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What is the chance of finding a shiny legendary?

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In geneations before 6

You have a 1/8192 chance to encounter a shiny Pokemon, this includes legendaries.

Edit: Zekrom, Reshiram and Kyurem are also shiny locked in generation 5 games(thanks to Dan for pointing it out).

Generation 6

While the chance to find shiny Pokemon is halved(1/4096), all the legendary Pokemon in X/Y are shiny locked(meaning you can't get them in their shiny variants).

Sources: this and knowledge
Hope I helped.

edited by
You should mention that Zekrom, Reshiram and Kyurem are Shiny Locked in the Gen V games :3
Thanks, I will edit it in. :]
:) [filler]