30 generations back (a thousand years?) you have over a billion ancestors, which is way more people estimated to have lived at the time, meaning your family tree at that depth contains the same people over and over. Of course your ancestry probably isn't uniformly distributed across the globe, but without modeling it mathematically my guess is that if you go back ~3700 years to when Abraham ostensibly lived you can find multiple people that appear in the ancestry of virtually everyone from the Old World.
Anyway intuition can often be poor when dealing with large numbers so if anyone has concrete math or research to share I'd be interested in being proven wrong.