I was thinking that you should take into account the fact that if you got several trillion dollars, that only entitled you to half of America's resources, and if you got infinite dollars it would only give you 100% of America's resources. It turns out that similar notions have already been studied and the expected value calculated for them on Wikipedia (well, they just assumed that the bankroll was US GDP and didn't look at a quantity theory of money solution specifically, but same diff).