In Pokémon's Gen II, if a Pokémon's Speed, Defense & Special IVs are all 10, and its Attack IV is 2, 3, 6, 7, 10, 11, 14 or 15, it will always be a shiny, which results in a 1/2^13 chance. In Gen III, the chances are the same, but with a different method. The chances would remain the same until Gen VI, where they were doubled (from 1/2^13 to 1/2^12). This only applies to regular wild encounters, though, as each game has methods for increasing the chances of finding a shiny Pokémon.
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