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Ever found and caught a particularly good or rare mon just while out and about? Not hunting for it or anything, just out of sheer chance.
Playing OR for the first time, I picked up the Latios you get mid-game and idly checked for its nature, only to see that it was shiny. No SR or anything, just sheer dumb luck. Hadn't been planning to use it at all, but I immediately made it the team mascot.