With an Easter Egger rooster there is no telling what you will get. It purely depends on the genetics of the rooster. Since a rooster does not lay eggs, you don’t have a lot of clues as to what genetics he has to pass down unless you know the genetic makeup of his parents. EE’s are not a breed so there are no set standards.
There are two different components to egg shell genetics if you keep it simple. There is one gene pair that determines if the base color is blue or white. There are a whole lot of different genes that control if any or how much brown is added. Green is just brown added to base blue. Think of it this way:
Base blue + no brown = blue
Base blue + brown = green
Base white + no brown = white
Base white + brown = brown
All those different genes that contribute to brown determine what the shade will be. You can get some real surprises here. Some of these genes are dominant, some are recessive, and some only have an effect if another one is present. This is where it really gets not simple. You can get a clue of what might happen by looking at the shade of brown your hens are laying, but you don’t know what the rooster may or may not be contributing to brown. But your main concern is the blue egg gene.
At that gene pair, he may have two blue egg genes, a split of one blue and one white, or two whites for the base color. If your EE rooster has two blue genes, he will give one to all his offspring and all of his daughters will lay blue or green eggs. The blue gene is dominant over the white. If he is split with one blue and one white, he will randomly give one or the other to his offspring. In theory half his daughters will get a blue gene and half will get a white. But those are just odds. You have to hatch enough chicks for the odds to mean anything. If he has two white genes, obviously he will not give any blue genes to his offspring.
Maybe instead of telling your friend what to expect, you are instead trying to solve the mystery of his genetics. If all the pullets lay blue/green, he probably has two blue shell genes. If you get some blue/green and some white/brown, he is obviously split. If you get nothing but white/brown, well darn.
You do happen to have one clue though, the rooster’s comb. The pea comb and the blue egg shell gene are really close together on the DNA. They are so close together that 97% of the time they will be inherited together. There are certainly no guarantees with this because I don’t know the genetic history of your EE. There are several breeds of chickens that don’t lay blue/green eggs but have pea combs. Somewhere back in his ancestry that 3% split may have occurred. The pea comb is dominant enough that you should be able to tell if he has a copy of that gene, though of course since it’s chicken genetics that can get complicated too. But if he has pea comb influence in his comb, your odds of him having at least one blue egg gene go up.
Good luck with it. I think you re solving a mystery more than knowing what to expect, but that may be even more fun and suspenseful.