Generally speaking, you need about 25 breeding pairs to maintain a healthy population for relatively monogamous species such as humans.
However, with herd animals such as livestock, the numbers skew differently, since each male maintains a harem of females. Generally speaking, a good ratio for non-isolated populations is 1 male to 25-30 females.
However, if you've got some control over the breeding, and you're starting from a small isolated population, then a closer to 1 to 1 ratio can produce satisfactory results.
Lets just look at a simple comparison:
Assume a herd of 20.
Monogamous breeding is pretty much a non-starter in this situation, so a 10/10 split is not useful with that approach. Plus, a sizable number of your potential breeding pairs in the second generation will be full siblings.
A 1/19 ratio would allow for rapid growth in population, and most potential breeding pairs in the second generation would be suitable, as they'd all be only half siblings.
Now, with a 10/10 ratio and non monogamous breeding, closely monitored, initial growth would be slower than a 1/19 ratio, but there'd be the greatest potential genetic diversity from the initial herd. Each mare could be bred by each stallion once, resulting in 100 individuals born solely from the first generation. Of course, the new generation could be bred with the non-related individuals from the first generation, after the first breeding season, as could all subsequent ones. You'll have thousands within a decade (pregnancy lasts 11 months, so just assume a little less than 1 pregnancy/mare/year).