Did you have few enough bills in your wallet that you could immediately and accurately apprehend how many there were? If not, then there were enough that you didn't know how many there were, and that $1 was one that might as well have not been there according to your initial coarse perception.
I think this works if the $1 represents an extra bill that you didn't know was in there, but not if you looked more closely at a specific bill and were happy to realize that it was a $1.
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.