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The chance gets higher the more interfamily marriages are in the recent generations of its personal family tree.
So if you marry a son and daughter of that couple the chance will be even higher
That is not true. If there are 17 or fewer unique ancestors going back 5 generations, then the chance that the child will be inbred is 100%. See the wiki:
https://ck2.paradoxwikis.com/Breeding#Inbreeding
Now, it is true that a parent with inbred only has a 25% chance to pass it on to a child, 50% if both parents have the inbred trait.
*pat on head* fiiiiiiiine boy
try reading in context, just parents close (like what OP did): chance left of kid coming out non-inbred
Inbreeding over generations: chance for inbreeding goes up.
I did read it. Try posting what you mean, then... boy. You said
Patently untrue that there is "always a chance." There is a chance *UNLESS* the inbreeding goes back far enough so that 17 or fewer ancestors through 5 generations are unique for the child. 100% chance of inbred is the opposite of always having a chance to not be inbred, isn't it? If you didn't mean "always" then why say it? Nice try, sport.
Then eventually I saw a way to unite with the nearby kingdom that was ruled by the same dynasty through a marriage between my daughter and their oldest son. The plan being that even though it was a normal marraige both parants were from the same dynasty so I could inherit and keep playing. Unfortuantly this plan resulted in what would best be described as a genetic dead end...
I laughed , I thought it was funny
It's not 100% in game or in real life. Actually even in real life there's less than a 40% chance that directly related family members breeding will actually produce offspring with redundant genes, aka inbred.
Get them to have a daughter, seduce the daughter. If that doesn't get you inbred, nothing will.
It's more percentage based really but the chances are far from absolute. Not that I'm advocating ♥♥♥♥♥♥♥ your sister in real life.
Unless she's hot.
Your kids with your sister would probably be fine. What happens with inbreeding is that, essentially, we all have genes with bugs in them. But we also have two copies of the genes for just about everything, one from each parent, and usually when one of those copies is bugged our cells can use the other copy and everything turns out fine.
When you're breeding too close to your own genetics, there's a chance that you and your sister will both pass on a bugged gene to your kid- and he won't have anything to correct with. That chance is slight, but still present, on the first generation of incest baby. It increases with each subsequent generation, because no new non-errored DNA is being introduced. Over multiple generations those errors compound and build up and start to manifest, and eventually you get this guy[en.wikipedia.org]. That's the result of a long chain of inbreeding, but note that it's still possible to get something like it after just one generation.