Actually, once you get back past your parents, it's more complicated. Each of your parents inherited half their chromosomes from each of their parents, but there's nothing to say which half of their parents' chromosomes they got. It isn't impossible that all of the genetic material from their mother was from her mother, but not likely. It isn't impossible that none of it except the X was from her. On average, it would be about half from each parent and so that 1/4, but it isn't going to be definitely that.

Also, as the genes are usually inherited on the chromoseomes they arrived on, a person has 23 sets from each parent, anywhere between 0 and 23 from each grandparent, but probably about 12. Next generation about 6 each, next about 3, next about 1 or 2, next - who knows? (Of course, there's a bit of shuffling about mixing things up a bit.)

Makes all that stuff about bloodlines in the aristocracy rather meaningless - except for the inbreeding.

Penny