Shiny Pokémon are incredibly rare, alternately colored versions of Pokémon. In Black and White, the base odds of encountering a shiny are 1 in 8192. While there's no direct 'Shiny Charm' in this generation, you can increase your chances through methods like the Masuda Method (breeding Pokémon from different real-world language games) or by repeatedly encountering Pokémon in areas with high encounter rates. Patience is key!
