# 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:** 3
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [January 24, 2005, 5:55am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/41 "2005-01-24T05:55:52Z")
> [@](#): > > Viva Freedom!! Freedom? You could have blasted **Q.E.D.** to your little heart’s content in the **BBQ Pit**. We only asked that you not attack other posters (pretty egregiously–_i.e._, for no reason at all, in this case) in **GQ**. I’m sure that we’ll all miss your little rants from now on, but we’ll try to carry on. [/Moderator Mode] ---
**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, 6:07am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/42 "2005-01-24T06:07:56Z")
> [@Rex Fenestrarum](#): > > 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. What, [this thread](http://boards.straightdope.com/sdmb/showthread.php?t=298349)? The one I didn’t post in? Good lord, **Rex** , you got all worked up over nothing. There just wasn’t any need for any of this. On preview, I see it’s too late. I was glad to see you came back after your self-imposed exile. Sorry to see you go like this. ---
**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, 6:16am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/43 "2005-01-24T06:16:39Z")
Errr…I meant [_this thread_](http://boards.straightdope.com/sdmb/showthread.php?t=267772). :smack: ---
**Author:** ![Roland\_Orzabal](https://avatars.discourse-cdn.com/v4/letter/r/c2a13f/32.png) [@Roland\_Orzabal](https://boards.straightdope.com/u/Roland_Orzabal)\ **Post date:** [January 24, 2005, 6:36am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/44 "2005-01-24T06:36:33Z")
Nice thread about lottery tickets, nice responses, bit of engaging discussion, _sweet mother of Og I hate QED and I hate TubaDiva I hate you ALL FUCK YOU I’M LEAVING!!!_ Did I miss something recently, or was that whole rant as out-of-big-ol’-_nowhere_ as it seemed? ---
**Author:** ![CynicalGabe](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@CynicalGabe](https://boards.straightdope.com/u/CynicalGabe)\ **Post date:** [January 24, 2005, 6:43am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/45 "2005-01-24T06:43:07Z")
/sound of crickets chirping… Wow. I was going to make a remark about threads on lottery tickets and mathematical possibilities not being the be-all and end-all of western civilization, and is really not something to get worked up over, but I think it would be wasted. ---
**Author:** ![Happy\_Lendervedder](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/happy_lendervedder/32/8488_2.png) [@Happy\_Lendervedder](https://boards.straightdope.com/u/Happy_Lendervedder)\ **Post date:** [January 24, 2005, 7:00am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/46 "2005-01-24T07:00:55Z")
I was made aware of this in the [ATMB](http://boards.straightdope.com/sdmb/showthread.php?t=298584) thread, and as the page loaded, I was trying to figure out how someone could have a meltdown in a GQ thread about lottery tickets. I thought maybe someone actually bought 13,383,816 lottery tickets, but somehow still ended up losing. ---
**Author:** ![InvidiousCourgette](https://avatars.discourse-cdn.com/v4/letter/i/e47c2d/32.png) [@InvidiousCourgette](https://boards.straightdope.com/u/InvidiousCourgette)\ **Post date:** [January 24, 2005, 7:42am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/47 "2005-01-24T07:42:48Z")
> [@Happy Lendervedder](#): > > \ a meltdown in a GQ thread about lottery tickets.\ Before I saw this thread, I would have said it was about as likely as, err, winning the lottery. ---
**Author:** ![picker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/picker/32/13969_2.png) [@picker](https://boards.straightdope.com/u/picker)\ **Post date:** [January 24, 2005, 3:52pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/48 "2005-01-24T15:52:14Z")
Now that was out the blue. I guess you could say he defenestrated himself. ---
**Author:** ![Flander](https://avatars.discourse-cdn.com/v4/letter/f/8c91f0/32.png) [@Flander](https://boards.straightdope.com/u/Flander)\ **Post date:** [January 24, 2005, 7:22pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/49 "2005-01-24T19:22:51Z")
Maybe we should sign him up for the SDMB Valentine’s exchange? Sounds like he needs love. We could all get him a lottery ticket (a losing one from last week) and a sweet card. I’ll burn him a copy of Bio Dome that doesn’t have any audio on it, too. 😉 Slight hijack (like it matters), why does it seem that, in FL, the winners seem to be elderly rich couples? The money needs to be awarded to someone that really needs it, like the guy who lost his job and needs to feed the kids, or the woman who needs to pay off her college loans because her $8/hour job she got with her degree won’t help. Or better yet, ME! If the first thing you say after winning the lotter is, “I’m going to buy another huge yacht,” or, “now I can afford to drive around that Bentley instead of this Mercedes SL600,” then you should have to give the money away to charity or something. [/hijack] ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 24, 2005, 7:49pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/50 "2005-01-24T19:49:15Z")
> [@](#): > > Slight hijack (like it matters), why does it seem that, in FL, the winners seem to be elderly rich couples? The money needs to be awarded to someone that really needs it, like the guy who lost his job and needs to feed the kids, or the woman who needs to pay off her college loans because her $8/hour job she got with her degree won’t help. Or better yet, ME! If the first thing you say after winning the lotter is, “I’m going to buy another huge yacht,” or, “now I can afford to drive around that Bentley instead of this Mercedes SL600,” then you should have to give the money away to charity or something. You know what they say, if you don’t play, you can’t win. Apparently, in Florida, it’s mostly elderly rich people who play. Which is probably a good thing: The guy who just lost his job and needs to feed the kids should not be wasting money on lotto tickets. And most of the rich folks who play _are_ giving their money to charity. ---
**Author:** ![Biffy\_the\_Elephant\_Shrew](https://avatars.discourse-cdn.com/v4/letter/b/e47c2d/32.png) [@Biffy\_the\_Elephant\_Shrew](https://boards.straightdope.com/u/Biffy_the_Elephant_Shrew)\ **Post date:** [January 24, 2005, 8:00pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/51 "2005-01-24T20:00:54Z")
Well, _that_ was one of the more spectacular flame-outs I’ve seen around here. It’s almost like it was caused by a 13,983,816’s-style death ray… ---
