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I know that If you breed a Pokemon with the everstone it passes down its Nature, but what about its ability, Gender, and IV?

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I'll answer them in order:

>1. The Ability of the mother has a higher chance of being passed down, rather than the other abilities available.
Hidden Ability - 60% chance of passing. 40% chance of the non-hidden ability. (20% each if there are two)
Non-Hidden Ability (if there are two) - 80% chance of passing. 20% chance of the other ability.

>2. Gender depends on the gender ratio of the particular Pokemon. Eg- If a Pokemon has the gender ratio 50 males/50 females then there is a 50% chance that the Pokemon will be male or female, but if it's 75 males/25 females there is a higher chance of the Pokemon to be male.

>3. IVs are passed down randomly, but atleast three IVs are taken from both the parents together.
This means that if the fathe has 31 IVs in attack and defense and the mother has 31 IVs in speed, there is a small chance that the baby will have 31 IVs in attack, defense and speed. However this is random, so it could also have no 31 IVs at all. Destiny Knot is given to a parent to pass down 5 IVs instead of 3 IVs.

Hope I helped!

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Just to elaborate #1...

Ability - from the female (or in a Ditto breeding sequence, the non-Ditto Pokemon)
* Hidden Ability - 60% chance of passing. 40% chance of the non-hidden ability. (20% each if there are two)
* Non-Hidden Ability (if there are two) - 80% chance of passing. 20% chance of the other ability.
added it in
Thank you this really helps
How Do you Know if you have More then 1 IV?