Our algorithm also takes in consideration hair color of the parents although sometimes we may put facial features first and hair color may not match. Hair is geneticaly predetermined but contrary to eye’s iris color genetic mechanism is not fully understood yet. At least two genes play role in how much pigment (actually multiple pigments) child will have and what will be result hair color. However, shade in particular is very hard to predict.
Black is the most common worldwide regardless of ancestors, ethnicity and complexion color. It is assumed that black is the original hair color of homo sapiens species. Second most common hair color is brown. While blond is in high demand it is rare for babies of non-european ancestry but thanks to genetics it is possible for brown haired parents to have blonde baby! Other colors are rather tricky. Only about 1.5% of world population have red hair and future redhead babies are often born blond or blond with slight red tinge.
Hair color often change during lifetime sometimes even multiple times. Many babies born with blond hair develop darker color as they grow up. For newborns changes from brown hair to blond are not uncommon too as the pigment ratios change.