- you also have to account for the highly likely probability that the jackpot will be split between multiple winners.
- even after that accounting, lotteries do sometimes have an expected value higher than the ticket price. The expected value of purchasing N tickets for the N lotteries that led up to and include the big lottery is still the standard 40-50%, but the N-1 previous paid out much less than expected, so the one with the big jackpot pays out more than expected.
Most lotteries have multiple winners of varying amounts, depending on how many of your numbers match and how many other people happened to pick the winning set of numbers. I suspect that in order to get a 50% chance of winning the jackpot, you would have to invest into considerably more than 86 million tickets.
Many lotteries make it hard to buy that many tickets. They may say tickets filled out by machines are invalid. Some limit how many tickets a retailer can sell in a day (for example if you know your busiest kiosk sells 2,000 tickets a day, flags are raised if someone starts selling 20,000 tickets per day).
I guess it's not fun for the regular players (who are the bread and butter of the lotteries) if a syndicate swoops in and takes the massive jackpots when the odds are in their favour.
You're not missing anything. It is technically possible to design and build a business focused solely on buying lottery tickets for profit (i.e.: buy enough to ensure good enough odds to win) But there are a number of risks. The list below isn't exhaustive:
* sharing the winning number with someone else
* do you buy every single ticket or enough to "virtually guarantee" a win? (and the fewer tickets you buy, the more risky it becomes)
* the logistics of purchasing that many tickets
I have even read stories of people trying this before - but haven't been able to find the link. The story I remember best is one man hiring a bunch of people to buy lottery tickets on his behalf.
Anyway. I'd love to see someone make a go of doing this "professionally", but when you have 172 million or more, the incentive isn't really there anymore.
But this assumes consistent buying in the past, while the original poster's statement assumed one-time buying binge once the jackpot hits the level to make it worthwhile.
- you also have to account for the highly likely probability that the jackpot will be split between multiple winners.
- even after that accounting, lotteries do sometimes have an expected value higher than the ticket price. The expected value of purchasing N tickets for the N lotteries that led up to and include the big lottery is still the standard 40-50%, but the N-1 previous paid out much less than expected, so the one with the big jackpot pays out more than expected.