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In Pokemon X/Y is it possible to catch a Pokemon with 6 IVs or a Pokemon with its hidden ability?

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In black and white 2 u can in dream world theres a place like that on x and y i think

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Yes

It has always been possible to catch a Pokemon with perfect IVs. However, the chances are just ridiculously low.
The actual chance of finding it would be (1/31) ^ 6 = 1/887503681 (Probability rule - n^r)

Pokemon with their hidden abilities can be found in Hordes or in the Friend Safari. For more information on those two places, refer to Bulbapedia or Serebii
>Horde Encounters are a new kind of wild Encounter where a horde of Pokémon appear and challenge you. These Pokémon can be anything from a group of one species of Pokémon, to a conglomeration of a couple that work togehter such as Miltank & Tauros, or who turn on eachother such as Seviper & Zangoose. These battles typically have the Pokémon at a significantly lower level so as to not overpower you, but it is essentially one-sided, requiring moves which take out the entire field to be at hand. You can cause them to occur by using Honey or Sweet Scent

Serebii

>The Friend Safari (Japanese: フレンドサファリ Friend Safari) is a facility in Kiloude City where Trainers can catch Pokémon that can not normally be found in their journeys.

Bulbapedia

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do you know the exact chance to find a hidden ability pokemon in a horde?
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Hidden abilities:

You can catch Pokémon with hidden abilities in horde battles or in the friend safari.

Horde battles sometimes randomly occur in tall grass, or you can make them happen automatically in tall grass by using the honey, or getting a Pokémon with the move sweet scent and using the move outside of battle. In a horde battle, there are 5 Pokémon that appear, and there is a chance that each Pokémon could have their hidden ability.

The friend safari is in Kiloude city, which you can go to once you defeat the elite four, by taking a train from Lumiose station. To the right of the city, you will find the friend safari. Once you have talked to the person inside, you can then catch Pokémon of different types, depending on how many friend codes you have registered. And if that friend in question is playing at the same time as you, there is a chance that the Pokémon in there will have their hidden abilities.


Perfect IVs

Yes, you can catch a Pokémon in the wild that has 6 perfect IVs, but there is a very low chance that this will happen. The exact chance is about 1/887503681, which makes it almost impossible.


So, it is possible to catch Pokémon with perfect IVs and hidden abilities. But catching ones with perfect IVs is much harder than catching ones with hidden abilities, so I suggest, if you're going to get Pokémon with perfect IVs, you should do it through breeding.

Source: experience and serebii

I hoped I helped!

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I'm pretty sure you copied my calculation.
Meh I don't really mind P:
I couldn't work it out myself :3
Are the chances larger in Heartgold? Because I have a Metagross I caught in the Safari and it has perfect ivs on Pokemomn Y. Now I'm trying to breed it for tournament battles in the new game. Its so weird.