the "expected value" of the ticket (calculated by summing the value of each prize, divided—or multiplied, depending on how the odds are expressed—by the odds of winning that prize). In my experience, the expected value of a government lottery ticket is usually no more than about half its price.
To be sure, with a subject like this, it's easy to get up on a soap box (one way or another), but let's not allow that fact to prevent a thorough examination of the subject. --Piledhigheranddeeper (talk) 15:33, 2 July 2008 (UTC)

The info here is only half full

The first line of the article seems to be very shallow. Well, though it ("lots") is the basic idea maybe the intro could be a bit more detailed. The word Lotto isn't explained in detail to differentiate it from the lottery ticket. I guess I could fill in the gaps but someone else can also help. Also do we need the list of countries with lotteries at the top? Can we introduce a section on wheeling systems and expand on it? I know something on wheeling but an expert hand on this would be good. Tx Idleguy 19:51, 22 October 2005 (UTC)

I agree, the initial definition is dire. The article badly needs to draw a distinction between a lottery (where zero prizes might conceivably be won) and a raffle (where all prizes are pre-designated and won, for example the UK's Premium Bonds, or the UK's EuroMillions Raffle) —Preceding unsigned comment added by 87.114.11.4 (talk) 15:33, 20 January 2010 (UTC)

Odds and Winnings

Any game which picks x amount of numbers from a to b is a lottery.

The difference between lotteries however, has to do with the payout amount for each.

For example, if you're running a lottery, you generally won't let people match any one number, because too many people will win.

The people who run the lotteries have the ability to shift up or down the level of prizes involved for each one, and they do it in their favor.

A top down lottery, is one in which the odds are made significantly difficult (some weeks no one wins) with six or seven numbers so that eventually one person will win a huge prize. One thing worth arguing over is that if you buy a $2 ticket you should expect some one to win a prize that week. Putting the money into the next weeks jackpot assumes that you will buy a ticket the next week, which is not always the case.

A bottom up lottery would be one in which most of the prizes are distributed to the bottom end of the lottery, with the remainder going to winners with more numbers. This system seems inherently more fair, although the prizes would not be as good. But in a draw where no one wins, do you really care how big the prizes are? At least more people would be satisfied.

LotteryOhYah 03:07, 24 October 2005 (UTC)

"But in a draw where no one wins, do you really care how big the prizes are?" That ignores the marketing aspect of the game. The allure of a huge (potential) prize probably draws a lot of players — perhaps even most of them. I think marketing also explains why most of the games use numbers. A game like Lotto 6/49 would be exactly the same game if you were asked to choose six from a list of 49 fruits and vegetables, instead of six from a list of 49 numbers. But virtually all the games use numbers, probably in part because a game without numbers would diminish the illusion that there's some significance to the different combinations. A quick perusal of lottery web sites — and even this discussion page — shows that a lot of people enjoy speculating about patterns and probabilities, even if most of that speculation is mathematically unfounded. The numbers make that possible. --Tedd (talk) 17:06, 29 December 2007 (UTC)

People being unsatisfied by the Lottery, prizes, and odds doesn't seem to stop them from playing. If you're not satisfied or if you think it's crooked, then the obvious answer is "DON'T PLAY!"; it's as simple as that, if you think about it, but people still play.

Largest Prizes

The $363m Mega Millions jackpot was actually bigger than the $365m Powerball Jackpot because of how the prizes are paid. Because of the structure of the annuities, Mega Millions annuities are worth about 55% of the advertised prize, but Powerball jackpots are worth about 46%. So the MM jackpot was about $30m bigger, in real dollars. 70.22.209.192 09:57, 24 February 2006 (UTC)

In Europe, as the prizes are paid tax free, they are worth 100% of the advertised prize, so on an after tax basis, the Euromillions €183m is bigger than both :) I've added the figures in $ and £ (based on exchange rate on that day), which values it at $220m, about $20m bigger than 55% of $363. The tax situation is mentioned in the article, but it might be worth adding in the notes section for the taxable prizes how much the winner actually got, unless it would make the table too detailed, do you know off hand how many took it as a lump sum vs annuity, and if those figures are easily available? MartinRe 10:54, 24 February 2006 (UTC)

Yes. How much tax is taken in the US lotteries? Seems to be a significant issue. In Australia winning are tax free. (Greg)


To answer the question above (Greg), Lottery winnings in the US are considered "taxable income." In Virginia, if any one of your tickets is $5001 or higher it is taxed at a rate of 25% Federal and 4% State immediately. If your ticket is $5000 or less, a W2 form is issued that would be filed with the next tax return. With that said, 25% and 4% are the MINIMUM tax deductions. Since the prizes are taxable income, depending on what your income for the year is, you could owe more than the minimum. Someone making a grand total, salary plus lottery winnings, of $30,000 for the year is going to pay less in taxes than the person who made $250,000 for the year. However, taxes owed by Lottery winnings can be written off by submitting losing tickets to off-set the taxes owed. If you've won $5,000 for the year submit $5,000 worth in losing tickets, and you won't have to pay a dime. The money you put into the Lottery in Virginia is considered a donation, in a sense, because it is contributed to the K-12 Education Program.

Who deletes contributions - and why?

  • I posted today on Wikipedia pages related to lottery, true random numbers generating, and, especially, the mathematics of lottery. I even offered free source code to generate true and unique random numbers.

I also offered one-of-a-kind links to free lottery software and systems. Moreover, I posted thorough but concise formulae to calculate lotto odds with the hypergeometric distribution probability. Such formulae are a must when it comes to an encyclopedic analysis of lottery.

Everything I posted was deleted shortly thereafter. Why?

My contributions showed absolutely unique theories. Not only that, but they have the most solid foundation: philosophical and mathematical. As Plato put it:

”Let no one enter here who is ignorant of mathematics”

Is it jealousy or does it represent a conflict of interest? Does the management at Wikipedia accept such behavior from editors who so easily delete original contributions?

Ion Saliu

Wikipedia is an encyclopedia, not a place to post your own theories. See Wikipedia:No original research. andy 19:18, 20 June 2006 (UTC)
I've run into this issue before where my mathematical contributions were deleted, so I empathize with you somewhat. Please try getting correct references for the info you posted. If your research is original and useful as you say, it is probably worth publishing somewhere first. --Amit 06:09, 18 July 2006 (UTC)

lottery as a system

This could do with a better scope. The Ancient Greeks chose some of their offices by lottery rather by election (this was seen as more democratic to avoid the effects of plutocracy). If you spend this much on your credit card you could in this prize, or submit your donation to the National Kidney Foundation or whatnot. Things like that. Not merely buying a lottery ticket. John Riemann Soong 00:22, 23 July 2006 (UTC)

That's true. Prize lotteries aren't the only kind. In modern times lotteries are used to pick people for jury service and were used in the US to pick conscripts for the Vietnam war. They have also been suggested as an alternative -- and fairer -- method of electing representatives in modern democracies. You wouldn't know that from reading the article though. -- Derek Ross | Talk 17:42, 9 September 2006 (UTC)

Rationality and lottery players

It may not alway be irrational for someone to play in a lottery even though the expected winnings are much lower than the price of the ticket because of the utility of money. The loss of one dollar might have only a tiny impact on one's life, while gaining millions of dollars would have a huge impact. The difference in impact might be greater than the odds of winning. The article has a very negative POV towards those who play the lottery and this might add some neutality to the article. This is explored in H.W. Lewis' book "Why Flip a Coin?: The Art and Science of Good Decisions." I don't have the book handy so I don't feel like trying to include his thoughts to the article.

I would also like to add, that this article seems to stress that the reward will be far less than what people think. Its true, Taxes and taking the Lump Sum will reduce the amount of money receaved, but for someone who has no money, 500,000 can seem like a billion dollars. And what they win is far more than they had previously (Unless your a senator). If a lottery winner is smart, they will hire a Tax Lawyer to take out the tax, then they will hire an accountant or go to a Bank and let them help with Investments and home buying etc. It also helps to move away...Move far away so your reletaves will not beg you constantly for money. And Change your name too...Magnum Serpentine 03:46, 13 November 2006 (UTC)
I agree with the above comments, but even they miss the point, it seems to me. I rarely buy lottery tickets (perhaps three or four over a thirty-year period), but I know many people who buy them regularly and my impression is that, for them, it's cheap entertainment. For a buck they get to dream about winning, joke about it with their friends, and enjoy the anticipation of the gamble, sometimes for days. That's an entirely rational choice on its own, quite apart from the odds or the size of the prize. I think that's why lots of scientists, engineers, and other people who are fully capable of calculating the odds buy tickets. --Tedd (talk) 16:57, 29 December 2007 (UTC)

History of Australian Lottery

I would have put this in the Australian Lottery section except that the history of other lotteries are also in this section (eg NZ, France, so on) I know that there is a rich and interesting history of national lotteries and so on in Australia: for example the Sydney Opera House had a good deal of its' overflow paid for by lotteries, though I haven't references other than first hand comments from people who bought tickets. Can't find any information on all that in the wikipedia though, and don't know enough about it to add my own.Thisfox 00:26, 5 September 2006 (UTC)

Men Vs. Women

I had heard a rumor that men win the lottery more than women - and no one knows why. But whats worse is that the margin was beyond scientific explanation.

