# Physically possible to cover every PowerBall number? **URL:** \ **Category:** Factual Questions\ **Created:** [January 10, 2016, 5:02pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699 "2016-01-10T17:02:03Z")\ **Posts on this page:** 20\ **Page:** 2
**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 11, 2016, 2:11pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/21 "2016-01-11T14:11:22Z")
> [@si\_blakely](#): > > You don’t need to to buy every ticket. > > Lotteries do not just pay out on (say) 6 numbers. They pay out on 5, 4 and maybe 3 numbers. So you cover all the 3 and some (if not all) of the 4 number combinations. In general, you should win enough to cover the cost of all the tickets from the 3 and 4 combo wins. It also costs a whole lot less than buying all the 6 number combinations. > > Your profit comes from any 5 or 6 combo wins you also collect. > > I did the maths once for the New Zealand lottery which was a Pick Six plus bonus ball, but it was a long time ago, and I don’t feel like doing the math again. Powerball even pays out on one number: the Powerball.[See here for prize chart.](http://www.powerball.com/powerball/pb_prizes.asp) They pay out on two, as well, but it’s the same as getting just the Powerball, so it doesn’t really count. Three and up work in various combinations of Powerball and non Powerball numbers. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [January 11, 2016, 4:36pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/22 "2016-01-11T16:36:59Z")
> [@si\_blakely](#): > > You don’t need to to buy every ticket. > > Lotteries do not just pay out on (say) 6 numbers. They pay out on 5, 4 and maybe 3 numbers. So you cover all the 3 and some (if not all) of the 4 number combinations. In general, you should win enough to cover the cost of all the tickets from the 3 and 4 combo wins. It also costs a whole lot less than buying all the 6 number combinations. > > Your profit comes from any 5 or 6 combo wins you also collect. I’d love to see the maths on that because I believe you’re wrong - at least for the UK National Lottery and the Euromillions. ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [January 11, 2016, 6:08pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/23 "2016-01-11T18:08:51Z")
> [@pulykamell](#): > > Powerball even pays out on one number: the Powerball.[See here for prize chart.](http://www.powerball.com/powerball/pb_prizes.asp) They pay out on two, as well, but it’s the same as getting just the Powerball, so it doesn’t really count. Three and up work in various combinations of Powerball and non Powerball numbers. I took the number of total possibilities divided by the odds of each option to give how much you would win on each one: 5 No Powerball - $25,000,000 4 Plus Powerball - $16,000,000 4 No Powerball - $800,000 3 Plus Powerball - $2,016,000 3 No Powerball - $3,528,021 2 Plus Powerball - $2,916,473 1 Plus Powerball - $12,707,168 Just Powerball - $30,501,184 For a grand total of $93,468,846 ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [January 11, 2016, 6:34pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/24 "2016-01-11T18:34:38Z")
> [@Hail\_Ants](#): > > I’ve tried explaining this to \*sooooo \*many people. The winning numbers have literally **NO** relation to each other whatsoever. This is why 1, 2, 3, 4, 5, 6 has the same chance as any other set. Imagine instead of numerals the lottery balls had pictures of animals on them. This way Elephant, Giraffe, Bear, Cat, Horse, Snake coming out would seem as random as Rhino, Squid, Mouse, Fish, Bird, Whale etc. And the integer numerals work _exactly_ the same way… > > > [@CarnalK](#): > > > > If that’s how you explain it, I can see how you get frustrated. Next time just say “you win by getting the same group of numbers, not a specific ordering of those numbers.” Me, I prefer the animals. The psychology of mental representation of numerals is _huge_ here. For better or for worse, numerals are frighteningly lubricious: humans prefer (re)cognizable sequences or groupings–and “rhinos, squids…are a group of animals” makes sense quickly; numbers are a hard thing to make sense of at all, and individual items of three or more, in our daily experience, come in packs (like a group of random animals) but are rarely cognized without order. So it’s hard to disabuse someone of that way of thinking, which has worked nicely for so long. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 11, 2016, 7:07pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/25 "2016-01-11T19:07:42Z")
