After five or so generations the odds of inheriting any DNA from any one individual in that generation is very small.
It’s a geometric progression. Two parents, four grandparents, eight great, sixteen great great, thirty two great great great. One thirty second is slightly over three percent, but of course you don’t inherit equal amounts from each grandparent.
...but of course you don’t inherit equal amounts from each grandparent.
Precisely. The closest split (assuming no relatively recent consanguinuity) is 12/11 or 11/12 on each side of the tree.