Well, this is my playground. The reason why it doesn't strictly double is because "most marriages are between sixth cousins", i.e. you don't add two independent people each generation, sometimes it's not a new branch on the tree, just a branch from another part of the tree. Not to mention death and infertility.
You may not realise it, but this is how the Ephraimite error is presented. Basically, we are all 'Israel', part of the lost 10 northern tribes. I wonder who the gentiles are .
I do understand why "it doesn't strictly double", but I have never heard of the Ephraimite error - I'll google it after I finish this post; it sounds interesting.
You may be interested in a paper about the Most Recent Common Ancestor (MRCA) by Rohde, Olson and Chang in 2004. It's got some pretty hefty mathematics in it, but as you say: that is your playground.
http://steveolson.com/uploads/2009/04/nature-common-ancestors2.pdf
Their analysis "suggest that the genealogies of all living humans overlap in remarkable ways in the recent past. In particular, the MRCA of all present-day humans lived just a few thousand years ago..." and they go on to say, "the MRCA appears in about the year 300 BC, and all modern individuals have identical ancestors by about 3,000 BC."
They quickly add, "Such estimates are extremely tentative, and the model contains several obvious sources of error, as it was motivated more by considerations of theoretical insight and tractability than by realism."
Nevertheless, it's an interesting idea - hence my earlier post.