> [@pulykamell](#): > > [(69 choose 5) \* 26 = 292 201 338](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=69%20choose%205%20*%2026), which is, of course, the odds on the back of the ticket. That implies that the first five are chosen without replacement, that is, no duplicates. Is that true? ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [January 11, 2016, 7:14pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/26 "2016-01-11T19:14:26Z")
> [@CookingWithGas](#): > > That implies that the first five are chosen without replacement, that is, no duplicates. Is that true? Well, of course. You can’t select a ticket with duplicate numbers - so the winners can’t have them either… How many people would play 7,7,7,7,7,7 if you could? And order does not matter. 1,2,3 is the same as 3,2,1 Except the powerball is distinct ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 11, 2016, 7:55pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/27 "2016-01-11T19:55:12Z")
> [@md2000](#): > > Well, of course. You can’t select a ticket with duplicate numbers - so the winners can’t have them either… How many people would play 7,7,7,7,7,7 if you could? Of course? You say that like it’s obvious, but it’s not obvious if you’ve never bought a ticket. There’s really no reason to disallow duplicates, so it’s a matter of arbitrary rules of the game. It’s not Bingo. I don’t make investments with a negative expected value so I’ve never bought a lottery ticket. Choosing 5 items from a group of 69 has a number of combinations (not permutations) of 69!/(5!64!) = 161,834,587,200 then multiply by 26 = 4,207,699,267,200. I see 292,201,338 quoted in a lot of places but how was it calculated? ---
**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 11, 2016, 8:05pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/28 "2016-01-11T20:05:57Z")
> [@CookingWithGas](#): > > Of course? You say that like it’s obvious, but it’s not obvious if you’ve never bought a ticket. There’s really no reason to disallow duplicates, so it’s a matter of arbitrary rules of the game. It’s not Bingo. I don’t make investments with a negative expected value so I’ve never bought a lottery ticket. > > Choosing 5 items from a group of 69 has a number of combinations (not permutations) of 69!/(5!64!) = 161,834,587,200 then multiply by 26 = 4,207,699,267,200. > > I see 292,201,338 quoted in a lot of places but how was it calculated? 69 choose 5 is 11238513. I’m not sure how you’re getting your number, because your formula looks right. Type your formula into Google, and [see](https://www.google.com/search?q=69!%2F(5!*64!)&oq=69!%2F(5!*64!)&aqs=chrome..69i57.2410j0j7&sourceid=chrome&es_sm=91&ie=UTF-8). You can also type, like I did in my first post “69 choose 5” and Google will return your result. ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [January 11, 2016, 8:09pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/29 "2016-01-11T20:09:39Z")
> [@CookingWithGas](#): > > Choosing 5 items from a group of 69 has a number of combinations (not permutations) of 69!/(5!64!) = 161,834,587,200 I think you missed a parenthesis. 161,834,587,200 is 69!/64!\*5! ---
**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 11, 2016, 8:16pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/30 "2016-01-11T20:16:01Z")
Also, [this is what a powerball drawing looks like](https://www.youtube.com/watch?v=Bup0TcbQeVs). The method for drawing and picking the balls does not allow for duplication (except for the Powerball itself, which is a separate machine and drawn from a pool of 26 numbers.) The regular numbers in Powerball and pretty much all at least American-style lotto “pick five or six numbers from a pool of 44, 54, 69, whatever” work the same way. A bunch of numbered ping pong balls are dumped into a machine and then the required number are siphoned off into a tube and not reintroduced into the shuffling mechanism. In other words, yes, it is a bit like Bingo or Keno. ---
