Or (tongue in cheek), you could always buy 2-3 tickets that all have the same numbers. That way if you win and someone else wins too, you still get most of the money. :-)
True, but I imagine for most people that going from never winning a lottery to winning a fraction of a lottery is still a much bigger step than winning a fraction of a lottery to winning a larger fraction of a lottery. If you want to max out your odds of a life-changing win, be OK with sharing. :)
Letting the computer choose randomly is not optimal, since the computer may choose one of the commonly hand-selected numbers. A better method is to build a list of commonly hand-selected number, then have the computer choose a number that is not in that list.
This method helps to improve the expected value from a lotto ticket (though it's still far less than the ticket price), but I'm curious what happens if someone purchases one of every combination. I hear that the odds of winning are something like 1 in 292 million. If it's only $2/ticket, isn't it nearly a sure thing to buy 292 million sequential tickets? Aside from splitting the jackpot with others, your expected outlay is $584 million, and your return is ($1.5 billion)/(number of winners). As long as there are < 3 winners, your expected return is 1.5-3x your investment.
Aside from the feasibility of buying/tracking 292 million tickets and the risk of > 3 winners, am I missing anything?
Unfortunately, yes. Present value of a future annuity (taking the lump sum now cuts the jackpot by quite a bit), and taxes. For ballpark calculations, I assume that each is going to cut the advertised jackpot in half. So for a $1.5 billion jackpot, your expected return is going to be a around $375 million (plus every single other prize, but that just adds about $20 million to the total), assuming no other winners.
Yes, your strategy will work, but not until the jackpot reaches even more ludicrous heights.
The feasibility of buying 292 million tickets (as you mention) is a key barrier: many lotteries (Powerball included) explicitly and deliberately require that tickets must be bought in person. So, just as a matter of time constraints, you'd need a (nontrivial) army.
Rough ballpark: 300 million combos - let's say you buy 6000 tickets/hour (which I think is actually optimistic probably by a full order of magnitude), for 25 hours a day (assume shifts and magic days), you're still looking at 2,000 person-days.
My tongue-in-cheek scheme: Operate a "lottery disappointment insurance" company. For (say) $1.50 you register your numbers with us, and we promise to pay out what you would have won had you bought a $2 ticket on the real lottery. Any large insurance company could easily afford the payout, and there should be sufficient spread between the official ticket price and the expected win to make it profitable.
Only downside is that if by some fluke it is not already illegal, it would be made illegal in a flash.
One thing I've considered in the past is that it would be fun to play the previous draw's winning numbers. First of all, having just won the lottery, I would think most people wouldn't bother to play the next week, so you clear out anyone regularly playing those numbers. Also most people intuitively think it's nearly impossible for the same numbers to be drawn twice in a row. (Which of course it is, but no more nearly impossible than any other set.) So maybe you wouldn't have to share. And if you won, you'd be an instant celebrity. However, 1) I really wouldn't want that kind of attention, and 2) I bet other people have the same idea, so it'd probably totally backfire.
Some quick calculations seem to indicate that even with sharing and tax taken into account, buying all tickets would be fairly profitable with the prize at this level, so why has nobody done it yet?
Physics and how much cash you would need to carry.
5 ticket combos per form and there are comb(69, 5) x 26 or 292,201,338 possible combinations meaning you would need to fill out 58,440,268 powerball forms (the last with only 3 combos on it).
At this point acquiring 58+ million forms is going to be a bit of a problem, followed by building the machine to fill out all the forms, and finally having to buy each set of tickets for $10 each (except, of course, the last form costing $6). I am pretty sure going from place to place as they run out of ticket rolls will also make it a bit difficult.
Expected value calculations are very hard to do here, because you need to estimate the number of people who will be buying tickets, which you need to calculate the odds of sharing a prize, as well as to determine the prize amount. And estimation is really hard because there's never been a prize this big.
FiveThirtyEight[1] estimates between 550 million and 1.2 billion tickets will be sold. Their best estimate is 1 billion tickets sold, giving odds of sharing the prize at 97%.
This makes the Expected Value of a $2 ticket $1.34. If you bought one ticket of every number, you'd be guaranteed to win, but after splitting the prize with the other winners and paying taxes, you will have lost money.
The powerball is a crappy lottery -- most other national lotteries give out a higher percentage of their intake. For instance, Lotto 6/49 in Canada reaches a par expected value around the $40 million dollar range.
