The jackpot is going to be over $500 million dollars. Even though there is a 1 in 171 million chance of winning, factoring in taxes and the increased chances of splitting the jackpot means that the ticket is only mildly positive expected value
, at best. Factoring in the time cost of checking the numbers probably makes it negative EV. Any strategy that involves picking numbers that are marginally less likely to be shared (sticking to numbers that aren't part of birthdays) also incurs a time cost versus getting random numbers, and the advantage is not likely to be worth it. So it's entirely rational not to play even now unless a person enjoys the lottery process itself.
1. This is a great advertisement for the lottery.
2. It would be interesting to see how often these types of jack pots occurred in private lotteries if competition with the state was legal. Given that this is great advertising and a private market lotteries would have to give a higher percentage in payouts due to competition and that this is a great form of advertising it might be a more common occurrence.
3. Some companies will probably do large company pools and buy a lot of tickets. If any of them win the big jackpot, it would destroy that company. This is especially true for start ups.
Full disclosure: I have never bought lottery tickets before, but now I am long a few tickets.