
Thank you, this is good to know. I’ll have to think about this some more.

Hm, I was working under the assumption that the “utility” with paperclips was just the number of paperclips. A universe with X − 10n + 3^^^^3 paperclips is better than a universe with just X paperclips by 3^^^^3 − 10n. Is this not a proper utility function?

The casino version evolved from repeated alterations to Pascal’s Mugging, so it retained the 3^^^^3 from there. I had written a paragraph where I mentioned that for oneshot problems, even a more realistic probability could qualify as a Pascal’s Mugging, though I had used a 1/million chance of a trillion paperclips instead of ^{1}⁄_{100}. I ended up editing that paragraph out, though.
Working with a ^{1}⁄_{100} probability, it’s less obviously a bad idea to pay up, of course. I don’t know where to draw the line between “this is a Pascal’s Mugging” and “this is good odds”, so I’m less confident that you shouldn’t pay up for a ^{1}⁄_{100} probability. I think it becomes a more obviously bad idea if we up the price of the casino, for example to 1 million paperclips. This still gives positive EU to paying, but has a fairly steep price compared to doing nothing unless you get pretty lucky.
Looking back, I think that one of the factors in my decision to retain such ludicrous numbers was that it seemed more persuasive. I apologise for this.
All that being said, thank you very much for your reply!
You’re absolutely right. I was starting to get at this idea from another of the comments, but you’ve laid out where I’ve gone wrong very clearly. Thank you.