The article presents new stochastic rules of nucleotide sequences in single-stranded DNA of eukaryotic and prokaryotic genomes. These discovered rules are candidates for the role of universal genomic rules. To reveal such rules, the authors represent any of genomic sequences in single-stranded DNA as a set of n parallel texts (or layers), each of which is written based on one of the different n-plets alphabets (n = 1, 2, 3, ...). Then comparison analysis of percentages of the 4n kinds of n-plets in the n parallel texts in such sequence is fulfield. In the result, unexpected stochastic rules of invariance of total sums of percentages for certain tetra-groupings of n-plets in different parallel texts of genomic DNA sequences are revealed.The presented rules significantly expand modern knowledge about stochastic regularities in long single-stranded DNA sequences, and they can be considered as generalizations of the second Chargaff's rule. A tensor family of matrix representations of interrelated DNA-alphabets of 4 nucleotides, 16 doublets, 64 triplets, and 256 tetraplets is used in the study. Some analogies of the discovered genetic phenomena with phenomena of Gestalt psychology are noted. The authors connect the received results about the genomic percentages rules with a supposition of P. Jordan, who is one of the creators of quantum mechanics and quantum biology, that life's missing laws are the rules of chance and probability of the quantum world.