Either my understanding of genetics or most people's understanding is wrong. Suppose you have a woman with roughly 100% African genes and a man with roughly 100

Either my understanding of genetics or most people's understanding is wrong. Suppose you have a woman with roughly 100% African genes and a man with roughly 100% German genes and they have a daughter. She will have 23 chromosome pairs, each with one African (A) and one German (G) chromosome. Now imagine she has a bunch of children and let's ignore cross-overs to simplify things. The 50% of genes that she contributes to each child can vary from 0% A and 50% G all the way to 50% A and 0% G. So having a child with 16% G would be perfectly normal (not even counting any contribution from the man, which would make it even more complicated). So the idea of dividing by 2 in each generation (great grandparent 100% X, grandparent 50% X, parent 25% X and so me 12.5% X) is an extremely crude approximation and having these genetic tests not match that doesn't necessarily mean that they are wrong.