My friends are getting shinies like randomly and i never even saw one in my 3 years of experience so... And also, is there any mathematic formula to represent the chances of meeting a shiny Pokemon?
Here contains the formula
(Trainer ID) xor (Secret ID) = E (First byte word of personality value) xor (Second byte word of personality value) = F If E xor F is less than eight, then the Pokémon is Shiny.
Not in the wild unless you chain them(only for diamond pearl and platinum) but you can use the Musuda Method to breed a shiny pokemon. Now this method wont always produce a shiny but it raises the chances of the egg being shiny. To do this method breed a pokemon with a pokemon from a different country i.e a german pikachu with a english ditto
Highly unlikly breed with someone like french pikachu