Mathematically speaking, if you start from a network of you and one other person, then each time your world doubles in size, it becomes, if you look at all the possible connections, four times smaller and then some. And the "then some" gets twice as big each and every time you double it.
The same dynamic applies in a general way to economic opportunity and savings as it does to networks. In other words, the financially well-off really do have it easier and it gets easier and easier as you go. The guy with 32 bucks in the bank has about 144 times the opportunities as the guy with 2 bucks. Think about that the next time some wealthy politician suggests a flat tax to "level" the playing field.