Hybridization of complementary sequences is one of the central tenets of nucleic acid chemistry; however, the unintended binding of closely related sequences limits the accuracy of hybridization-based approaches to analysing nucleic acids. Thermodynamics-guided probe design and empirical optimization of the reaction conditions have been used to enable the discrimination of single-nucleotide variants, but typically these approaches provide only an approximately 25-fold difference in binding affinity. Here we show that simulations of the binding kinetics are both necessary and sufficient to design nucleic acid probe systems with consistently high specificity as they enable the discovery of an optimal combination of thermodynamic parameters. Simulation-guided probe systems designed against 44 sequences of different target single-nucleotide variants showed between a 200- and 3,000-fold (median 890) higher binding affinity than their corresponding wild-type sequences. As a demonstration of the usefulness of this simulation-guided design approach, we developed probes that, in combination with PCR amplification, detect low concentrations of variant alleles (1%) in human genomic DNA.