Doing a quick bit of estimating, if his parents were worth $10MM USD, and he reached $100billion in net worth, then he increased their wealth 10,000 times. Note that it is not yet inherited, as he achieved that wealth while both parents were alive.
I'd surmise that anyone that increases their wealth 10,000 times more than their parents is self made.
If Bill's parents only had $100, and he reached a million (10,000 times higher), then he'd still be "self-made".
To me at least, anyone who increases that much is impressive, regardless of what they started with - it's the multiple that is key.
So I guess the question is what is the probability of the child of a multimillionaire increasing their wealth by 10,000 times?