Steve Mount works through the math of "relative finder" predictions from 23andMe (and by extension, other personal genome tests): "Genetic genealogy and the single segment".
He does a nice short explanation of a point that is counter-intuitive to many people. You don't actually share much DNA with your relatives by descent, and because chromosomes are inherited in chunks, you quickly (within 6 generations) get to a point where you're not likely to have any DNA in common at all. Yet...you do have to have DNA from somebody, which means that if you do share DNA, you'll probably share a big chunk of it.