You're looking at the (potential) benefits and ignoring the costs. The costs are not negligible: "Thirteen percent of US citizens play the lottery every week. The average household spends around $540 annually on lotteries and poor households spend considerably more than the average." (source).

I'm only commenting to the rationality of one individual buying one ticket, not the ethics of the existence of lotteries.

Buying a second ticket doubles your chances, obviously.

Buying one ticket takes you from zero to one, buying two tickets takes you from one to two. 1/0 = infinity, 2/1 = 2. Buying anything more than 1 ticket has sharply diminishing utility. I realize this is a somewhat silly line of argument, so I'm not going to sink any more energy defending it.

For each timeline where you buy a lottery ticket there is one where you don't. Under MWI you don't make any choices -- you choose everything, always.

I don't think we understand each other on this point. I was referring not to choosing, just winning. And the measure of the winning universes is a tiny fraction of all universes. But that doesn't matter when the utility of winning is sufficiently large. And the chance of a given individual buying a ticket isn't 50% in any meaningful quantum-mechanical sense, so "For each timeline where you buy a lottery ticket there is one where you don't" isn't true.

You've never been poor, have you? :-/

No, and I wouldn't recommend that a poor person buy lottery tickets. My original claim was that buying lottery tickets can be rational, not that it is rational in the general case.

It is just as trivial to show that you should spend all your disposable income and maybe more on lottery tickets in this scenario.

That's true. People also say that you should donate all your disposable income to MIRI, or to efficient charities, for exactly the same reasons, and I don't do those things for the same reason that I don't spend all my money on lottery tickets - I'm a human. My line of argument only applies when you want a Widget and have no other way of affording it.

I don't really feel strongly enough about this to continue defending it, it's just that I'm quite sure I'm right in the details of my argument and would welcome an argument that actually changes my mind / convinces me I'm wrong.