Even to keep among the 'rich' list assuming you inherited it all takes enormous talent because money inflates away.
There may be a bigger incidence of luck (I am not sure of this either btw - almost all the contacts you get as a rich person are very much the effect of you being rich) but unless you're well prepared to take full advantage of it, there will be no returns.
What I will concede though: Luck when you're poor might mean securing a week of food. Luck when you're a billionaire probably means the stock market goes on a 15 year bull run.