1) You’re correct that “known finite iterations” can be treated as “single-shot” by defining a complete strategy and not caring about intermediate states. “unknown ending conditions” may or may not be reducible in this way.
2) You can’t get away from utility. You have to define how much better a universe with X − 10n + 3^^^^3 paperclips is than a universe with X or a universe with X − 10n (where X is starting paperclips, n is number of wagers you’ll make before giving up or hitting the jackpot).
3) using ludicrous numbers breaks most people’s intuitions (cf scope insensitivity), and you should explain why you don’t use a 100-sided die and a payout of a trillion paperclips.
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 one-shot 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!
1) You’re correct that “known finite iterations” can be treated as “single-shot” by defining a complete strategy and not caring about intermediate states. “unknown ending conditions” may or may not be reducible in this way.
2) You can’t get away from utility. You have to define how much better a universe with X − 10n + 3^^^^3 paperclips is than a universe with X or a universe with X − 10n (where X is starting paperclips, n is number of wagers you’ll make before giving up or hitting the jackpot).
3) using ludicrous numbers breaks most people’s intuitions (cf scope insensitivity), and you should explain why you don’t use a 100-sided die and a payout of a trillion paperclips.
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 one-shot 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!