Most of the time genetics is not like mixing colors. You have genes that can be dominant, incompletely dominant, recessive, hypostatic or epistatic, and sometimes act as a modifier. The expession of or lack of an expression by a gene determines the color of a bird. Some genes work together to produce a color of a bird. Take for example the color blue. First a bird has to have the genes to make the bird black. There are a number of different gene combinations that can be used to make a bird black, so all black birds do not have the same genes. The action of a blue gene is to dilute the black in a chicken to a blue color. So all blue birds are black under the blue but not all birds that are black have the same genes.
This gives you an idea of how complicated genetics can be.
Tim