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?
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?
Hopefully that your bank balance is such that whatever you carry in your wallet pales into insignificance.
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.