It's a minor point and probably not worth much more effort, but I'm still confused. If I'm ignorant enough about my total wealth that a finding that a bill turns out to be a $1 instead of a $5 doesn't cause me change my best estimate of my non-wallet wealth, then why isn't it $4 worth of bad news? I don't see the flaw in that reasoning.
Oops, the above should be, "total wealth differences in the region of $4", not "total bank account wealth differences". Hm. This is an interesting problem in approximate rationality - if your estimate of "bank account + wallet" and "bank account" is pretty much the same total number, and you learn how much money is in your wallet, what have you learned?
The other day I went to get some productivity-enhancement M&Ms from the candy machine at work. When I opened my wallet, I didn't immediately see a $1 bill. Then I looked some more and I found one, and I was happy! But of course that doesn't make any sense. If that bill hadn't been a $1, then it would have had to be a $5 or more, with an expected value of $5+, which is an amount that I certainly would not have paid for a bag of M&Ms, most excellent though they may be. This means that I preferred a bag of M&Ms to $1 (that's why I went to the candy machine in the first place), $1 to $5+ (I was happy when the bill turned out to be a $1), and $5+ to a bag of M&Ms (I wouldn't have bought them at that price). Not too surprising I guess, but still kind of weird.