From Bulbapedia, the community-driven Pokémon encyclopedia.
[[File:PokéRadarShinyProbability_IV.png|thumb|right|The formula for the probability of finding a Shiny
Pokémon. n<sub>c</sub> is the number of Pokémon in the chain, up to 40.]]
Based on the formula depicted at right, the probability of encountering a Shiny
Pokémon can be approximated as 1/8000 for a chain of 1, 1/7800 for a chain of 2, 1/7600 for a chain of 3, and so on up to 1/200 for a chain of 40. Note that it takes a while for a chain to start paying off - the probability does not exceed that of the [[Masuda method]] until a chain length of 33. After that point, the probabilities start to increase very strongly, with a chain of 40 having double the probability (1/200) compared to a chain of 39 (1/400).
As all Pokémon games prior to Generation V perform calculations strictly with integers, there exist some roundoff errors in the probability determination (as noted by the ceiling function in the formula). A game-accurate list of probabilities for each chain is as follows: