In economics this is called "social mobility" and it is measured to analyze the success of economic and social policies, whereby, generally, it is considered that having a high social mobility index is a desirable thing in a country. That's because a country with high social mobility is a country where the American dream is happening more often...
Social mobility works both ways: in a country with high social mobility, it is more likely that a child will be much poorer, or much richer than the parents.
There is a paper by the OECD analyzing by how much different factors (family wealth, education, etc.) affect wealth of children across different countries: http://www.oecd.org/centrodemexico/medios/44582910.pdf
What you find is that you need the freedom to be able to take a risk and fail. If you come from a household living paycheck to paycheck and just barely scraping by, you start off with a very risk averse mentality and never really escape it. When the big opportunity shows up, if you were risk averse your entire life it is unlikely that you will take the shot.
https://despair.com/products/overconfidence sums it up best: "Before you attempt to beat the odds, be sure you could survive the odds beating you".
Do you happen to have a source? I'd not heard this and was curious as to the amount.
However:
Several writers claim that Maxwell set up a million-dollar trust fund for Gates. A 1993 biographer who interviewed both Gates and his parents (among other sources) found no evidence of this and dismissed it as one of the "fictions" surrounding Gates's fortune. Gates denied the trust fund story in a 1994 interview and indirectly in his 1995 book The Road Ahead.[2]
So I'm inclined to think it's not true, although it does seem a fairly wide-spread story.
But at the same time, Bill Gates did come from a rich family, so he wasn't going to starve if Microsoft didn't work out.
[1] http://philip.greenspun.com/bg/
[2] https://www.cs.mcgill.ca/~rwest/link-suggestion/wpcd_2008-09...
Even someone with a $1mil trust fund can make terrible enough choices to end up homeless.
And then, the thing is that family who was struggling the whole time, won't agree on dropping the best university with wonderful perspectives for some kind of crazy (at the moment it was very "crazy").
People are not "just risky" by default, they are influenced heavily by their life, and as someone mentioned here already, a lot of rich guys came from pretty decent living families, who can afford to fallback if something. For instance, a lot of world travellers, who try to live differently, actually have some passive income, property of just loads of cash, just in case something will go wrong.
http://www.forbes.com/sites/afontevecchia/2014/10/03/there-a...
Quote from your own source...