- A mathematical model and a computer simulation were used to study PCR specificity. The model describes the occurrences of non-targeted PCR products formed through random primer-template interactions. The PCR simulation scans DNA sequence databases with primers pairs. According to the model prediction, PCR with complex templates should rarely yield non-targeted products under typical reaction conditions. This is surprising as such products are often amplified in real PCR under conditions optimized for stringency. The causes for this ‘PCR paradox’ were investigated by comparing the model predictions with simulation results. We found that deviations from randomness in sequences from real genomes could not explain the frequent occurrence of non-targeted products in real PCR. The most likely explanation to the ‘PCR paradox’ is a relatively high tolerance of PCR to mismatches. The model also predicts that mismatch tolerance has the strongest effect on the number of non-targeted products, followed by primer length, template size and product size limit. The model and the simulation can be utilized for PCR studies, primer design and probing DNA uniqueness and randomness.