The real losers of lottery schemes like this are the people who buy tickets when the prizes are low.
I think logistics and risk the main reasons. On average you can expect the jackpot to be split 3-4 ways, and the lump sum payout will only be ~900M. I'm not sure what the other prizes add up to, but obviously they're going to be significantly less than the jackpot. So given that it would cost almost $600M to buy all the combinations, it is very possible that you could end up with a loss in the tens of millions, if not more. It's not the most likely result, but it would certainly be a consideration.
The bigger issue though is how much it would cost to buy and redeem ~300 million tickets. Since you're choosing your numbers, someone is going to have to physically type in each set of numbers at sale. So at a minimum it's going to take like 5 seconds per set just to produce them. Or about 70 years, working continuously for 16 hours a day. Obviously you wouldn't do it all yourself, but even assuming retailers were willing to just continuously produce tickets for you all waking hours, you would need 4000 people working in parallel, 16 hours a day, to get the tickets printed in under a week. And that's just the time to physically type in the numbers. They're also each going to need to store and transport the thousands of tickets. Then you have to redeem them, a process which would likely take longer. So as a rough estimate, say 8000 person-days (8-hour days) overall. Plus overhead for bookkeeping, management, etc. Even so, that would only cost on the order of single millions; a rounding error compared to the jackpot. But can you even find thousands of people willing and able to do this job? They would have to be relatively trustworthy as well.
Given the risk, no one is going to lend you the money to do this. So you would need access to half a billion dollars. I imagine most people with those resources have better things to do with their time. (Although if the draw were in a few months, maybe Donald Trump would have a go.)
I'm wondering the same thing. I'd guess it's the risk of having too many winners coupled with the fact that any entity with that much cash to "invest" has regulations preventing them from investing in a lottery. (There's also the hassle of the logistics of printing and storing that many tickets.)
That only works if there can be only one winner. If you spend $250Mto win $292M, that seems like a sure bet. But someone else wins too, then you only won $146 million, so you actually lost $104M. I'm skeptical that the math works out, even if you're the only winner, though.
The lottery is pretty much designed so that the expected value (EV) of a ticket is much, much lower than what you pay for it. They always make more money than you win.
Game Theory -- if other people know about this, they will attempt; but knowing they know means they know you know, which leads to a prisoners dilemma: if you both play, you lose, but if just ones does, that one wins.
Without having the numbers or doing the maths, I'd guess that if you include the odds of another person or people also winning the EV would drop below 100% return.
I play lotteries when under some simple assumptions I believe the EV to be in my favour - usually when there have been many rollovers.
Taking a MWI view, I consider it to be a way of transferring money to other universe versions of myself, and when you have a good EV, that represents a cheap inter-universe transfer rate.
I dunno. The marginal utility of having a dollar (edit: apparently these tickets cost two dollars, but that doesn't change my answer) in my pocket is zero. Not near zero, but identically zero. My life differs not even a little bit based on whether I have that dollar or not.
The expected value of a lottery ticket is small but nonzero.
I don't know about that. Office pools are kind of fun[1], and I'm not a big gambler since college where I played a bit of poker[2] and powerball scratches the itch. I don't think anyone with the money would actually buy millions of tickets.
1) although if you end up being the designated ticket buyer and buy 120 tickets without one number showing up on any of the quick pick picked tickets, you are going to take a lot of crap for a while.
2) I was good enough that it paid for pizza for a while though I never got into online or tournaments at the local casino.
[+] [-] tunesmith|10 years ago|reply
[+] [-] dkokelley|10 years ago|reply
[+] [-] mleonhard|10 years ago|reply
[+] [-] dkokelley|10 years ago|reply
Aside from the feasibility of buying/tracking 292 million tickets and the risk of > 3 winners, am I missing anything?
[+] [-] MatthaeusHarris|10 years ago|reply
Yes, your strategy will work, but not until the jackpot reaches even more ludicrous heights.
[+] [-] kgrin|10 years ago|reply
Rough ballpark: 300 million combos - let's say you buy 6000 tickets/hour (which I think is actually optimistic probably by a full order of magnitude), for 25 hours a day (assume shifts and magic days), you're still looking at 2,000 person-days.
[+] [-] unknown|10 years ago|reply
[deleted]
[+] [-] tbyehl|10 years ago|reply
http://www.nytimes.com/1992/02/25/us/group-invests-5-million...
[+] [-] ck2|10 years ago|reply
It's something like $900 million lump sum.
