[lozaning]

If you live in a state where you can play jackpot only, which is 2 picks for $3 and no eligibility for partial matches, there's a positive EV anytime the cash payout is more than $453,863,025.00

Accounting for taxes ruins it a bit, but once the jackpot gets high enough it's dumb not to buy a ticket.

[Retric]

That also assumes single winners, more interestingly it ignores the diminishing marginal utility of money.

Consider your personal utility function, at 70 what odds would you need to play double or nothing with your entire life’s savings. If it takes more than 50.1:49.9 odds then you like most people don’t have a linear view of money.

[JanisL]

The expected utility of buying that ticket is quite poor though which is the thing that really matters for most people. You get a sense of this when you consider that the vast majority of the time you lose your initial investment. If you have any other options to get returns on your money you are going to have the opportunity cost of that to deal with too and that's what makes the lottery ticket unappealing from a utility point of view.