I believe the odds are 1/8192, unfortunately :/ And you're of course not guarenteed 1 out of the 8192 tries. It could be 2/16384. It's so much work, and I guess that's why I don't have one xD
I have terrible luck with shiny Pokemon. The only shiny I've ever come across was Bidoof :/ And then the two Pokemon I tried soft-reseting for (Tepig and Giratina) I never got shiny forms of. Maybe I just quit too soon. I really want a shiny Weavile though; it's pink and yellow.