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Pokémon Black and White introduced a mechanic known as a Critical Capture. When you throw a Pokéball, it has a low chance of pausing in midair, making a metal noise, wiggling once on the ground, and then capturing.

My questions are: what is the chance of a Critical Capture happening and what is the capture rate when it occurs?

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I can't tell you what the chances for a critical capture are, except that I read somewhere that it's "about the same as a critical hit." Based on what I've seen, that seems about right, but it's hardly exact.

What I can tell you, however, are the mechanics behind how captures work and how the mechanics of a critical capture work.

Essentially, there is some calculation that is performed 4 times. It can result in either a success or failure, which is depending on many factors, including the pokeball you used, the status condition of the pokemon you're targeting, its hp, capture rate, etc. For each success the calculation yields, the ball tilts one time. If all 4 succeed, then you catch the pokemon.

For a critical capture, the calculation is performed only once. If that one is a success, you capture the pokemon. If not, it escapes. It's that simple.

Disclaimer: I don't remember where I initially found this information.

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Can a critical capture fail? –  Raven Dreamer Apr 9 '11 at 2:56
    
@Raven Yes it can, if that singular check fails. –  StrixVaria Apr 9 '11 at 2:59
    
Nice information, unfortunately it seems nobody knows the calculation determining whether or not a Critical Capture succeeds or not. –  Kevin Y Apr 9 '11 at 3:11
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@Kevin Y: The capture rate is the exact same as the chance that the pokeball would "tilts" at least once. All a critical capture means is that it has to pass one check instead of four. Each time the pokeball "tilts" normally, there's a chance for the Pokemon to escape. –  Sapph Apr 9 '11 at 4:02
    
So from the linked page: "Then generate 4 random numbers between 0 and 65535, inclusive. For each number, check whether it's less than b; if so, the ball shakes once". So, the chance of it succeeding is the same as the chance that a random number in [0, 65535] is less than b. –  Sapph Apr 9 '11 at 4:02
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