I fundamentally disagree that the resulting distribution isn't more or less equal. It's basically randomly distributed around 45, with a pretty small standard deviation to boot...
Of course it's randomly distributed around 45 -- conservation of money at work there.
As for the std deviation, the normal rule of thumb is "95 percent of samples fall within 2 std deviations". So basically, all but the highest and lowest. Well maybe two highest, because of the 0 dollar lower bound. A standard deviation of half your starting pool seems pretty high, even if we all have equal chances of being at the far end of the spectrum of results.
