PokéBase - Pokémon Q&A
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Using an ability, or not

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Best answer

First, 6x resistance= 1/8 damage
Now lets find the abilities that give a resistance to a type: Thick Fat and Heatproof.
Now we need to find a Pokémon with this ability and that already has a 1/4 resistance to a type.

We can start with Thick Fat.

Dewgong has a 1/4 resistance to ice. Add in Thick Fat, and it becomes 1/8.
Same with Spheal, Sealeo and Walrein.

For Heatproof, only two Pokémon can have it and they don't get a 1/4 resistance in the first place.

No Pokémon can be 1/8 resistant without an ability, because no Pokémon can have a 1/4 resistance from only one type.

Source: Experience, here, here, here and here.

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Thanks!
Great answer! However, in gen-6, what about trick or treat, which adds ghost, or forests curse, which adds grass?
I think there are more...
Those are moves and not abilities, but if you want i could try to add those.
There are more with abilities.
Others either add an immunity or protect against a bit (like 25% less damage or something) or arent restricted to a certain type
Nevermind