The is a difference between In-Breeding [breeding brother/ sister] and line Breeding [breeding offspring back to there parents].
Here is a example of a, 3 times in and once out. line breeding program.
By Dr Charles R H Everett & Craig Russell
My personal research in breeding has led me to begin gathering and collecting articles and books by cockers of long ago; these men of the past preserved several different breeds of chickens for hundreds possibly even thousands of years. During that time they maintained type and vigor to an unparallel degree. It is my belief that their methods of breeding should be examined in detail to be utilized by the modern preservationist. Let me add, however, that this article is not an endorsement or defense of cockfighting; neither will I belie them in any manner. Instead, it is a heartfelt acknowledgment to men who perfected the art of breeding chickens. Further, I believe the modern preservationist can learn much more from the breeding techniques of cockers than he/she can from textbooks on commercial poultry breeding. (Note* It should go without saying that at all times you must select for vigor and type regardless of the breeding system utilized. Cocker Tan Bark states, Good breeding is only a matter of intelligent selection of brood fowl (Tan Bark, Game Chickens and How to Breed Them, 1964, p. 27). What the ole time cockers strove for was prepotency. They desired to be able to predict with reasonable accuracy the outcome of any particular mating. For this reason, no cocker worth his salt would have consistently used the out-and-out system. Granted, at times they did cross, but very carefully. Their records consistently indicate that when they did cross they did so using the same strain of fowl they were hoping to improve. Of course, they were looking for gameness, but using their methods a breeder can breed for type, fertility, egg production, etc. The first system I would introduce was utilized by William Morgan, of Morgan Whitehackle fame, and some of the English cockers. It is a form of breeding known as 3 times in and once out. This system was used to produce, in cockers terms, a pure strain. The following chart will explain how the system works. First Generation Hen Cock ½ hen ½ cock
Second Generation Hen to son Cock to daughter ¾ hen ¾ cock
Third Generation Hen to grandson Cock to granddaughter 7/8 hen 7/8 cock
Fourth Generation Hen to ggrandson Cock to ggranddaughter 15/16 hen 15/16 cock
Now in the 5th generation you breed the 15/16 hen to the 15/16 cock. Then, choosing the best hen(s) and cock(s) you begin again (Narragansett, The Gamecock, 1985, pp. 44-45). C. A. Finsterbusch recommends the same breeding strategy in his famous book Cockfighting All Over the Word page 152153. If they chose to continue line breeding these fowl were what they termed seed stock. Seed stock was never pitted. Instead, they were crossed to a different strain to produce their battle cocks. Battle cocks were never used in breeding pens if this system were employed. Or, at this point you choose the three to five best hens and begin the clan mating system. Alva Campbell who created the Campbell Blue Boones during the early years of the twentieth century line bred his outstanding pullets to one cock, Daniel Boone, for eleven straight years (Histories of Game Strains, Grit and Steel, no date given, p.26). D. H. Pierce claimed his Wisconsin Red Shufflers were line bred for 35 years with no loss of vigor or gameness. (Histories of Game Strains, Grit and Steel, no date given, p. 20). How did these men accomplish this when so many modern textbooks on poultry genetics maintain this is impossible to do? I have discovered several key answers. First, an inbreeder must breed only from his most vigorous specimens (Tan Bark, Game Chickens, 1964, p. 28). Second, they culled ruthlessly. Third, in any form of line breeding the youthfulness of the stock used cannot be overstated. Fourth, they often carried on the same mating (One cock to one hen) for four or five years. Thus, in twenty years it was possible to have only produced four or five distinct generations. When cockers happened upon a cock and hen that produced winners in the pit, then they mated these two year after year. Fifth, they kept accurate records of every mating and often practiced single matings. Sixth, they only attempted close inbreeding on free range giving the birds every advantage of producing constitutional soundness and vitality (Tan Bark, Game Chickens, 1964, p. 28). These six keys allowed the cockers to be greatly successful at the art of breeding game fowl centuries before the advent of modern genetics. Many cockers practiced variations of the rolling-matings and clan-matings systems. When practicing the rolling-matings they would often include side matings of line breeding. When using the clan system the large breeders often kept five to seven clans. (They called them yards.) With the clan matings they most often used the matriarchal system as advocated by Dick Demansky. At times they would create new clans or yards of full sisters when a particular hen within the clan produced exceptional sons. Thus, this one hen became prepotent in the new yard through her daughters. Like those of traditional farmers, for whom poultry was an important part of the subsistence, the methods of cockers have often been disparaged by modern experts. But for serious preservationists and small flock owners in general their tried and true methods are among the surest ways to turn simple reproduction into serious breeding and systematic flock improvement. One of the truly wonderful things about raising chickens is that you the breeder can choose your own system of breeding to create your own strain. Yes, you can even experiment! Regardless of how you personally feel about the sport of cockfighting, these men of a by gone era have much to teach us. So, why not learn from the original preservationist: cockers?
Information found at Ultimate Fowl Wikipedia