Assuming that the bull does not have a dilution gene, a heterozygous black bull will always sire some black and some red calves. After a black bull has sired red calves, he is proved to be heterozygous black. At that point, calling him double-black is meaningless. His parents may both still be black, but his calves will be both black and red. Gold calves are the product of a set of dilution genes acting on the genes for red color.
Red color dilutes to gold, just like black color dilutes to gray.
Any animal with genes for black color that is also carrying the dilution gene will be gray. However, because much misunderstanding exists about these terms, it is always best to question when you purchase, rather than after you have gold or gray calves on the ground. You may hear someone say there is an 87 percent chance that the bull is homozygous, meaning that the bull has three progeny on the ground out of red dams, and all of them are black. With no red calves out of three, there is an 87 percent chance that the bull is homozygous black. Once a bull sires a red calf, he is proved to be heterozygous.