This doesn’t work because dice is the plural of die.

You could possibly replace it with sheep? That would give you your white/ mammal red herring. Unfortunately, I think that whale and the other mammals are swap-able- there are either species or literary references for all of those to possibly fit the white group- shame as it's a great red herring and I kept putting it in with blue! Good effort :)

Thanks for the feedback, I made a couple of changes. Dice is listed as both a singular and plural form in some dictionaries, but I agree it was a bad choice for the category. I think it would be a stretch to swap one of the other mammals with whale. It may be a cultural difference, but I haven't heard any of the other the mammals referred to as white, and couldn't find and species with those names when searching for them.