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [January 24, 2005, 8:39pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/52 "2005-01-24T20:39:24Z")
> [@pulykamell](#): > > Tax-free _and_ paid up front in commie Canada? I know you’re kidding, but wouldn’t that be more a _socialist_ side-effect than a _communist_ one? I think we’ve seen something like this thread once before. Or was it about someone using a 1960’s style death-ray once to steal 13,383,816 lottery tickets in 20 minutes in 1960? ---
**Author:** ![CynicalGabe](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@CynicalGabe](https://boards.straightdope.com/u/CynicalGabe)\ **Post date:** [January 24, 2005, 9:13pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/53 "2005-01-24T21:13:35Z")
> [@InvisibleWombat](#): > > I think we’ve seen something like this thread once before. Or was it about someone using a 1960’s style death-ray once to steal 13,383,816 lottery tickets in 20 minutes in 1960? Sounds like a B-movie I saw once. But I only watched about 20 minutes of it… ---
**Author:** ![InvidiousCourgette](https://avatars.discourse-cdn.com/v4/letter/i/e47c2d/32.png) [@InvidiousCourgette](https://boards.straightdope.com/u/InvidiousCourgette)\ **Post date:** [January 24, 2005, 9:22pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/54 "2005-01-24T21:22:13Z")
> [@CynicalGabe](#): > > Sounds like a B-movie I saw once. But I only watched about 20 minutes of it… Was it something to do with this real big trench? If so I saw it too. Only watched about a quarter of it. Had to leave after that because I was feeling breathless. ---
**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, 11:01pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/55 "2005-01-24T23:01:15Z")
I just find it amusing that Rex got to 999 posts before exploding, thus covering every possibility in a simple Pick-3 state lottery. As it stands, he won’t even get a free ticket. Anyhoo…I remember infomercials for lottery systems that essentially organized your numbers for you. If you were buying hundreds of tickets a week (and no doubt some people do), these systems would ensure you had the greatest possible coverage with minimal overlap. The friendly enthusiastic shill… errrr, host, demonstrated the checking procedure and damn if he didn’t show a bunch of 3-out-of-6 lines, two 4-out-of-6 lines, and even a 5-out-of-6 line. Had _me_ convinced, let me tell you. To change the channel. ---
**Author:** ![CynicalGabe](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@CynicalGabe](https://boards.straightdope.com/u/CynicalGabe)\ **Post date:** [January 25, 2005, 2:07am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/56 "2005-01-25T02:07:59Z")
Poor Rex. Think he’ll return? /Leaves open obvious opportunity for joke about _how long_ he’ll return for. ---
**Author:** ![Scruloose](https://avatars.discourse-cdn.com/v4/letter/s/e68b1a/32.png) [@Scruloose](https://boards.straightdope.com/u/Scruloose)\ **Post date:** [January 25, 2005, 10:44am UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/57 "2005-01-25T10:44:28Z")
Why does this thread make me think of Frank Grimes? ---
**Author:** ![Annie-Xmas](https://avatars.discourse-cdn.com/v4/letter/a/ecc23a/32.png) [@Annie-Xmas](https://boards.straightdope.com/u/Annie-Xmas)\ **Post date:** [January 25, 2005, 1:02pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/58 "2005-01-25T13:02:00Z")
Was that the movie with three word early 80’s title song performed by that good looking new wave group? ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [January 25, 2005, 1:56pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/59 "2005-01-25T13:56:09Z")
> [@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? > > Would that situation also be illegal under the “lottery syndicate” laws? Why on Earth would/should that be illegal? The lottery is still getting exactly the same amount of income as it would if all those 50,000 tickets were bought by individuals, and it is still paying out the same prizes. If the winner has an agreement to share his prize with 499 others then why not – it’s his money. You’re still not improving your odds - well, OK, you now have more chance of winning a prize, but that prize will be correspondingly smaller because you’ll have to share it with the others. So overall, there’s no “edge” to be had… UNLESS, of course, the total payout is bigger than the possible number of combinations, which only happens in a rollover. Even in such cases, why should the lottery organisers care? It just means more income for them, as more tickets are being bought. ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [January 25, 2005, 2:15pm UTC](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155/60 "2005-01-25T14:15:26Z")
While it’s not necessarily particularly relevant to the issue of whether it could be done today, there is one case where successfully buying up all the tickets in a state-run lottery was of some historical significance. In the late 1720s the city of Paris defaulted on an issue of municipal bonds. In order to partially repay the bond holders, or at least distract them, the city organised a monthly lottery. Owners could buy a 1 franc ticket for each 1000 francs they held in the now otherwise worthless bonds. The government also chucked in about half a million francs to the prize. One of those holding bonds was the young Voltaire. Working with the mathematician [Charles Marie de La Condamine](http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/La_Condamine.html), he succeeding in setting up a syndicate that was able to repeatedly buy up all the tickets. (I presume by persuading other owners to sell them their bonds and thus their right to buy tickets.) Thus they were profiting by the half million from the government on each draw. Their total profit was on the order of 6 million, with about half a million of this going to Voltaire. This coup significantly helped towards allowing him to live most of his life as a writer in considerable financial security. [Previous page](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155.md?page=2) [Next page](https://boards.straightdope.com/t/how-many-lottery-tickets-must-be-bought-to-assure-every-combination-of-numbers/286155.md?page=4)