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Are Shiny chances for legendaries truly random?

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I am in love with certain shiny legendaries. If I save before meeting one, and reload the game again and again approximately 8,192 times, is there any chance I could get a shiny Pokemon? Or, are shiny chances for legendaries static?
I'm pretty sure you can get a shiny starter this way, but I'd like to know if there is really a 1/8,192 chance of getting a shiny legendary or not.

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It doesn't work like that. You could do that a million times and still not get a shiny. But apart from Victini, Reshiram and Zekrom, yes, saving and reloading can get you a shiny version. Also, starters work the same way. The 1/8192 is real. If you think it through, The chance could be 1/16384 (double of 1892).

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1/1892 is not set in stone as far as chances, it's more of a rough estimate. And so long as a Pokemon can even be shiny, the same chances will apply to it's shininess.

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Its like 1,892 pieces of papers in a bag, and one piece is shiny. XD