You could say the same thing about going to a movie. I find playing the lottery for a large jackpot more entertaining.

Sure, it depends on personal preference. For me personally I don't get much thrill out of gambling and would much rather spend the money on a movie. From the perspective of someone trying to increase their wealth even a +EV lottery is rarely worth it. The decision to buy a ticket should be based mostly on non-financial factors such as entertainment value.

I guess it didn't come out very clearly, but I was agreeing that EV should not be much of a factor when considering whether or not to buy a ticket, and disagreeing with the reasoning why.

I mildly disagree.

While it varies from person to person, big prizes like the lottery hold disproportionate utility because it represents the only way people will break a certain threshold of wealth.

Imagine all the stuff you want to buy or do, and how much it would cost to do each one. Like let's say you want to start your own business and it would take $100,000. It's entirely reasonable that someone can make or save or borrow $100,000, so the idea of spending your life on 1 cent shots to try and win that seems silly compared to going out and earning it by conventional means. But if you want to do something that costs $10,000,000, it's something that's pretty out of reach for most people and entering a $1 lottery is worth more utility even though it carries thr same EV.

I agree with you that above a certain payout utility starts flattening out - that most people don't dream of doing something with $500,000,000 that they can't do with $100,000,000. To that end, I think we all agree that there isn't a significant difference between a big jackpot and a huge jackpot.

But I think there is a significant difference in utility between the baseline jackpot ($15 million?) and a medium one ($150ish million).

Average and median are two different things.

It's just a geometric distribution.

Let P(x) = P(1st success on trial #x)
E = P(1) + 2*P(2) + 3*P(3) + ...
= p + 2pq + 3pq^2 + ...

Anyone with a calculator can see that that approaches N.

For something like the Powerball, without any calculation we know it's close to (e-1)/e =~ 63.212%
The 50% mark will be at approximately N*ln(2)

Taxes, the probability of splitting a jackpot, and the actual present value of the jackpot, all need to be taken into consideration in calculating EV.

When I mention "present value" I am referring to the fact that the advertised jackpot total is actually the total payout of a long term (20 years, IIRC) annuity. Most lotteries also have lump sum option which is considerably less that the advertised total.

In the end, with the probability of winning so low, the EV is academic. My personal take on lotteries is that I simply refuse to play any game where the house takes 50%. Slots on the Vegas strip are a better deal than state lotteries Lotteries truly are a tax on the mathematically illiterate.