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Vladimir_Nesov comments on Value of Information: Four Examples - Less Wrong
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My prior assumption is that if someone offers me a weird bet about which I have very little information, the odds are stacked against me some way or other. The only reason I'd take the bet would be if the amount is small enough that I want to see what the trick is.
This is discussed in footnote 2. (And focusing on this problem isn't in the spirit of LCPW.)