Also $2B seems insane. At this point I think it would make sense to make it easier to win.
The marginal utility decrease from buying a ticket is close to zero for many/most people whereas the marginal utility increase from winning $2bn is essentially infinite. So the motivation for buying tickets is pretty clear in mathematical terms as long as you optimize expected marginal utility rather than expected value.
Somewhere around half goes to prizes, another quarter to running the lottery, and the remaining bit is the proceeds for state funds. It's not especially effective as a source of fundraising, but it's a hack of a lot better than Vegas.
I have spent about a thousand dollars on lotto tickets through my life (including the rebate from my meagre winnings), and I've spent that amount on things that were a lot less entertaining per dollar. You're buying dreams and the flight of fancy, not any tangible benefits.
Mathematically though, your odds on a single ticket don't change, and realistically even a smaller jackpot is going to be life changing. So does it really matter?
I still bought a bunch of tickets. I'll just hope that I'm in a simulation and the real me is the one on the outside running it :) If I win, prepare for world peace.
Jackpot winning and odds is almost irrelevant, but is the only focus of most literature.
There are thousands of winners multiple times per week, and they do not split those smaller prizes. Several of which are over $1,000,000
regarding relative utility, I spend more on a cocktail