n=1 to maximize the probability I find out how utils are measured.
You can't outthink a tautology. You don't care about maximising the probability of finding out how utils are measured more than utils themselves by definition.
True, I am being somewhat flippant. However, I'm being upvoted more than I am when I take my time thinking about a comment, so I must be doing something right.
This problem was invented by Armok from #lesswrong. Discuss.