PokéBase - Pokémon Q&A
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Alright. I have Pokemon X. When I beat the game, I went to Mewtwo's cave. I saved in front of Mewtwo. I had lots of different poke balls with me. I waited for about 4 or 5 turns when Mewtwo's health was red. I threw Timer Balls at it. It seemed like the more I threw, the more resistant Mewtwo became. I did eventually catch it with a Dusk Ball, but I'm still curious as to why. I even threw other balls at Mewtwo, like Ultra Balls and Pokeballs. The Pokeballs actually got closer to catching Mewtwo than the Ultra Balls. I don't understand that either.

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It's really luck.

I mean, assuming the same method of catching was used in Gen V (if it wasn't, something similar at least), and assuming Mewtwo has the same catching rate as most legendaries (3) then the chance of catching would roughly be 7.1% with a bunch of Timer Balls, 3.5% with a bunch of Ultra Balls or 6.2% with a bunch of Dusk Balls.

It's all just considered by luck - you just got really unlucky/lucky in many ways. xD
But you caught it now, so I wouldn't worry. :3

Hope I helped. :)
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Thanks. I was really confused on how the poke ball almost caught it but the ultra balls broke fast. I thought Mewtwo was glitches.