# How many lottery tickets must be bought to assure every combination of numbers? **URL:** \ **Category:** Factual Questions\ **Created:** [January 22, 2005, 10:36pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155 "2005-01-22T22:36:48Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![asterion](https://avatars.discourse-cdn.com/v4/letter/a/4da419/32.png) [@asterion](https://boards.straightdope.com/u/asterion)\ **Post date:** [January 23, 2005, 4:47am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/21 "2005-01-23T04:47:22Z")
Now that I think about it, my machine numbers might be off by a factor of 200. If I’m right, it’d be 84 or 149 machines, depending on the situation. ---
**Author:** ![jsleek](https://avatars.discourse-cdn.com/v4/letter/j/8dc957/32.png) [@jsleek](https://boards.straightdope.com/u/jsleek)\ **Post date:** [January 23, 2005, 5:06am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/22 "2005-01-23T05:06:42Z")
Does this mean if the prize is over $14 million, it’s reasonable to buy a ticket? ---
**Author:** ![CynicalGabe](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@CynicalGabe](https://boards.straightdope.com/u/CynicalGabe)\ **Post date:** [January 23, 2005, 5:34am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/23 "2005-01-23T05:34:46Z")
> [@jsleek](#): > > Does this mean if the prize is over $14 million, it’s reasonable to buy a ticket? No, it only has to be over $13,383,816 ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 23, 2005, 5:53am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/24 "2005-01-23T05:53:25Z")
> [@CynicalGabe](#): > > No, it only has to be over $13,383,816 No. Lest we’re dodging taxes, we have to take into account federal tax (28%), state tax, and city tax. Also, we have to take into account the payout system of the lottery. Is it a bulk payment? Is it spread out over 20 years (interest free of course)? If so, I would reckon that you’d have to win around $25-$30 million to break even. ---
**Author:** ![Rex\_Fenestrarum](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rex_fenestrarum/32/7265_2.png) [@Rex\_Fenestrarum](https://boards.straightdope.com/u/Rex_Fenestrarum)\ **Post date:** [January 23, 2005, 5:55am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/25 "2005-01-23T05:55:36Z")
> [@feldman](#): > > the correct number is what you get from 49_48_47… > > an excerpt from my old math book: > “In February of 1992, an Australian investment group came very close to cornering the market on all possible combinations of six numbers from one to ffourty-four in the Virginia state lottery. The group bought 5 million of the possible 7.05 million tickets in a lottery with a $27 million jackpot. Only time prevented them from getting the other 2 milion tickets. The group was the only winner; their profit: approx. $22 million. Since then, the Virginia State Lottery COmmision (and other states) have written regulation to rpevent individuals and groups from cornering the market.” Does no one else remember this story? I saw something about this - whether it was a full-blown documentary on TLC or Discovery or just a story on 20/20 I don’t remember - but I _do_ remember that the Aussies hired an army of people - college students, housewives, etc. - to actually buy all the tickets from convenience stores. They gave each person a list of what range of tickets to buy and a wad of cash… And they ended up buying 5 million tickets in less than a week\*. Even our wannabe mod QED says that it’d _only_ take 46 machines to buy 13m tickets in a week - a couple of hundred people hitting a couple of hundred stores for 8-10 hours a day should be able to do this with ease - especially since the places that sell the most lottery tickets - i.e. convenience stores - are _indeed_ open 24 hours a day, 7 days a week. - - Of course, the Aussies took several months to get the money together and divie up all the numbers and hire the “runners”, but the actual ticket purchases did indeed take less than a week. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [January 23, 2005, 6:21am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/26 "2005-01-23T06:21:39Z")
> [@pulykamell](#): > > No. Lest we’re dodging taxes, we have to take into account federal tax (28%), state tax, and city tax. Also, we have to take into account the payout system of the lottery. Is it a bulk payment? Is it spread out over 20 years (interest free of course)? If so, I would reckon that you’d have to win around $25-$30 million to break even. In the States, perhaps. Here in Canada, it’s tax free and paid up front. But, see, you’re still getting jobbed. The higher the jackpot the likelier you are to have to share it. Around here once it hits eight digits, interest in the draw goes up and tickets sold go up; the likelihood of one than more person winning increases dramatically. It might be worth it if the jackpot goes over $14 million if you’re the only one playing the game, or if the prizes weren’t divvied up, but they are. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 23, 2005, 6:31am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/27 "2005-01-23T06:31:48Z")
> [@RickJay](#): > > In the States, perhaps. Here in Canada, it’s tax free and paid up front. Tax-free _and_ paid up front in commie Canada? :eek: I keed, I keed. Are gambling winnings in general not taxed in Canada? ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [January 23, 2005, 7:13am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/28 "2005-01-23T07:13:06Z")
