Very interesting - I've been working on a family tree, and though it is only 8 generations at its deepest, is wide and contains over 1,800 people, and I am now working on filling in these annoying voids, or attempting to link family fragments to mine who say they are related but I can't find the link, and make any corrections, etc.
Add to this journey my recent DNA testing, which has brought some 369 people potentially into my family. However, the most related someone is to me is 0.68% (and as yet they are "anonymous"). The only person of that list who I KNOW is already in my tree is related to me because our great-grandmothers were sisters, or we share a great-great grandfather. (Actually, we share a great-great grandfather AND his wife, our great-great grandmother, so how does that not double the amount of shared genes?) And yet, according to the test, we share only 0.13% genes, which I assume is rounded up from 0.125%, but who knows. Is it possible to share so little when, according to your math, if we are 3rd cousins, then we should share over 4 times as many genes? When it hit me that this is ACTUAL shared genes rather than AVERAGE ASSUMED shared genes. I guess we ACTUALLY share less than 50% in each generation of cousins. How else to explain this, unless the test is wrong? Similarly, there are people more related than this in the test, for example one who shares 0.50%, so we should at LEAST be third cousins, right? - and yet we cannot find a single family surname that is familiar going back as far as we traced. What is going on here?
Another thought - with the rise of DNA testing and law, I wonder if ACTUAL shared genes will be a determining factor in certain cases. Under the law someone could have a dozen great-grandchildren, but they won't all have the same percentage of DNA from their shared great-grandfather. Used to be things would be willed "to the oldest" but might things in the future be willed "to the descendent who shares the greatest ACTUAL percentage of my DNA?"