Can anyone verify this?

71.201.95.224 15:26, 10 September 2006 (UTC)

Men play it more. There is no statistical reason why one sex would be more likely to win than other, unless they buy more tickets. Rob.derosa 06:36, 18 October 2006 (UTC)

Just a thought of mine, but could it be that women are more likely to pick "birthdays" rather than any random numbers, thus limiting themselves to the first 31 numbers?
This could affect the amount won (because they would be more likely to have to share the jackpot with other birthday-players), but not the odds of winning. Any ticket has the same chance of winning. 67.185.114.32 23:28, 11 January 2007 (UTC)
Assuming this is true, keep in mind that random chance is always a possible explanation. Rob could very well be right, but the very premise of the question is flawed. If something is possible, then it is not "beyond scientific explanation" no matter how improbable it seems. Imagine flipping a coin 1,000 times and always getting heads. It's highly improbable, but it would in no way be "beyond scientific explanation" as there is no law of nature that would force it to land as tails, no matter how many times it had previously landed as heads. Likewise, there is no law of nature that would force a female win, no matter how large the percentage of previous male wins were. --Icarus (Hi!) 03:21, 26 January 2008 (UTC)

100 versus 1

Would you be better of buying 1 ticket every drawing or waiting and buy 100 tickets every 100 drawings? I'm guessing going big once in awhile is better. —The preceding unsigned comment was added by 209.206.165.13 (talk) 08:57, 4 February 2007 (UTC).

0 out of 0 because they take half your money either way. Sagittarian Milky Way 17:53, 31 May 2007 (UTC)
You're better off to buy 100 tickets on 1 draw than to buy 1 ticket on 100 draws. To see how this works, consider a very simple lottery where you pick one of nine numbers. For a single ticket you have 8 chances in 9 of losing. If you buy one ticket on two separate draws your combined chance of losing is 8/9 times 8/9, or 0.790, which means that your combined chance of winning is 1-0.790 or 0.210. However, if you were to buy two tickets on one draw your chance of losing would be 7/9, making your chance of winning 1-7/9, or 0.222 — slightly greater. For a real-world lottery the improvement in the odds of winning is very small, though. For example, in the Canadian Lotto 6/49, where you choose 6 numbers out of 49, your odds of winning are 1 in 13,983,816. There are about 100 draws in a year (twice a week). If you play one ticket for each of the 100 draws your combined odds of winning are about 1 in 139,839. If you buy 100 tickets on a single draw (and skip the rest) your odds of winning are about 1 in 139,838. So the difference is very, very small.--Tedd (talk) 17:58, 28 December 2007 (UTC)
But of course if you bought tickets over several draws, there would be a chance of winning both draws and hence more money. Its not that simple —Preceding unsigned comment added by 116.15.43.1 (talk) 16:08, 29 September 2008 (UTC)

Images

I think this needs some images, if wanted, I could find some 6/49 tickets or Scratch 'N Win tickets and scan them to put on this site. —Preceding unsigned comment added by 24.129.239.143 (talk) 03:29, 28 December 2007 (UTC)

Italicise names of lotteries?

I have checked a few style manuals and it seems that names of lotteries are not normally italicised. I'll do some clean up. Nurg (talk) 03:59, 29 March 2008 (UTC)

Winners lose their money after a few years

There is an internet meme, stating that MOST Lottory winners lose their respective fortunes after a few years, due to lack of financial education, self-hype and over exuberance. IS there any relevant information about this phenomenon..? Procrastinating@talk2me 17:53, 14 September 2008 (UTC)

UK National lottery syndicate

What about adding a UK national lottery syndicate site to the external links section... nationallotterysyndicate.co.uk —Preceding unsigned comment added by Buckyuk uk (talkcontribs) 09:01, 14 June 2009 (UTC)

There are lots of such sites. There is no need for such a link. 2005 (talk) 09:08, 14 June 2009 (UTC)

Poor economic arguments in article

The article currently contains a few passages of completely uncited economic arguments. All strongly say that playing lotto's a "bad economic choice", the only concession given is that players receive some value in the entertainment factor. Entirely based on long term averages and expected outcomes.

