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If you create a trait with birth = 0 and inherit_chance = 100, does that effectively create a trait that only your ancestors can have?

In other words does the inherit_chance attribute take precedence over the birth attribute?

birth- Given number out of every 10000 characters born will receive this trait, (e.g., 100 = 1%)    

inherit_chance- A newborn can inherit the trait from a parent (optional); if both parents have the trait, uses two trials of same chance    
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    I would think that the Sayyid trait works along the lines of what you susggest. It never appears at random and is always inherited from a Sayyid father. The only notable difference is that Sayyid mothers instead pass on the Mirza trait to their children, unless there is a Sayyid father.
    – CrusaderJ
    Feb 24, 2015 at 14:32

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Not sure if the files were updated in a recent DLC, but the 00_traits.txt file (in common folder) now suggests that inherit_chance is applied before the generic birth, and would therefore take precedence.

# inherit_chance = X    - Chance of passing on the trait to children
# birth = X             - How many characters out of 10000 are born with this trait (when not inherited)

Anecdotally, syphilitic has an value for inherit_chance, and no birth value, and I have seen it be inherited. This does seem to be what you want.

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