OK her in Canada tonight is the drawing of Lotto Super 7
You have to pick 7 numbers between 1 and 49 to win $20 Million.
I have a friend who claims the more tickets you but the better you odds of winning. He says tht if you go out and buy 20 million tickets your odds get better.
I say your odds stay the same.
Any one have the math to settle this one
Assuming you don’t keep playing the same set of numbers, of course your odds get better. Think of it using simpler number: if I ask you to pick a number between 1 and 10, your odds of picking the correct number are 10 to 1. If I let you pick two numbers, your odds are 10 to 2 (or 5 to 1). Same idea with the Super 7 drawing.
Well, as long as you pick 20 million different number combinations, of course your odds improve. If your probablility of winning on any particular combination is two in a trillion, then buying 20 million tickets improves your chance to one in twenty-five thousand (which still sucks, but it’s a substantial improvement).
[nitpick]The probability of picking the correct number in JeffB’s example is .2, making the odds 4 to 1.[/nitpick]
I believe that this has already successfully been accomplished. I can’t seem to find the specific info, but as I recall, a venture capital group bought something in the neighborhood of $1,000,000.00 worth of tickets. And then they won ($20 million, if I remember correctly). There was a big stink about it, but for a reason that wasn’t readily obvious to me. It seems that the stores that sell a winning ticket get a bonus (which is considerable with large winnings). It seems that the investment group bought all the tickets through the main lottery commission, thus bypassing all those that are part of the distribution network. Not sure how it turned out, but I think the investors got their money, and then the rules were change so that you could only buy tickets through a retail outlet.
Of course while your odds of winning increase, your expected return will in all likelihood decrease the more tickets you buy. The expected return on n tickets, assuming they all have different numbers (the best case), will just be n times the expected return on one ticket. And presumably the expected return on one ticket is negative.
In other words, the greater odds of winning don’t make up for the larger stake you have to put up to get those odds.
Yes, you could always buy enough tickets so you had every possible combination but it would cost you more than the prise was worth.
Math Geek and Skogcat: Not always. In the situation vertigo describes, the group did the math and knew that it was worth it. Sometimes it is a good idea to play the lottery, but it doesn’t get that high very often.
(This is, of course, only applicable to lotteries like Powerball, where the prize goes up every week it isn’t won.)
Patricinus. As the responses so far make clear, if you select a different set of 7 numbers each time you buy a ticket, then the more tickets you buy, the greater the chances that one of your sets of seven numbers will match the winning set that comes out of the Lottery machine.
In the discussion you had with your friend, you may have been confused by a related issue, which is that no particular set of seven numbers is any more likely to come up than any other. Each of these players has precisely the same chance of winning:
Player 1: 2, 13, 17, 19, 23, 31, 47
Player 2: 1, 2, 3, 4, 5, 6, 7
Player 3: 2, 4, 6, 8, 10, 12, 14
Some people find this hard to accept or understand, because the winning numbers are chosen at ‘random’. The fact remains that any combination of seven permitted numbers is just as likely to arise as any other.
Even if you’ve calculated the odds and effectively guaranteed yourself a win, there’s still risk. Imagine the odds of winning are 1 in 13 million (if I recall correctly, that’s about what picking 6 numbers out of 49 works out to). If the jackpot gets up to 14 million one week, you simply go plunk down 13 million dollars so you’ll get one of every single combination, and when your number gets called, you go collect your 14 million, making a cool 7.7% profit in a week’s time. Where’s the risk? Oh yeah, someone else can win too, and then you spent 13 million bucks to only win half of 14 million. Whoops.
Ah yes, hadn’t thought of that.
My Mum used to choose 1, 2, 3, 4, 5, 6 in Lotto (just six numbers) because she expected that other people would avoid runs like that considering them to be less likely to win. That made sense to me to begin with, but then I thought, if Mum thought of that, plenty of other people would have as well. I did see a run come up once and there were a high number of winners.
Wikkit: you’re right of course; if the expected return on the ticket is positive then more is better.