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RichardKennaway comments on Why you must maximize expected utility - Less Wrong
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Maximizing expected utility can be paradoxically shown to minimize actual utility, however. Consider a game in which you place an initial bet of $1 on a 6-sided die coming up anything but 1 (2-6), which pays even money if you win and costs you your bet if you lose. The twist, however, is that upon winning (i.e. you now have $2 in front of you) you must either bet the entire sum formed by your bet and its wins or leave the game permanently. Theoretically, since the odds are in your favor, you should always keep going. Always. But wait, this means you will eventually lose it all. Even if you say "just one more and I'll stop", it'll be mathematically optimal to keep repeating this behavior. This "optimal" strategy does worse than any arbitrary random strategy possible.
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?