I was hoping someone who has really good egg genetics would answer...so I will try, and if I am wrong, then hopefully someone will correct me.
As I understand it...brown plus white will generally give brown as brown is dominant. (???)
IF one of the parents has one of the blue genes (and I think there are 2 blue genes)....then blue parent plus brown parent will give you 50% brown and 50% green...more or less.
IF one of the parents has both blue genes....then blue parent plus brown parent will produce 100% green????
IF one of the parents has both blue genes...then blue parent plus white parent will produce shades of blue....100% ???? As blue is dominant (?)
IF one of the parents is a very dark brown layer (like a Marans or Welsummer)...then dark brown parent plus blue parent will give you the Olive Green shades. If you breed that first generation back, you get darker green shades.
That is assuming there are no other genetics hidden as it takes genes for the egg shell which is either white or blue, then genes to produce the tint which supplies the tinting over the base color. Brown tint over blue shell produces green shades. Clear/white tint over blue shell produces blue shades. Brown tint over white shell produces brown and various beige shades. Clear/white tint over white shell produces white shades.
Then there is even a tint in the bloom in some hens...the bloom is the antimicrobial coating added at the last to ward off germs...that can change things even further and produce "purplish" eggs or "grey" eggs.
Okay...please if I am wrong someone correct me as I want to get this down in my head too...but that is what I have gleaned thus far.
Lady of McCamley
EDITED TO ADD: I found this article that explains things in pretty easy language and appears to be in depth and accurate, and endorsed by the Chicken Chick:
https://scratchcradle.wordpress.com/2012/07/01/gms1-genetics-of-egg-color/
EDITED FURTHER TO ADD: If you keep working through the mini-series on egg genetics, section 3, Scratch Cradle shows a photo of almost hot pink Croad Langshan eggs as the 'ideal" color for Croads, but the left photo of the brown tints with some pinkish tan, from my research, appears to be the reality...Croads have been exaggerated lately as having a purple egg (which I would LOVE to have), but that is not normal for them...they are actually a brown egg layer, originally a dark brown layer that was instrumental in developing Marans. Some are breeding for purple eggs with Croads, but think plum not the hot pink shown in the photo (which appears to have been removed from the uk site). Some Croads appear to have a tint in the bloom when applied over a brown egg gives a purplish/plum hue. Some mutts and EE's will do that too. I would absolutely LOVE to get a purple egg layer, hence my trying to understand egg genetics.