> [@Rex Fenestrarum](#): > > Even our wannabe mod QED… I’m not aware that this is a running joke in which **Q.E.D.** shares the humor, so I’m not sure why this appellation appears in your post. Unless I see **Q.E.D.** joking about this, I do not expect to see such references in **GQ**. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [January 23, 2005, 8:49pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/29 "2005-01-23T20:49:10Z")
> [@pulykamell](#): > > Tax-free _and_ paid up front in commie Canada? :eek: > > I keed, I keed. Are gambling winnings in general not taxed in Canada? Nope. In fact, I occasionally hear radio commercials from companies that will help you recover the “withholding tax” that was grabbed if you won a sizable American lottery or casino game. This sounds like a bit of a scam to me, though, since I thought it was a simple matter of filling out a tax form, though I expect many Canadians don’t bother. ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [January 23, 2005, 11:52pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/30 "2005-01-23T23:52:53Z")
If you really want to make a zillion dollars by “beating the system” there are much cleverer ways of doing it: [Or at least there used to be.](http://gscentral.net/larsen.htm) ---
**Author:** ![PastAllReason](https://avatars.discourse-cdn.com/v4/letter/p/f07891/32.png) [@PastAllReason](https://boards.straightdope.com/u/PastAllReason)\ **Post date:** [January 24, 2005, 1:19am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/31 "2005-01-24T01:19:19Z")
> [@Bryan Ekers](#): > > > [@pulykamell](#): > > > > Tax-free and paid up front in commie Canada? > > I keed, I keed. Are gambling winnings in general not taxed in Canada? > Nope. In fact, I occasionally hear radio commercials from companies that will help you recover the “withholding tax” that was grabbed if you won a sizable American lottery or casino game. This sounds like a bit of a scam to me, though, since I thought it was a simple matter of filling out a tax form, though I expect many Canadians don’t bother. It is true that lottery winnings for individuals are not taxable in Canada as a “windfall”. Gambling, however, may be taxable if the person is “in the business of gambling”. From the Revenue Canada [bulletin](http://www.cra-arc.gc.ca/E/pub/tp/it334r2/it334r2-e.html) (scroll down to section 10 on gambling profits), here are the general conditions that used to determine whether gambling income is taxable: "Although no one factor may be conclusive, the following criteria should be considered in making the determination: (a) the degree of organization that is present in the pursuit of this activity by the taxpayer, (b) the existence of special knowledge or inside information that enables the taxpayer to reduce the element of chance, (c) the taxpayer’s intention to gamble for pleasure as compared with any intention to gamble for profit as a means of gaining a livelihood, and (d) the extent of the taxpayer’s gambling activities, including the number and frequency of bets" So, if you’re a professional poker player in Canada you’d better get income tax advice. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [January 24, 2005, 2:01am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/32 "2005-01-24T02:01:47Z")
> [@pulykamell](#): > > Tax-free _and_ paid up front in commie Canada? :eek: > > I keed, I keed. Are gambling winnings in general not taxed in Canada? As has already been pointed out, windfalls aren’t taxed, but you are supposed to pay taxes if you gamble as a living. Nobody plays the 6/49 or Super 7 for a living, so no, they pay no taxes when they win. However, some people do make good livings gambling on horses, and of course there’s professional poker players. However, although such people would have to pay taxes on their winnings, they can also write off losses. Whereas I can’t write off the price of all the 6/49 tickets I’ve bought that got me bupkus. ---
**Author:** ![Rex\_Fenestrarum](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rex_fenestrarum/32/7265_2.png) [@Rex\_Fenestrarum](https://boards.straightdope.com/u/Rex_Fenestrarum)\ **Post date:** [January 24, 2005, 2:56am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/33 "2005-01-24T02:56:20Z")
What? No follow-ups from Q.E.D., our Lord and Master? You mean to tell me that Q.E.D. hasn’t come in here and used his “junior mod” status to make us feel like lesser human beings? Methinks that the SDMB - as well as our Lord and Master, Q.E.D. - is slipping! ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [January 24, 2005, 3:07am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/34 "2005-01-24T03:07:53Z")
Where’s this “Q.E.D. - junior mod” crap coming from? It’s the second reference I’ve seen to it today. ---
**Author:** ![samclem](https://avatars.discourse-cdn.com/v4/letter/s/a9a28c/32.png) [@samclem](https://boards.straightdope.com/u/samclem)\ **Post date:** [January 24, 2005, 3:20am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/35 "2005-01-24T03:20:39Z")
> [@Rex Fenestrarum](#): > > What? No follow-ups from Q.E.D., our Lord and Master? You mean to tell me that Q.E.D. hasn’t come in here and used his “junior mod” status to make us feel like lesser human beings? > > Methinks that the SDMB - as well as our Lord and Master, Q.E.D. - is slipping! **Rex** This is the second warning you’re getting in the same thread. **tomndebb** warned you in post #28 above. Cut this crap out! Do it again, and you’re likely out of here. Understood? **samclem** GQ moderator. ---
