ABSTRACT Upon the emergence of SARS-CoV-2 in the human population, it was conjectured that for this coronavirus the dynamic intra-host heterogeneity typical of RNA viruses would be toned down. Nothing of this sort is observed. Here we review the main observations on the complexity and diverse composition of SARS-CoV-2 mutant spectra sampled from infected patients, within the framework of quasispecies dynamics. The analyses suggest that the information provided by myriads of genomic sequences within infected individuals may have a predictive value of the genomic sequences that acquire epidemiological relevance. Possibilities to reconcile the presence of broad mutant spectra in the large RNA coronavirus genome with its encoding a 3’ to 5’ exonuclease proofreading-repair activity are considered. Indeterminations in the behavior of individual viral genomes provide a benefit for the survival of the ensemble. We propose that this concept falls in the domain of “stochastic thinking,” a notion that applies also to cellular processes, as a means for biological systems to face unexpected needs.