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It's entirely random. There's a certain numerical ratio giving the odds of one turning up on any given roll. The odds of not getting a candy corn pony are immensely higher than the odds of getting one. However the ratio isn't changed by how many horses you have created. The odds might be 1 candy corn in 12,000 (and that's just a for example number. Ammit is the only one who knows what it really is.) Every horse you create, the odds are the same, one in 12,000. Sometimes, you get the lucky one. If you're really lucky, you can get more than one fairly close together.

It's like the odds of getting a dead foal if both mare and stallion carry frame. Every time, it's one chance in four of the dead foal. You could have four dead foals in a row, and then a living one. The odds didn't change, just the luck.