Catch rate/Capture method (Generation III-IV)/Probability of capture

The probability p of catching a Pokémon, given the values a and b calculated above, approximates a/255. However, due to rounding errors produced when calculating b, this approximation can be significantly inaccurate: all a values greater than 200, for instance, yield the same b value, 65535 (which results in a 99.994% chance of a successful capture).

For a constant probability p, the probability P that a player can capture the Pokémon with no more than r tries is:
 * [[File:Catch formula 4.png]]

Note that this is the cumulative probability function for a. The of r is 1/p, that is to say, on average, a Pokémon that can be caught with probability p will be caught with 1/p tries.

The inverse problem, the number of tries, r, needed to have a probability P of capturing a Pokémon is:
 * [[File:Catch formula 5.png]]