**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 11, 2016, 8:18pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/31 "2016-01-11T20:18:48Z")
> [@AlsoNamedBort](#): > > I think you missed a parenthesis. 161,834,587,200 is 69!/64!\*5! Ah, nice figuring it out. The formula **Cooking** posted is correct, but must have been entered wrong. 69!/(64!5!) is equivalent to 69!/64!/5!, not, like you found, 69!/64!\*5! ---
**Author:** ![si\_blakely](https://avatars.discourse-cdn.com/v4/letter/s/d9b06d/32.png) [@si\_blakely](https://boards.straightdope.com/u/si_blakely)\ **Post date:** [January 11, 2016, 10:36pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/32 "2016-01-11T22:36:41Z")
> [@Quartz](#): > > I’d love to see the maths on that because I believe you’re wrong - at least for the UK National Lottery and the Euromillions. Yeah, the numbers are quite different to what I remember: so the UK National lottery (6/59, 49% of ticket price goes into the prize pool) works out as Winnings =Tickets Purchased\*( (Pick 3 Prize/Chance of Pick 3)+ (Pick 4 Prize/Chance of Pick 4)+ (Pick 5 Prize/Chance of Pick 5)+ (Pick 5 + Powerball Prize/Chance of Pick 5 + Powerball)+ ((Jackpot Value+(0.49\*(2\* Tickets Purchased)))/Chance of Jackpot)) \<- 49% of your ticket purchase investment is added to the Jackpot (approximately) Using the figures from the National Lottery web page and a cost of £2 per ticket Pick 3 Prize = £25 Pick 3 Chance = 96.167 Pick 4 Prize = ~£100 Pick 4 Chance = 2180 Pick 5 Prize = ~£1000 Pick 5 Chance = 144415 Pick 5 + Powerball Prize = ~£50000 Pick 5 + Powerball Chance = 7509579 Chance of Jackpot = 45057474 So starting with buying every ticket (45057474 tickets) the Jackpot has to be about 32 million to break even, with no sharing of the Jackpot. You also need to invest 90 million for virtually no return. As the Jackpot goes up, you can buy fewer tickets, but the risk of missing the Jackpot increases and you can’t break even without winning the Jackpot. So for a 50 million Jackpot, you could buy 66% of the tickets and maybe make 2.5 million return (on 60 million investment), but you have a 1/3 chance of missing the Jackpot and losing most of your investment. And of course, this is a statistical analysis - you need to run this many, many times to get these theoretical returns, and the UK national lottery does not accumulate to a 32 million pound Jackpot all the time. So yes - harder than I worked out previously (or maybe I got better at math), but I suspect that there have been changes made to make it harder to do this - the old UK National Lottery (6/49) is a different selection of balls - you needed a lower than 10 million jackpot to make it worth while buying all the tickets. ---
**Author:** ![Tired\_and\_Cranky](https://avatars.discourse-cdn.com/v4/letter/t/a87d85/32.png) [@Tired\_and\_Cranky](https://boards.straightdope.com/u/Tired_and_Cranky)\ **Post date:** [January 12, 2016, 2:20am UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/33 "2016-01-12T02:20:52Z")
> [@LSLGuy](#): > > Nobody says a single person can possibly do this alone using home equipment. But it’s completely trivial for any kind of organized operation run like a business. > > The slips can be printed on the same kinds of high speed printers any big business uses to print tens of thousands of phone / electric / credit card bills per hour. A million credit card bills is all in an ordinary day’s work for some companies. You have to buy the tickets in person and I think in most or all states, in cash. So you need an army of people walking around with $292 million. And you need the logistics to make sure that the tickets can be retrieved to find the winner. None of your buyers can steal cash or tickets and none can get mugged on the way to or from the lottery agent. This isn’t a trivial problem. This article suggests it’s not possible. [Could you guarantee yourself a Powerball jackpot?](http://money.cnn.com/2016/01/11/news/powerball-jackpot-win-guarantee/index.html) Furthermore, because of the likelihood of sharing the big prize, the expected value of the ticket only climbs above $2 when the grand prize is about $1.6 billion.We’re not there yet. Finally, if it gets there, you only expect to break even but there is risk in the distribution of those outcomes… Whether you make or lose money buying every ticket depends solely on being the only winner, or at least no worse than 1 of 2. According to that article, with 440 million tickets sold, you have only a 55% chance of being the sole winner or 1 of 2. With the greater number of tickets sold this week, the odds of multiple winners (and your odds of going bust) only climb. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 12, 2016, 2:28am UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/34 "2016-01-12T02:28:33Z")
> [@pulykamell](#): > > Ah, nice figuring it out. The formula **Cooking** posted is correct, but must have been entered wrong. 69!/(64!5!) is equivalent to 69!/64!/5!, not, like you found, 69!/64!\*5! Well, damn. Thanks. That’s why I was never an A student. I had all the concepts but screwed up on execution. ---
**Author:** ![Aji\_de\_Gallina](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aji_de_gallina/32/260_2.png) [@Aji\_de\_Gallina](https://boards.straightdope.com/u/Aji_de_Gallina)\ **Post date:** [January 12, 2016, 5:01am UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/35 "2016-01-12T05:01:06Z")
Can you buy a “multiple” ticket? Here in Peru it’s a six-ball draw, but if you choose 7 numbers you play (and pay) all possible combinations. Hence, you can chose all numbers and combination in one ticket. ---
**Author:** ![Hail\_Ants](https://avatars.discourse-cdn.com/v4/letter/h/dc4da7/32.png) [@Hail\_Ants](https://boards.straightdope.com/u/Hail_Ants)\ **Post date:** [January 12, 2016, 6:05am UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/36 "2016-01-12T06:05:03Z")
> [@Hail Ants](#): > > I’ve tried explaining this to sooooo many people. The winning numbers have literally NO relation to each other whatsoever. This is why 1, 2, 3, 4, 5, 6 has the same chance as any other set. Imagine instead of numerals the lottery balls had pictures of animals on them. This way Elephant, Giraffe, Bear, Cat, Horse, Snake coming out would seem as random as Rhino, Squid, Mouse, Fish, Bird, Whale etc. And the integer numerals work exactly the same way… > [@CarnalK](#): > > If that’s how you explain it, I can see how you get frustrated. Next time just say “you win by getting the same group of numbers, not a specific ordering of those numbers.” > [@Leo\_Bloom](#): > > Me, I prefer the animals. The psychology of mental representation of numerals is _huge_ here. For better or for worse, numerals are frighteningly lubricious: humans prefer (re)cognizable sequences or groupings–and “rhinos, squids…are a group of animals” makes sense quickly; numbers are a hard thing to make sense of at all, and individual items of three or more, in our daily experience, come in packs (like a group of random animals) but are rarely cognized without order. So it’s hard to disabuse someone of that way of thinking, which has worked nicely for so long. Because lotteries involve calculating ‘odds’, or math in general, people instantly are convinced that the ‘numbers’ on the balls also figure into it somehow. Other than the total number of balls and the number of them chosen, they do not. At all. They’re just convenient labels and could be anything (like random animal names). I’ve explained this to many people and they really don’t seem to believe me. It’s worse with [Quick Draw,](http://nylottery.ny.gov/wps/portal/Home/Lottery/Home/Daily+Games/QUICK+DRAW) which we have in the New York Lottery. It’s basically keno, 20 numbers are drawn out of 80 every four minutes. You try to match one to ten of them each game. But the Lottery screen shows the numbers being picked as animated balls flying towards a grid of the numbers 1-80 lined up in eight rows of ten each. So people constantly hoot & holler over ‘patterns’ or rows or columns that are ‘hot’ when they get picked multiple times. I try to remind them the screen is just a colloquial representation, that the numbers are not being picked like throwing darts at a board. Therefore any and all apparent ‘patterns’ are utterly meaningless. In the end I just remind myself that lotteries are a tax on stupid people… 😃 ---
