The download version on the Wii.
I've been finding shiny Pokemon ONLY on this game, it's kinda nice when 3 hours of game play gets you a shiny Ivysaur xD or a Shiny Lucky Haunter (which I use in EX)
In Pokémon Rumble, Shiny Pokémon may rarely appear. They will always tip over when defeated. The chances of their appearance are unconfirmed, although they appear to occur more often than in the core series. Shiny Pokémon are always given a special trait, a blue name in menus, and a star below their picture on the Collection screen. Some Shiny Pokémon can be obtained by the use of passwords. (Source)
So the chance in Pokemon Rumble is... >1/8,192!
Source: Above Link
