One more thing: If some balls have less than a 1/50 chance, then in order to make the probability add up to 100% that you will get a ball, some balls will have a more than 1/50 chance. Which balls are those? I will pick them and win - thanks in advance.
Ask your computer smart-guy these things and see what he says.
This sounds like the story of the Virginia Lottery (VL) when an Australian group tried to buy all the tickets.
They got enough investors to cover all the combinations, some 7 million. They had VL entry tickets with all the combinations filled in (I think using a computer printer). They just waited until the jackpot was big enough, $28 million, to make it worth the effort.
They then started buying tickets at many sites. They only had 3 days, but it’d take 81 printer-days to print all the tickets. The one thing they did do (which is now barred) is they bought tickets directly from (I think) 7-11/Southland’s main office in Virginia, rather than from a retail outlet.
They only got half of their tickets scanned, but they did win. I can’t recall if they had to split it with someone else, though. And their investors, who eventually will get a 2 or 4 times return on their investment, won’t see all of that until the 20 year annuity is paid off. Not worth the hassle, IMO.
I will. Thank you, you all tried hard. I just thought that it’s harder to built a computer than it is to destroy a computer. So, by the same token, I thought that it’s harder to pull balls in any order or configuration thah to pull them randomly. Apparently, different laws apply.
Gawd, there’s so much illogic being thrown around here, it’s making my brain rot.
Johnson, your idea would work…except for a few small flaws.
Let’s assume you only bought half the number of possible combinations and quit when you were ahead. That would happen half the time. The other half of the time you would be so royally screwed your ass would be hurting the rest of your life.
But maybe you’re not playing the powerball, but just the pick 3 or pick 4. Look at the math. pick 3: 1000 combinations, payout of $500. Pick 4: 10,000 combinations, payout $5,000.
This means that in order to insure a win, you’d have to spend twice what you’d make once you won. You’re trying to play a game with a 50% house advantage. That’s almost twice what Keno steals from you (up to 27% house advantage) and NO ONE who is the least bit knowledgable about gambling theory plays keno.
Now, what if you played only half the numbers on pick 3? 50% of the time you’d lose all your money ($500). 50% of the time you’d make $500, breaking even. End result, you lose $250 for every $500 you spend. In other words, same result, different figures.
Chas E As it has been said numerous times in this thread, the powerball odds around 1 in 80 million. I don’t know where you get your 1 in 12 million odds from, but it’s probably a local or state lottery when the pot doesn’t get up to 12 million very fast.
Now, ignoring the $100,000 pot from getting 5 numbers without the powerball (which will happen once in 49!/(44!*5! times (or 19 million)) and ignoring the $1 prize of hitting the powerball (1 in 42 times), there are a number of factors that must happen to ensure a profit from the lottery.
Let’s assume a 40% tax on your lump sum winnings. This means that, in order for you to have positive expectation by playing the lottery, the pot must be AT LEAST $133.5 million and you must be the only one to win. Problem is, when the pot gets up that high, the chances increase significantly (due to all the other people playing) that the pot will indeed be split.
In other words, the lottery is a tax of people who are bad at math.
Speaking of bad at math…
49!/(44!*5!) = 1.9 million, not 19 million.
And to pre-emptively strike an argument I know will come up: no, you don’t need to play all the numbers. Yes, 99.99999% of the population will have made a profit once they win the lottery because they amount the had put in until that point is nowhere near what they’re getting back. But overall the lottery is a bad investment because everyone BUT the winner will never show a profit. Ever.
I agree entirely about the illogic and the futility of playing the lottery, Enderw23. In general, it is a sucker’s game (expected value of the ticket greater than the cost being the exception). My point was that you could get on a lucky run, fully realizing that in the long run you lose.
That said, Enderw23, I’ve got this to say to you–listen and listen well–you are entirely correct. As I was putting this reply together, I realized I was operating under the misguided and unthinking assumption that the Pick 3 payout is $1,000, and that you’d therefore be bouncing around the break-even point. Put together a few wins in a row, and you’re ahead. Since the payout is in fact only $500, you’d have to get very lucky indeed to come out ahead.
