PokéBase - Pokémon Q&A
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I want to know

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depends on your luck with the catch rate formula, could be one, could be an infinite amount but the average comes out to be something like 30 i think. this page explanes catch rate.

http://bulbapedia.bulbagarden.net/wiki/Catch_rate

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it depends, i would suggest putting a status effect on it to make it easier to catch by the way (:

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It all depends on the catch rate of Reshiram, 45. Using an Ultra Ball and lowering HP may cause a better chance of catching it but its all by a formula. You would have about a 34.9% of capture.
http://www.metalkid.info/Pokemon/Calculators/CatchRate.aspx

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Reshiram has a good catch rate (because you need to catch it in-game) so yeah it should take less than 10 Ultra Balls. I caught mine with a Quick Ball on the first turn!
I caught it with a Poke Ball at the 10th turn.