I think you are right on. Let’s do this for clarity. The recognized symbol for a Blue egg gene is an upper case “O”. The upper case shows it is dominant. The symbol for a recessive white is a lower case “o”.
If a rooster is O,o and a hen is O,o each will randomly give one of those genes to the offspring. In half the cases the rooster will give an O. That may be paired with the hen’s O or o, giving you either O,O or O,o. If he gives an o, that may be paired with an O or an o from the hen giving you an O,o or o,o. So ¼ of the time, you get O,O, ½ the time you get O,o, and ¼ of the time you get o,o.
O,O or O,o will give blue or green eggs because O is dominant.
If a rooster has o,o and the hen is O,o you get half O,o and half o,o. Half colored.
If the rooster is o,o and the hen is O,O you get O,o. All colored.
You can keep playing with this all you want but hopefully you got the idea. You can look up Punnett Squares if you want to see this graphically.
There is a trick to greatly improving your odds of getting a chicken with a blue egg gene. The blue egg gene is real close to the pea comb gene on the DNA. They are so close on the DNA that 97% of the time the pea comb gene and the blue egg gene stick together. This only applies when there are no other pea comb genes or blue egg genes in the genetic mix, but I’ll take 97% as a real good guess. So try to pick offspring that have the pea comb for pullets and for cockerels.
There is even another trick with this. The pea comb gene is partially dominant, not fully dominant. That means if the chicken has one dominant pea comb gene and one recessive not-pea comb gene, you’ll see the effects of the pea comb gene, but it will not be a pure pea comb. I call it wonky and it’s a bit hard to describe, but think of a slightly raised line up there. So if you get one with a pure pea comb instead of a wonky pea comb, you have pretty good odds of having one pure for the blue egg gene instead of one split blue and white.
