Dilution of the blood of a specific horse happens as each generation is produced. An own son or daughter will have 50%, an own grandson or granddaughter will have 25% and an own great grandson or great granddaughter will have 12.5%. Geneticists tell us that a parent must carry 10% of a desired blood in order for that blood to have any influence on the offspring. Therefor, blood from the great, great grandget would only be equal to 6.25% and would have NO influence in the blood. So, in order to preserve bloodlines and qualities/traits/characteristics of a particular horse, it is very necessary to do line breeding or inbreeding.

Here are the definitions for your easy reference:

Line Breeding: This is the mating of more distantly related animals. One or more common ancestors exist in the pedigree further down the line from the parents or direct siblings. The ultimate goal of line breeding is to carry on certain traits, strengthen the type and uniformity of the breed - thus improving the breed.

Inbreeding: The mating of two closely related horses. For example: mother to son, father to daughter, brother to sister, half sister to half brother. You want to concentrate on desirable genes to produce quality offspring; however, you must be careful not to produce faulty traits.