**Author:** ![devilsknew](https://avatars.discourse-cdn.com/v4/letter/d/4da419/32.png) [@devilsknew](https://boards.straightdope.com/u/devilsknew)\ **Post date:** [January 24, 2005, 5:08am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/36 "2005-01-24T05:08:17Z")
I know how many tickets you need to actually guarantee winning, but how much would the _odds of winning_ increase if you had a group of, say 500, playing 100 unique combinations each for a total of 50,000 tickets? What kind of an edge is that…does it even register enough to make a difference? Would that situation also be illegal under the “lottery syndicate” laws? ---
**Author:** ![devilsknew](https://avatars.discourse-cdn.com/v4/letter/d/4da419/32.png) [@devilsknew](https://boards.straightdope.com/u/devilsknew)\ **Post date:** [January 24, 2005, 5:29am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/37 "2005-01-24T05:29:16Z")
I guess I should clarify. I mean, what if the 500 were all acting individually but had a friendly agreement with the other 499 that they would split any winnings evenly after taxes-- no contracts or incorporations just an honorable collective–499 gifts. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [January 24, 2005, 5:31am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/38 "2005-01-24T05:31:15Z")
> [@devilsknew](#): > > I know how many tickets you need to actually guarantee winning, but how much would the _odds of winning_ increase if you had a group of, say 500, playing 100 unique combinations each for a total of 50,000 tickets? > What kind of an edge is that…does it even register enough to make a difference? It’s easy to calculate your odds. Divide the overall odds of winning the jackpot by the number of unique numbers you wish to play. For example, if the overall odds of winning are 1 in 10,000,000 and you buy 50,000 tickets, the odds of you hitting are 1 in 200. Better, but still not great. ---
**Author:** ![Rex\_Fenestrarum](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rex_fenestrarum/32/7265_2.png) [@Rex\_Fenestrarum](https://boards.straightdope.com/u/Rex_Fenestrarum)\ **Post date:** [January 24, 2005, 5:47am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/39 "2005-01-24T05:47:01Z")
Fine. For once and for all, fuck the SDMB and all of the mods here that obviously _hate_ both the “blue states” as well as the concept of “fair use”. If I was only as _cool_ as Q.E.D maybe I’d be a mod here. But since I’m a less human being, I guess I can’t be. No wait… If only I was a liberal, yet totalian wien Oh no! My “second warning”! Fine. For once and for all, **fuck the SDMB** and all of the mods here that obviously _hate_ both the “red states”, anything that’s outside of their “world view” as well as the concept of “fair use”. If I was only as _cool_ and annoyingly _liberal_ and\or as “knowledgeable” as Q.E.D, then maybe I’d be a mod here. But since I’m a lesser human being, I guess I can’t be. No wait… If only I was a bleeding-heart liberal - yet strangely totalitarian when it comes to IP issues – then maybe would I be accepted here… But since I have this nagging need _to make sense_, I guess my opinion doesn’t count – just like anyone else that tries to post anything “pro-Christian” or “pro-faith” or “pro-Red State” or “pro-consumer” or “Pro-EFF” on this message board. I suppose that it’s hardly surprising, really, as the SDMB has always been “all the news that fits our views”. It’s funny to hang out in GQ and see the responses to a question like “Are Gays Against God??” only to see all the mods jump in about how this is a “loaded question” and how “accepting of other world views we should be”, yet when someone posts a question like “How many kittens does George W. Bush kill every time I disagree with his administration?” the mods are (unsurprisingly) absent. Of course, many of you know about the first time I was “banned” from this board. It was back in July 2004 in a thread where someone asked about how they could extract the audio from _a DVD that they already owned_. Of course, TubaDiva and Q.E.D _just had_ to jump in the thread and ramble about how ripping the audio from a DVD is a crime against humanity, and how anyone that would want to do that is _less human than a child molester_ in the SDMB’s eyes. Of course, I was shouted down in that thread, after arguing that… gosh darn it, those people have something called “fair use rights”… I was advised to “leave” the SDMB by TubaDiva and so I did… for six months. But boredom got the better of me, and I came back. Don’t expect me to do the same this time. Not that _you_ care, but I’ve seen this happen a million times… and that’s why I’m fully prepared to go back to my “native” message board at Ars Technica… where I can express a contrary opinion and not be shouted down… where I can spew the occasional _ad hom_ without fear or retribution from overzealous mods. Because it won’t be here. > **[Electronic Frontier Foundation](https://www.eff.org/)** > > Defending your rights in the digital world [http://www.ars-technica.com](http://www.ars-technica.com) Viva Freedom!! ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 24, 2005, 5:50am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/40 "2005-01-24T05:50:18Z")
Kinda saw that coming. [Previous page](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155.md?page=1) [Next page](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155.md?page=3)