OK, the terms I use are meant to clearly identify genotypes, which is necessary when trying to predict offspring. White-Eyed is an incompletely-dominant trait. If a bird has one copy, there will be some white-centered ocelli feathers, but others that don't show white centers. This I'd refer to as "Single-Factored White-Eyed", but could also be called "split to White-Eyed". If a bird has two copies, there will be all or mostly-all ocelli with white centers.
The problem is that, in trade, "White-Eyed" as a term will be used for either "Single-Factored" or "Double-Factored", despite being different genetically. A "Single-Factored White-Eyed" will pass on the mutation to only half of its offspring, while a "Double-Factored" bird will pass it on to all. Pairing two "Single-Factored" birds would give 25% NOT White-Eyed, 50% Single-Factored White-Eyed, and 25% Double-Factor White-Eyed. Pairing two Double-Factored birds would give 100% Double-Factored offspring.
Now, here's the tricky part -- "Pied". What people call "Pied" in the trade is a bird about 50% splashed with white feathers, rather haphazardly. It turns out there are two mutations of the same gene -- one, when a bird has two copies, results in a white peafowl. That mutation is called White. The other, when a bird has two copies, results in a Dark Pied peafowl. That mutation is called Pied. See, the two are what are known as alleles -- two different versions, and in this case mutated versions, of the same gene. That means there are three possible versions for this gene -- Normal, Pied, and White. Since a bird can have only two copies, the possible combinations are:
Normal / Normal = Normal
Normal / Pied = Normal split to Pied (one or a very few white wing feathers, small white spot under beak)
Normal / White = Normal split to White (randomly-placed few white feathers, could be on wing or anywhere else, typically little or no white spot under beak, thus sometimes hard to distinguish from "Normal split to Pied")
Pied / Pied = Dark Pied (white symmetrical markings on wings, some white in center of back/tail/train, white bib)
White / White = White (solid white bird)
Pied / White = Pied (about 50% white bird, white markings random and typically not symmetrical)
If you are looking to produce Pied birds, one easy way is to cross White with Dark Pied. The result would be 100% Pied offspring. Most Dark Pied birds offered for sale are "by-products" of breeding Pied X Pied, since that pairing results in 25% Dark Pied, 50% Pied, and 25% White.
The same ratio applies to Silver Pied, which is essentially a Pied bird with two copies of White-Eye, i.e. Pied Double-Factor White-Eyed. But "Silver Pied" became the trade name. When Silver Pied X Silver Pied offspring are produced, you get 25% Dark Pied Double-Factor White-Eyed, 50% Pied Double-Factor White-Eyed (aka Silver Pied), and 25% White. Those White birds, however, will also be Double-Factor White-Eyed, but being White covers that up. Though they look just like "regular" White peafowl, genetically they will have the addition of two copies of White-Eyed. So Whites from Silver Pied breeding are different genetically than Whites from Pied breeding, and it's important to know which you're buying. Additionally, the White could be covering up other colors -- if you bred any color Silver Pied with another of the same, those 25% White birds will also be homozygous for that color. If, for example, a White male you buy came from Purple Silver Pied X Purple Silver Pied breeding, and you breed that White male with a hen of any other color, you'd find his daughters are all Purple. The lesson is that you can't
see anything under the White, since White erases everything. But the genes are still there, regardless.
If you breed him to the hen, and get
any White offspring, then I was wrong, and the birds are actually Pied. If they are both Dark Pied, there would be no White offspring -- all would have the same Dark Pied markings as the parents. If both parents are Double-Factor White-Eyed, then all offspring will be as well. If one parent is Single-Factor, then half the offspring will be Double-Factor and the other half Single-Factor. If the male is Cameo and the female is Purple, then all the daughters will be Cameo and all the sons will be IB in color, but split to Purple and Cameo. These IB split to Purple and Cameo sons would be valuable in that they'd produce a few Peach daughters when paired with a female
of any color, as well as Purple, Cameo, and a few IB daughters. So don't think these IB sons are a "waste" by any means. If the hen is split to Bronze, then half the offspring will also be split to Bronze, and the other half won't be -- but you couldn't tell either way just by looking. That would be on top of everything I already mentioned.