[paul.fr]

If i have 50% of my mothers and fathers genes, does my child have 25% of their grand parents and my childs children have 12.5% and so on?
Is it that simple?

[another_someone]

In general, it is that simple (with the exception of those genes that are not equally inherited from both parents - e.g. the X and Y chromosomes, and the mitochondrial chromosomes).

[rosy]

We-ell, statistically speaking that's about how it works out, but it ain't as simple as all that... if we consider 3 pairs of genes, then...
If grandparents have gene pairs:
Maternal grandmother
1=ab 2=cd 3=ef       
Maternal grandfather
1=gh 2=ij 3=kl       
Paternal grandmother
1=mn 2=op 3=qr       
Paternal grandfather
1=st 2=uv 3=wx
The parents will have gene pairs:
Mother (one of each set)
1=ag/ah/bg/bh
2=ci/cj/di/dj
3=ek/el/fk/fl
Father
(again, one of each set)
1=ms/mt/ns/mt
2=ou/ov/pu/pv
3=qw/qx/rw/rx

Lets say mum and dad have the first gene pair of each set (it makes no difference as whatever they have will be 50:50 for each of their parents):
Mother
1=ag 2=ci 3=ek
Father
1=ms 2=ou 3=qw

Now their child will have one pair from each row:
1=am/as/gm/gs
2=co/cu/io/iu
e3=q/ew/kq/kw

Now each pair is selected randomly and independently, so there's no reason beyond statistical improbability why the child shouldn't be
1=am 2=co 3=eq
Which if you refer back to the grandparents has written both grandfathers right out of the genetic line.

Obviously this doesn't really happen, because although we have only 26 pairs of chromosomes, when zygotes (sperm and egg cells) form, chromosomes (except for the X and Y sex chromosomes) cross over so that each chromosome that ends up in the offspring is a hotchpotch of genes from both grandparents.

So it would take more generations than I've shown above for any one ancestor to get written out, but the principle remains the same.

[paul.fr]

Rosy, thank you is the least i can say.