[+] [-] aqme28|10 years ago|reply
[+] [-] me_again|10 years ago|reply
Only downside is that if by some fluke it is not already illegal, it would be made illegal in a flash.
[+] [-] pavel_lishin|10 years ago|reply
[+] [-] ethbro|10 years ago|reply
[+] [-] zappo2938|10 years ago|reply
[1] http://fivethirtyeight.com/features/billion-dollar-powerball...
[+] [-] tempestn|10 years ago|reply
[+] [-] kybernetikos|10 years ago|reply
[+] [-] protomyth|10 years ago|reply
5 ticket combos per form and there are comb(69, 5) x 26 or 292,201,338 possible combinations meaning you would need to fill out 58,440,268 powerball forms (the last with only 3 combos on it).
At this point acquiring 58+ million forms is going to be a bit of a problem, followed by building the machine to fill out all the forms, and finally having to buy each set of tickets for $10 each (except, of course, the last form costing $6). I am pretty sure going from place to place as they run out of ticket rolls will also make it a bit difficult.
[+] [-] simonw|10 years ago|reply
Another attempt in Australia in 1992: http://www.nytimes.com/1992/02/25/us/group-invests-5-million...
[+] [-] bryanlarsen|10 years ago|reply
FiveThirtyEight[1] estimates between 550 million and 1.2 billion tickets will be sold. Their best estimate is 1 billion tickets sold, giving odds of sharing the prize at 97%.
This makes the Expected Value of a $2 ticket $1.34. If you bought one ticket of every number, you'd be guaranteed to win, but after splitting the prize with the other winners and paying taxes, you will have lost money.
The powerball is a crappy lottery -- most other national lotteries give out a higher percentage of their intake. For instance, Lotto 6/49 in Canada reaches a par expected value around the $40 million dollar range.
The real losers of lottery schemes like this are the people who buy tickets when the prizes are low.
1: http://fivethirtyeight.com/features/billion-dollar-powerball...
[+] [-] tempestn|10 years ago|reply
The bigger issue though is how much it would cost to buy and redeem ~300 million tickets. Since you're choosing your numbers, someone is going to have to physically type in each set of numbers at sale. So at a minimum it's going to take like 5 seconds per set just to produce them. Or about 70 years, working continuously for 16 hours a day. Obviously you wouldn't do it all yourself, but even assuming retailers were willing to just continuously produce tickets for you all waking hours, you would need 4000 people working in parallel, 16 hours a day, to get the tickets printed in under a week. And that's just the time to physically type in the numbers. They're also each going to need to store and transport the thousands of tickets. Then you have to redeem them, a process which would likely take longer. So as a rough estimate, say 8000 person-days (8-hour days) overall. Plus overhead for bookkeeping, management, etc. Even so, that would only cost on the order of single millions; a rounding error compared to the jackpot. But can you even find thousands of people willing and able to do this job? They would have to be relatively trustworthy as well.
Given the risk, no one is going to lend you the money to do this. So you would need access to half a billion dollars. I imagine most people with those resources have better things to do with their time. (Although if the draw were in a few months, maybe Donald Trump would have a go.)
[+] [-] dkokelley|10 years ago|reply
[+] [-] asift|10 years ago|reply
[+] [-] Jemaclus|10 years ago|reply
The lottery is pretty much designed so that the expected value (EV) of a ticket is much, much lower than what you pay for it. They always make more money than you win.
[+] [-] mmanfrin|10 years ago|reply
[+] [-] corin_|10 years ago|reply
[+] [-] brianpgordon|10 years ago|reply
This paradox is related to the https://en.wikipedia.org/wiki/Interesting_number_paradox
[+] [-] ck2|10 years ago|reply
last Saturday 25 people won that $1M prize
curious to see how many this time around tomorrow
[+] [-] mesozoic|10 years ago|reply
[+] [-] kybernetikos|10 years ago|reply
Taking a MWI view, I consider it to be a way of transferring money to other universe versions of myself, and when you have a good EV, that represents a cheap inter-universe transfer rate.
[+] [-] monochromatic|10 years ago|reply
The expected value of a lottery ticket is small but nonzero.
[+] [-] protomyth|10 years ago|reply
1) although if you end up being the designated ticket buyer and buy 120 tickets without one number showing up on any of the quick pick picked tickets, you are going to take a lot of crap for a while.
2) I was good enough that it paid for pizza for a while though I never got into online or tournaments at the local casino.