How do you find shiny and legendary Pokemon?

The Probability of encountering a shiny Pokemon is 1 out of 8192. This doesn't mean that every 8192 battles one a shiny Pokemon will be encountered, just that it's extremely improbable. It is possible to encounter a shiny rare Pokemon (The legendary birds, Regi, Mewtwo etc.) even eggs may hatch a shiny Pokemon. sources on the internet claim that breeding a shiny Pokemon grants a much higher chance of the offspring being shiny too. in which case the best way to get any shiny Pokemon would be to get a shiny Ditto (easier said than done)and breeding it with any Pokemon you want.

Breeding a shiny does increase the chance of hatching one to roughly 1:600, i believe, but then you have to hatch each and every egg individually because it is determined when the egg is made what the Pokemon is. That will take forever and most people give up before any success. Search "chaining shiny Pokemon" and you will find mass amounts of information on catching them with the pokeradar app. Basically if you see a Pokemon 40 times in a row the 41st will be shiny, but it is tricky.

For Legionaries, resetting seems to be the only legit way to do it, although there is rumor that if you just stand in front of the Pokemon for a few hours before attacking it will be shiny. The latter has not been tested.

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Wrong. Read this my friend. http://www.serebii.net/games/shiny.shtml