Powerball even pays out on one number: the Powerball.See here for prize chart. 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’d love to see the maths on that because I believe you’re wrong - at least for the UK National Lottery and the Euromillions.
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
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.
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
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. You can also type, like I did in my first post “69 choose 5” and Google will return your result.
I think you missed a parenthesis. 161,834,587,200 is 69!/64!*5!
Also, this is what a powerball drawing looks like. 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.
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!
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.
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?
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.
Well, damn. Thanks. That’s why I was never an A student. I had all the concepts but screwed up on execution.
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.
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, 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… 
Ohio actually has a page you can go to where you can see what keno numbers are “hottest” and “coldest.” :rolleyes:
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.
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…”