This is not rigorous probability math, but:
Assuming 700-800 years ~ 30 generations
If each generation has 2.1 kids that survive to reproduce 2.1 offspring...
That would result in 4.6 billion descendants living today. So today, with a world pop of 7 billion, the odds are pretty good that you share a common ancestor with anyone else from 800 years ago. Those odds improve significantly if you make considerations for europeans breeding mainly with europeans.
I bet 43/44 presidents are probably related to Charlemagne, too.
Again, this is not rigorous probability analysis as there are some other considerations but it gives an idea
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