In the international versions of Pokémon Crystal, the player could receive the Odd Egg from the Day-Care Man at the Pokémon Day Care on Route 34. This change was likely due to the Pokémon Mobile System GB not being a part of the international version of Pokémon Crystal.
Pokémon hatched from the Odd Egg can have one of two different sets of possible IVs (Attack/Defense/Speed/Special): 0/0/0/0 (not Shiny) or 2/10/10/10 (Shiny). Due to gender being determined by IVs in the Generation II games, this means that all hatched Pokémon will always be female (except Tyrogue, which is always male). Additionally, Shiny Pokémon hatched from the Odd Egg will always have Grass-typeHidden Power with power 31, while non-Shiny Pokémon will have Fighting-type Hidden Power with power 49.
In the Japanese version of Pokémon Crystal, there is a 50% chance the hatched Pokémon will be Shiny (IVs 2/10/10/10) and a 50% chance it will not (IVs 0/0/0/0).
In the international versions of Pokémon Crystal, there is a 14% chance the hatched Pokémon will be Shiny (IVs 2/10/10/10) and an 86% chance it will not (IVs 0/0/0/0), but the chance of any particular Pokémon species hatching from the Egg and the chance of any given species being Shiny are not uniform.