In Game of Thrones, everybody knows knows (wink wink) that Joffrey is not the son of Robert Baratheon; he’s the incestual love child of Jamie and Cersei. But do we really know what? The assumption that we are making — at least based on the evidence provided by the HBO series — is that Joffrey is Jamie’s son because of they both share blond hair, while King Robert had dark hair. King Robert also had four bastard sons, all of whom had dark hair, and Cersei’s other two children, Myrcella and Tommen, also have fair hair. Therefore, it follows, that Cersei’s three children are the product of her and Jamie’s incest.
Right? Maybe not.
Over on MadArtLab, a PhD student in genetics, Elizabeth Finn, did the math, so to speak, and could not conclusively rule out that Joffrey (or in fact, all three Baratheon siblings) were not Robert Baratheon’s children. It’s a very lengthy and fascinating piece, if you’re interested in the science of genetics, but for our purposes, let’s just examine this paragraph:
If we consider just the bastard children that are mentioned in the books, [Ned Stark] didn’t have enough evidence to really make this determination. We know of four bastard children, all with dark hair. If Robert is homozygous BB, then this is by far the most likely outcome. However, if Robert is heterozygous Bb, he would still have dark hair, and it would still be fairly likely for four bastard children to have dark hair (think about flipping a coin and getting four heads in a row). When you add in the fact that some of his mistresses and whores likely had dark coloration as well, it becomes even more likely that all four illegitimate children have dark hair. So as far as Ned knows, Robert could well be Bb. And if he is, then the fact that he had three blonde children with the almost certainly bb Cersei Lannister is again reasonably likely. This is why Tyrion remarks that Joffrey’s – and hence Cersei’s – claim would be foolproof if she had had even one child with Robert: someone with dark hair married to someone with light hair having some children with light hair and some children with dark hair is utterly normal.
Did you follow that? In simpler terms, we don’t know if Robert was a BB (dominant for dark hair) or a Bb (one dominant and one recessive). If his bastard children came from dark haired women, it’s likely they would have dark hair. If Robert was a Bb, since Cersei is a bb, then it wouldn’t be unusual for the two to have three fair-haired children. So, as Tyrion reasoned, if even ONE of those children is Robert Baratheon’s, then there’s a decent likelihood that all three could be.
We know that Cersei and Jamie had sex, and we also know that Robert and Cersei had sex, and that Robert is not sterile (see: bastard children) so if Ned Stark’s assumption was based purely on hair color, then it’s quite possible that Ned Stark was wrong and that Joffrey actually is the rightful heir to the Robert Baratheon’s throne.