There’s a variety of ways to cross horses, and a variety of types of crosses. One type of cross I’ve worked with is the Triple Cross which is a multi-generation breeding project intended to develop a cross-bred horse that is a nearly even blend of three different breeds. There are three methods of achieving this type of cross. The easiest two involve a process I call flip-breeding in which the breeding is flipped between two extremes, and it has two variants, the other process is one I call a Triangle Breeding program due to how the three lines are bred together forming a triangle.
The flip method of breeding is rather simple, you start with two 50/50 crosses of breeds A/B and A/C. Breed the 50/50 crosses to breed A creating a 75/25 A/B cross and a 75/25 A/C cross. Breed the 75/25 A/B cross to breed B and the 75/25 A/C cross to breed C. This will create a 37.5/62.5 A/B cross and 37.5/62.5 A/C cross. The next generation breed those back to the A breed, and continue flipping the breed being bred back to each generation. Eventually you will get to a point in which the horses will have about 33% of the A breed and 66% of the B and C breed. Anytime the A breed is low in both horses, you can breed those together and the resulting horse will be close to having 33% of each breed.
The variant of this is to use a 50/50 cross of the B/C breeds to flip the breeding between a purebred of the A breed and the 50/50 cross. This is much cleaner and simpler. Simply start by breeding a purebred with the 50/50 cross to get a 50/25/25 (A/B/C) cross, and breed that to the purebred line A to get a 75/12.5/12.5 (A/B/C) cross. The breed that to a 50/50 B/C cross to get a 37.5/32.25/32.25 (A/B/C) cross, and keep flipping the breeding between the purebred A line and the 50/50 B/C line. Eventually you’ll get close to a 33/33/33 (A/B/C) triple cross in which the A breed should remain dominant throughout. If instead of breeding the 50/25/25 (A/B/C) cross to the purebred A line you breed it to the 50/50 B/C cross instead, the dominant breed will vary between the B and C breeds somewhat randomly.
The final method is one I call the Triangle Breeding program which relies on a closed breeding pool of about 4 horses in each generation breeding them in, roughly, a triangle formation formed by 3 breeding lines of horses starting with purebred horses of breeds A, B and C. Line A to Line B, Line B to Line C, Line C to Line A. So, starting with 3 lines of purebreds, A, B and C, you breed Line A with Line B to create the next generation of Line A, Breed Line B with Line C to create the next generation of Line B and do the same with Line C and Line A to create the next generation of Line C. Keep repeating this process with each successive generation of the three Lines (A, B and C) and by the 8th generation you will get to an almost even blend of 33% of each breed in the three lines with each line having one breed dominant over the other two, and by 21 generations there will be an even 33.33333% of each breed.
Each method will, in fact, hit the same points in the generational sequence at the same time, the first two methods; however, are far easier to manage and not as complicated to keep track of in the long run.
Some graphs from when I devised the Triangle Breeding program initially.