Nowhere is it mentioned that for most players (and non players for that matter), without lotto the chance that they'll one day be able to live very comfortably, extravagantly even, without having to work for their income is zero. With lotto, that's increased to one in several million. Yes, there's expected losses and on average you'd do much better investing in blue chip stocks, but those that value the chance that they'll one day be wealthy (people that may otherwise have slim chance of ever achieving wealth) more then the ticket price, it's a good economic decision. Even before you factor in the entertainment value. Themania (talk) 09:38, 23 June 2009 (UTC)

Odds Error, but I can't change it because the page is locked

There's a statement suppose one buys one lottery ticket per week. 13,983,816 weeks is roughly 269,000 years; In the quarter-million years of play, one would expect to win the jackpot only once. In fact the odds of winning the jackpot by entering once a week every week for 13,983,816 weeks is pretty much exactly 2/3, far from an uneqivocal expectation of winning.Fizzackerly (talk) 22:18, 30 January 2010 (UTC)

  • Public Domain Beach, Chandler B., ed. (1914). The New Student's Reference Work. Chicago: F. E. Compton and Co. {{cite encyclopedia}}: Missing or empty |title= (help)

Here is a link I usually put in the external links sections. It is rather a semi-external link since it goes to Wikisource. I think it is of historical interest. Per the directive I found, I leave it here for another editor to put in the external links section if it seems worthwhile. Bob Burkhardt (talk) 19:46, 3 February 2010 (UTC)

No morality §?

Lotteries are morally repugnant for a number of reasons: 1) they make people rich for doing nothing at all in societies where money is a life or death issue, 2) they prey on the poor and ill-informed who are unable to understand either the primary moral issue or the facts of probability as they concern the games, and 3) they encourage magical thinking generally in those who most need the opposite, especially about the nature of money, how to get and keep it, etc. There are reasons that while ancient they were generally outlawed in the west until 30 or 40 years ago. 72.228.177.92 (talk) 02:32, 23 February 2010 (UTC)

Opinions are not put into the article unless there is a compelling reason. Even then, they must be well-sourced and balanced. The article must remain neutral and not push a particular point of view. Wperdue (talk) 02:47, 23 February 2010 (UTC)
Actually that's false. If it were simply my opinion or that of a few naysayers that would be true, but in fact the article is unbalanced for a lack of presentation of the moral position which was until recently the accepted and consensus one. At the very least a more detailed discussion of that reversal would give balance, not take it away. 72.228.177.92 (talk) 02:57, 23 February 2010 (UTC)
None of the tags seemed to match the current state though, nor is there any current discussion of the issues the named above, so I removed them. 72.228.177.92 (talk) 03:49, 23 February 2010 (UTC)

Time for a separate article?

Isn't it about time for a separate article on all the countries with national lotteries and respective details? Then this article can be more about the history and concept and the other about the countries. Do people agree? Any suggestions for a title, I've never started an article so am not really familiar with naming conventions, but would be happy to execute it. Joost 99 (talk) 11:43, 26 July 2010 (UTC)

I support this idea. The current article is much too long and there is too much detailed content about current lotteries in specific countries. This should be separated out from the general overview article. Ontyx (talk) 03:01, 10 August 2010 (UTC)

EuroMillions Flags

Should this not use the flag of each individual country, whilst Switzerland isn't part of the EU, the entire EU doesn't take part. // Finns 11:48, 21 November 2010 (UTC)

Difficult to locate the downsides or criticism of lottery

I just read the article looking for the negative impacts of a lotto and it took me a while, because there is so much going on in the article. I finally found it in the 'Probability of winning' section, but it seems like the article has either grown too large or is not organized well. While I know some people hate criticism sections, it seems clear that at least some of the content needs to be broken out into subsections or additional articles.M4bwav (talk) 16:54, 9 December 2010 (UTC)

Federal taxes on Lottery winnings

Most articles about federal taxes on lottery winnings tell you that 28% will be withheld from your gross winnings. If your winnings are over $1,000,000, you are better off to have 35% withheld. The reason is that 28% is not enough to cover the true tax liability and you could pay a penalty for underwithholding. The 35% rate is slightly more than the true tax liability, so you will receive a refund when you file.

Lottery lover — Preceding unsigned comment added by Lotto lover (talkcontribs) 18:39, 27 March 2011 (UTC)

Irrational

If you need sources for anything can someone please explain this paragraph, its the 3rd or 4th from the top?

The purchase of lottery tickets is, from the perspective of classical economics, irrational. However, in addition to the chance of winning, the ticket may enable some purchasers to experience a thrill and to indulge in a fantasy of becoming wealthy. If the entertainment value (or other non-monetary value) obtained by playing is high enough for a given individual, then the purchase of a lottery ticket could represent a gain in overall utility. In such a case, the monetary loss would be outweighed by the non-monetary gain, thus making the purchase a rational decision for that individual.

