The present disclosure describes the thermodynamic design and concentrations necessary to design probe compositions with desired optimal specificity that enable enrichment, detection, quantitation, purification, imaging, and amplification of rare-allele-bearing species of nucleic acids (prevalence <1%) in a large stoichiometric excess of a dominant-allele-bearing species (wildtype). Being an enzyme-free and homogeneous nucleic acid enrichment composition, this technology is broadly compatible with nearly all nucleic acid-based biotechnology, including plate reader and fluorimeter readout of nucleic acids, microarrays, PCR and other enzymatic amplification reactions, fluorescence barcoding, nanoparticle-based purification and quantitation, and in situ hybridization imaging technologies.