**Author:** ![Lord\_Feldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lord_feldon/32/341_2.png) [@Lord\_Feldon](https://boards.straightdope.com/u/Lord_Feldon)\ **Post date:** [January 12, 2016, 6:07am UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/37 "2016-01-12T06:07:47Z")
> [@Hail\_Ants](#): > > So people constantly hoot & holler over ‘patterns’ or rows or columns that are ‘hot’ when they get picked multiple times. Ohio actually has a page you can go to where you can see what keno numbers are “hottest” and “coldest.” :rolleyes: ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [January 12, 2016, 1:55pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/38 "2016-01-12T13:55:59Z")
> [@CookingWithGas](#): > > Of course? You say that like it’s obvious, but it’s not obvious if you’ve never bought a ticket. There’s really no reason to disallow duplicates, so it’s a matter of arbitrary rules of the game. It’s not Bingo. I don’t make investments with a negative expected value so I’ve never bought a lottery ticket. > > Choosing 5 items from a group of 69 has a number of combinations (not permutations) of 69!/(5!64!) = 161,834,587,200 then multiply by 26 = 4,207,699,267,200. > > I see 292,201,338 quoted in a lot of places but how was it calculated? > [@pulykamell](#): > > Also, [this is what a powerball drawing looks like](https://www.youtube.com/watch?v=Bup0TcbQeVs). The method for drawing and picking the balls does not allow for duplication (except for the Powerball itself, which is a separate machine and drawn from a pool of 26 numbers.) The regular numbers in Powerball and pretty much all at least American-style lotto “pick five or six numbers from a pool of 44, 54, 69, whatever” work the same way. A bunch of numbered ping pong balls are dumped into a machine and then the required number are siphoned off into a tube and not reintroduced into the shuffling mechanism. In other words, yes, it is a bit like Bingo or Keno. Yes, sorry, the Canadian lotteries I’m most familiar with, and most other larger north American “pick” lotteries, are based on a bunch of light (ping-pong) balls drawn out of a whirling mass in a cage, a variant on the Bingo system, and a generally fairly visible obviously fairly random draw. When these lotteries were unique and a big deal, this used to be shown live on TV after the nightly news. Much like Bingo, number order did not matter, just which numbers (except for the one “bonus” or “power” or whatever number), and there was only one of each possible number in the machine. Sorry, i assume everyone must have seen one of these drawings at some time on TV. Picking random numbers was easier than the logistics of ensuring a stub from every ticket was delivered to a vat and the logistics of fairly pulling winning stubs once the lottery got into the millions of tickets. ---
**Author:** ![IDtenT\_Error](https://avatars.discourse-cdn.com/v4/letter/i/e19b73/32.png) [@IDtenT\_Error](https://boards.straightdope.com/u/IDtenT_Error)\ **Post date:** [January 12, 2016, 4:48pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/39 "2016-01-12T16:48:15Z")
> [@Lord\_Feldon](#): > > Ohio actually has a page you can go to where you can see what keno numbers are “hottest” and “coldest.” :rolleyes: New York has that right on the screen the numbers get displayed on. :eek: ---
**Author:** ![Hail\_Ants](https://avatars.discourse-cdn.com/v4/letter/h/dc4da7/32.png) [@Hail\_Ants](https://boards.straightdope.com/u/Hail_Ants)\ **Post date:** [January 12, 2016, 9:41pm UTC](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699/40 "2016-01-12T21:41:08Z")
> [@IDtenT\_Error](#): > > New York has that right on the screen the numbers get displayed on. :eek: Yeah, they list them as ‘Hot’ or ‘Not’. I love joking to my gambling friends, _“Oh! Those numbers are ‘Hot’ so play them! No wait, they’re worn out, the ‘Not’ ones are due to hit now! No wait, they’ve got the whammy on them! No wait…”_ 😃 [Previous page](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699.md?page=1) [Next page](https://boards.straightdope.com/t/physically-possible-to-cover-every-powerball-number/742699.md?page=3)