Rare variant enrichment and quantification was achieved by allele-specific, competitive blocker, digital PCR for aiming to provide a noninvasive method for detecting rare DNA variants from circulating cells. The allele-specific blocking chemistry improves sensitivity and lowers assay cost over previously described digital PCR methods while the instrumentation allowed for rapid thermal cycling for faster turnaround time. Because the digital counting of the amplified variants occurs in the presence of many wild-type templates in each well, the method is called "quasi-digital PCR". A spinning disk was used to separate samples into 1000 wells, followed by rapid-cycle, allele-specific amplification in the presence of a molecular beacon that serves as both a blocker and digital indicator. Monte Carlo simulations gave similar results to Poisson distribution statistics for mean number of template molecules and provided an upper and lower bound at a specified confidence level and accounted for input DNA concentration variation. A 111 bp genomic DNA fragment including the BRAF p.V600E mutation (c.T1799A) was amplified with quasi-digital PCR using cycle times of 23 s. Dilution series confirmed that wild-type amplification was suppressed and that the sensitivity for the mutant allele was <0.01 % (43 mutant alleles amongst 500,000 wild-type alleles). The Monte Carlo method presented here is publically available on the internet and can calculate target concentration given digital data or predict digital data given target concentration.