Vaniver comments on Value of Information: Four Examples - Less Wrong
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But what if your friend offers you to stick the gum to any other coin and let you see which way it lands, to get a feel on how the gum "might" affect the result*, and then offer you this deal? How would you calculate Vol then?
This tends to be very context dependent; I don't know enough about biology to estimate. The main caution here is that people tend to forget about regression to the mean (if you have a local measurement X that's only partly related to Y, you should not just port your estimate from X over to Y, but move it closer to what you would have expected from Y beforehand).