Bear in mind that I’ve only bought lottery tickets three times–for a large Powerball drawing and two Big Game drawings–because I know full well you lose in the end. That’s why I haven’t thought it through fully.
Now back to the illogic…
Alas, it wouldn’t work. You’d lose your shirt.
In our lotto game, the 6/49, there are 13.9 million possible numbers. So to nail the jackpot, you’d have to pick out at least $13.9 million worth of tickets. Obviously, you lose money if the jackpot is less than $13.9 million, but even when it’s more, odds are you’ll win less than $13.9 million because it will be shared with another winner. The odds of hitting a $13.9 million jackpot alone are very poor. The higher it is, the more people play.
No matter what the jackpot is, the average payout per jackpot winner will always be less than $13.9 million (or whatever the appropriate number is with your local lottery.) They plan this stuff really well. 
I’m sure the Ontario Lotto Corporation would LOVE for you to buy 13.9 million tickets every draw. Hell, they’d probably set up a bank of lotto machines just for you. They know you’d only average about $8-9 million in winnings per draw, even on high jackpots.
(An advantage in playing the lotto in Canada, which simplifies the calculations, is that lottery winnings in Canada are completely untaxable and paid up front. If you win a million, you show up, they give you a $1,000,000 cheque, and you keep it all.)
For all my comments about the odds, I play the lottery because IT’S FUN. It’s cool to dream about winning and it’s cool when you get a little prize. It costs money, but it’s an entertainment expense. It’s only “futile” if you’re actually counting on winning it.
rick, you’re forgetting one thing… in this scheme, you win the jackpot AND all the other prizes too.
Chas, this is true, but let’s add them up.
As I said, at a rate of taxation of 40%, the jackpot needs to be at 133.5 million to break even on your experiment. This doesn’t count all the other prizes, so let’s do that.
$100,000 for all five numbers. You’ll have that happen 41 times. That’s 4.1 million.
$1 for the powerball. That will happen 1.9 million times.
Total $6 million dollars.
Even if we assume that getting 4 numbers nets you 10 grand (which I can’t guarantee), it’s not going to be a lot more. End result: You can now play when the jackpot is at 127.5 million and break even. If you’re lucky enough to have the jackpot at 133.5 million you’ll make 6 million dollars on your 80 million dollar investment.
Not bad…but considering the risk of spliting the pot (and thus losing 13 million) I’d much rather have a hot pole rammed up my ass than try for a jackpot.
Besides, if you or your investers have $80 mil to blow on the lottery, I can think of a few better (and safer) uses for your money.
I’ve played all the numbers in lotteries and won.
It was a credit lottery on a dial-up bulletin board. For 1000 credits (10 minutes of your pre-paid time), you picked four numbers out of nine. (No repeats, similar to state lottos.) To encourage people to play, they’d up the jackpot by 1500 credits for every ticket sold. Soon, it was up to about 1,000,000 credits.
Being the math major, I realized that I only had to spend 126,000 credits to cover all the combinations. I had just bought 200,000 (for $20), and so I played.
Then I realized that their game doesn’t stop once all the possible tickets are bought. I played again later that week, and bought “6 7 8 9” over and over to boost the pot. Bingo, won again.
The sysops of the board were out of town that week, so I was tempted to squeeze out as much profit as I could. But they were friends, so I didn’t. When they got back and saw that I had won twice in a week, I told them how I did it. One of them thought he would make the game more difficult by requiring 5 out of 9, but I told him the combination totals would be the same: (9!)/(5!(9-5)!) = (9!)/(4!(9-4)!)
There were two other local boards that had the same software, but with larger unwon jackpots, about 2,000,000 credits each. I joined and won them. They later merged and added together my credits. The sysop even let me give half of them to my fiancee.
So for $60, I got virtually unlimited access to 3 bulletin boards that were planned to be big money makers. When the last one went under, I was tempted to sue for $150 for the unused credits on their system. (By this time, it’s ownership had changed so much that they wouldn’t have known that I didn’t pay for them in the first place.) :D:D