Super-resolved localization microscopy (SLM) has the potential to serve as an accurate, single-cell technique for counting the abundance of intracellular molecules. However, the stochastic blinking of single fluorophores can introduce large uncertainties into the final count. Here we provide a theoretical foundation for applying SLM to the problem of molecular counting in such a way as to mitigate errors introduced by stochastic blinking. We show that by redundantly tagging single-molecules with multiple blinking fluorophores, the accuracy of the technique can be enhanced by harnessing the central limit theorem. The coefficient of variation (CV) then, for the number of molecules M estimated from a given number of blinks B, scales like ∼ 1/√Nl, where Nl is the mean number of labels on a target. As an example, we apply our theory to the challenging problem of quantifying the cell-to-cell variability of plasmid copy number in bacteria.