7

edits
# Changes

→Shiny Probability: Need to distinguish between the probability of a given patch being shiny, and 1 out of the 4 patches being shiny.

====Shiny Probability====

[[File:PokéRadarShinyProbability_IV.png|thumb|right|The formula for the probability of ~~finding~~patch ~~a~~being Shiny~~ patch~~. 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~~ patch being Shiny 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. Since up to 4 grass patches can shake at a single time, this probability can be up to 4 times as high, giving the player about a 1/50 chance of finding a shiny patch at a chain length 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). While the probability of finding a Shiny patch increases as chain length increases, normal non-Shiny patches will always have the usual 1/8192 chance of containing a shiny Pokemon.

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: