Is this TED-ed video completely wrong? In the video https://www.youtube.com/watch?v=YiydsMxOdM8 about "What can DNA tests really tell us about our ancestry?" there is a claim that recombination increases the variance in the contribution of our distant ansestors.
A claim is that without recombination the process is deterministic (or atleast having lower variance than in the case with) for example they mention that a six generation ansestor would have a 1/64 ratio of the genes without recombination. Eventhough it is not posible due to the discrete nature of our 46 chromosomes naturally making it approximated poison distributed with lambda of 46/64 without recombination. See the video around 2:50.
With recombination my intuition would be that the variance would fall due to the decrease in relative variance with increased sample size. So I honestly just think they are completely wrong, but I think there is something I might have misunderstood.
Can you help me?
 A: There's a bit of biology and statistics in it, but they are not wrong. In recombination, all the chromosomes from both parents will duplicate before splitting, see below image

If there is no recombination (left side of diagram), all chromosomes being equal (which is not true of course), for every chromosome, the 6th generation has 1/64 chance of inheriting the exact copy from the 1st generation parent.
If there's recombination, as on the right side of the diagram, the proportion of DNA inherited from one parent can now range from 0 to 1. This variation is introduced every generation, hence the video's claim that recombination increases the variation of inheritance from our ancestor.
I am not so sure what you mean by sample size. To my knowledge selection will act against recombination to reduce the variance in genetic inheritance. If an ancestor has too many non-beneficial genes, these will be swept out in the population, leading to reduced representation. You can check more about it here
