The original encounter chance for a wild Shiny Pokémon in Pokémon Gold and Silver was approximately 1 in 8,192.
That extremely low probability made Shiny Pokémon one of the rarest discoveries in the early games. The alternate coloration was determined when the Pokémon was generated, and a Shiny Pokémon also produced a distinctive sparkle animation when sent into battle.
The second-generation games included a famous guaranteed Shiny red Gyarados at the Lake of Rage. That fixed encounter allowed players to see the feature without relying on chance, but it did not change the odds for ordinary wild encounters elsewhere.
The base odds were later improved in Pokémon X and Y to 1 in 4,096. Breeding mechanics could also produce different odds in later or modified circumstances, so the 1-in-8,192 figure specifically describes ordinary early-generation encounters rather than every Shiny method.