Every gene (except gene 30 & 31) can mutate into an entirely new gene. So if you’re looking for a specific mutation, you must breed two cats that each possess one of the traits you need to combine to have a small chance at achieving that mutation. That’s obvious, but there are other measures you can take to improve your odds.
You’re much better off, for instance, if the Kitties you’re breeding possess the two desired traits as primary genes. In that case, the odds of getting your mutation are somewhere around 14%. If both required traits are recessive in the cats you’re breeding, that probability can drop to less than 1%.
Purebred cats have four of the same gene in the block for a certain Cattribute. This makes them highly valuable for breeding. Since they’re guaranteed to pass on that trait, the odds of a mutation if you breed with a cat that has the partner gene are greatly increased. If you can find a second purebred that has that partner gene, your chances are even better – in fact, the highest possible.