"Why not posit that (in any given big bang) there will be some excess of one or the other polarity of matter, as a result of Quantum Uncertainty?
I know I know, not very rigourous. Just my 'gut' feeling, really."
The obvious cheat solution is the anthropic principle. We cannot see all the universes where matter and antimatter annihilate each other, only ones that don't have this property.