Shiny Chance

Shiny Pokémon can be obtained in a number of different ways, each with their own odds. As of version 0.6.8, the only ways to augment the chances of encountering shinies are to equip the Shiny Charm or have Starf Berries growing in the Farm (at full ripeness, each Starf plant gives a 1.5% boost).

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Trivia
Shinies as of version 0.3.0 increase click damage at a 150% rate compared to normal Pokémon.