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Danerys' great-grandfather (Aegon V) married a Blackwood, meaning that his children (Dany's grandparents) were half-Blackwood. When they married and reproduced, THEIR children (Dany's parents) were also half-Blackwood.
So, Damerys herself is (genetically) half Blackwood and half Targaryen.
I'm pretty sure it doesn't work that way. Dany, Viserys and Rhaegar are more than half Targaryen and less than half Blackwood even if no other bloodlines were introduced.
First of all you have to suspend knowledge of any previous Targaryen history if you assume Egg is full Targaryen.
Egg's kids (Jaehaerys II and Shaera) would be half Blackwood and half Targaryen. Jaehaerys II and Shaera had two kids from incest, Aerys II and Rhaella. They would both be 3/4 Targaryen and 1/4 Blackwood, and they mated as well.
Dany, Viserys and Rhaegar should be more like 7/8 Targaryen and 1/8 Blackwood each because the Blackwood genes would be diluted by repeated incest.
Still, that doesn't work out because we know various families intermarried with the Targaryens. I took a quick look at the Targaryen family tree. If I read correctly, Egg's mother (Dayne), grandmother (Penrose) and great-grandmother (Martell) were not Targaryens.
In summary, Dany has lots more Targaryen blood in her than just half (but I am not a geneticist, LOL).
I am very certain that ancestry DOES "work that way."
Teacher: "If I have a glass that is half juice and half water, and I blend that glass with another glass that is half juice and half water, what are the percentages of juice and water in the combined beverage?"
ThirdCoast: "Three-quarters juice and one-quarter water."
Teacher:
I actually spent some time trying to understand this mysterious "increasing percentage of Targaryen ancestry," and I think I may have found the thought process that ThirdCoast followed. It is based upon entry-level genetics.
Let's assume that every Targ trait is dominant and that every Blackwood trait is recessive. Let's also assume that all of these traits are found on a single gene, which passes from generation to generation as a whole. The Targ gene is "T" and a "pure Targ" would be "TT." The Blackwood gene is "B" and a "pure Blackwood" would be "BB."
If we breed a Targ and a Blackwood (Generation 1 or G1), the results (Generation 2 or G2) would LOOK like a Targ, despite the fact that one half of the genes of each (the recessive half) would be Blackwood. The genetic makeup of each G2 offspring would be TB, with the T being dominant.
Now, G2 brother and sister breed. Assuming four offspring (Generation 3 or G3), we would expect one child to be TT, two children to be TB, and one child to be BB. TT would be "pure Targ," the two TBs would look Targ but still carry one-half Blackwood genetics, and BB would be "pure Blackwood."
If two offspring from G3 with TT genotype breed, you are back to "pure Targ" in G4. If a G3-TT and a G3-TB breed, you would expect 3/4 of the G4 offspring to be TT (pure Targ) and 1/4 to be TB (looking fully Targ, due to the dominant gene, but still carrying the Blackwood gene).
As long as any TB is born into the family, there still exists the possibility of a "throwback" to a BB.
Of course, genetics aren't nearly that simple.