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RichardKennaway comments on Why you must maximize expected utility - Less Wrong
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This is the St. Petersburg paradox, discussed here from time to time.
It isn't really very much like the St. Petersburg paradox. The St. Petersburg game runs for a random length of time, you don't choose whether to continue; the only choice you make is at the beginning of the game where you decide how much to pay.
Or is it equivalent in some subtle way?