I didn't see anything in the classical economics article about what is rational or not. I also want to know what book you got this stuff about indulging in fantasies. Ok its probably true but where does it say that?

This refers to the common notion of economic rationality, really nothing more than common rationality in an economic context. 72.228.189.184 (talk) 00:18, 1 April 2012 (UTC)

Probability of winning

The section on propability of winning contains too many analogies for an encyclopedic article. Also, it is a common misconception (created by people who don't understand how statistics work) that if the odds are 1:10, then you will have buy 1 ticket a week for 10 weeks to be sure to win. In reality, if the odds are 1:10, it will be 1:10 for each of the weekly tickets. -- leuce (talk) 10:01, 6 January 2012 (UTC)

If the odds of winning an event are 1/10, and you participate in 10 such independent events, the chances of winning at least once are 1 - 0.910 = 1 - 0.3486784401 = .6513215599, or just over 65%. StuRat (talk) 18:44, 31 March 2012 (UTC)

Social corruption

The § doesn't really capture what is at core contemptible and corrupt about government run numbers rackets. It's that it encourages the idea of getting money for nothing, instead of working for it. The racket degrades and in a sense is a purposeful effort to deny the relation between the value of money and its basis in work/labor in addition to encouraging magical and self defeating thinking in the masses. 72.228.189.184 (talk) 17:55, 31 March 2012 (UTC)

I agree that it undermines the work ethic, but don't believe this is the intent. StuRat (talk) 18:45, 31 March 2012 (UTC)
Or rather more to the point, the current text refers to Marx, but doesn't really make clear how, via that theory's assertion that money prices embody social relations, that impacts this article's topic, whence the corruption (of the function of society). As far as intent, yes aware that it finances education in the States, but 1) that thing funded doesn't really seem to be working well and 2) financing "education" with something that is like "anti-education" is a kind of essential corruption/contradiction. The intent is irrelevant if the harm equals or exceeds any benefit. 72.228.189.184 (talk) 00:16, 1 April 2012 (UTC)

Merge from Lotology

The article Lotology is a poorly sourced stub that would easily fit as a mention in this article. - SummerPhD (talk) 13:23, 13 August 2014 (UTC)

It's utterly unneeded. Send it AFD, since the prod was removed. oknazevad (talk) 13:40, 13 August 2014 (UTC)
I am not proposing deletion, but a merge. - SummerPhD (talk) 13:51, 13 August 2014 (UTC)
And I'm saying it should just be deleted outright. I see no reason to merge a non-notable stub into this article. The most this article should have one sentence saying that some people collect old lottery tickets, using the Mental Floss article as a source. Anything more would be utterly WP:UNDUE. Even then, it's such a non-notable piece of trivia I would remove it from the article anyway. So the other article should just be deleted, not preserved in any fashion. oknazevad (talk) 14:54, 13 August 2014 (UTC)
I'll let this run for any other opinions. If you would like to take it to AfD before then, feel free. - SummerPhD (talk) 15:51, 13 August 2014 (UTC)

Page Restructuring

A decent amount of material on this page should be moved to Lotteries by country. The article also is very short on references, and has too much trivia.

Anyone here with any thoughts on potential changes? Power~enwiki (talk) 04:16, 4 July 2017 (UTC)

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Housing and rental lotteries

I think that the frequency and prevalence of housing and rental lotteries might warrant adding a section or brief mention of housing and rental lotteries, or a separate article on the topic housing and rental lotteries. MaynardClark (talk) 17:46, 26 April 2019 (UTC)

Chances of matching different numbers of balls in a 6-from-49 lotto

The table in this article states the chances as 1 in 2.3, 49, 1176, …, 13983816, while Lottery mathematics#Odds of getting other possibilities in choosing 6 from 49 states these as 1 in 2.2938, 2.4212, …, 13983816. This needs a clarification. -- Paddu (talk) 07:12, 14 December 2019 (UTC)

i checked the history. it was originally entered correctly. someone changed it thinking they were wrong, but they calculated the chances for a particular number to match a particular ball, not the chances of any of the numbers to match any of the balls. so i reverted that edit.· Lygophile has spoken 17:39, 23 September 2020 (UTC)

Wiki Education assignment: Research Process and Methodology - FA22 - Sect 200 - Thu

This article was the subject of a Wiki Education Foundation-supported course assignment, between 22 September 2022 and 8 December 2022. Further details are available on the course page. Student editor(s): XingboGao (article contribs).

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