Is marrying my own sister a good idea?

It's usually fine, especially if you have a succession law which lets you control who inherits, such as elective. Children with the inbred trait are relatively rare (Zoroastrians are less likely to get the trait) and they often die anyway.

For the best of both worlds, marry your sister for the opinion and piety and take concubines (ideally with good traits) for breeding.

Correction years later.

It turns out there are two separate, different mechanics both labeled divine marriage in the game.

• The first is applied to a religion, and only carries an opinion and piety bonus, e.g. the Zoroastrians in vanilla.
• The second is applied to dynasties, and carries the other mechanics discussed below. This is not used in the vanilla game, but is available for mods.

Additionally, lunatic is potentially an outcome of incest at the same base rate as inbred (before potential modifiers)

Source

This obviously changes the calculus, however, it turns out unless there's sustained incest going on, inbred risk isn't that high.

Running the numbers from the source, a first generation "clean" brother/sister pairing has a 10% chance of inbred or lunatic in a child. However, the second generation brother/sister pairing would have a whopping 88% chance. However, if the second generation brings in fresh blood, and has the third generation (cousins) pair up, things are back down to a 6% chance. Thus concubines and fresh blood are definitely recommended.

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The Zoroastrian "divine" marriage have these effects in vanilla:

• 25% fertility (aka 75% reduction)¹
• 20% of base chance of having the inbred trait pop up²
• +10 opinion for vassals, +25 for vassal priests
• 50/100/200/300 piety on marriage depending on rank
• One more thing that probably doesn't have an actual effect³

So in general it's a good idea, but you want to have concubines around to make up for the fertility issue.

¹This is controlled by DIVINE_BLOOD_FERTILITY_MULT in defines.lua

²The exact mechanics behind the chance of having the inbred trait show up out of the blue (not inherited, which is 25%) are unknown, unlike other congenital traits which have a moddable fixed chance of appearing, but it is generally assumed that close marriages have a higher chance. This is controlled by INBRED_DIVINE_BLOOD_TRAIT_CHANCE_FACTOR in defines.lua

³There is an additional effect LUNATIC_DIVINE_BLOOD_TRAIT_CHANCE_FACTOR which I think has no effect since lunatic does not have a base chance of appearing at random or inheritable.

I think it's more of a good idea in CK2 than in real life. Unless you're playing moralistically you can easily have more than one kid. Just make sure that the kid that inherits isn't the one with the inbred. Kill any of your children that are... defective.