Methods, systems, and kits for estimating fetal fraction in a mixed fetal-maternal DNA sample are disclosed, by molecular counting of a predetermined set of informative sequences. These find use in detecting and quantifying variations in gene dosage, e.g., due to gene duplication, or to variations from the normal euploid complement of chromosomes, e.g., trisomy of one or more chromosomes that are normally found in diploid pairs, in the context of non-invasive prenatal testing.