PokéBase - Pokémon Q&A
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I just thought about this as I have been thinking about shiny hunting, IVs, and pokerus and wondered what the chances would be.

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There are 32 possible values (0-31) for each of the 6 stats, which makes it 1 in 32^6 or 1 in 1,073,741,824!

However, you could reduce this when breeding if one of the parent's stats is already 31 by making it hold a power item to guarantee passing on that stat. That would make it a mere 1 in 33,554,432.

If you for some reason already had 2 Pokemon with perfect IVs in every stat, that would guarantee 3 of the baby's IVs would be 31 (3 random stats are passed down). So the chances for the remaining 3 would be 1 in 32,768, still pretty unlikely.

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It is possible but not likly as your chance is 1 in 1,073,741,824!You may think this is a lot but get the right nature and breed and with lots of eggs and even more luck you can do it! You do need the right nature but I think there is an item to increase the chance of getting the same nature.When breeding for things like this I like a pokemon with magma armoror flame body to half the steps to hatch(magmar and slugma are easy to get or litwick for Generation 5).

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