During thymic education, strongly self-reactive T cells are selected against, while weakly self-reactive cells are positively selected. However, the probability of an antigen being self derived and the number of self-peptides have never been properly defined. We merge algorithms for: cleavage prediction, TAP binding probability estimates and MHC binding properties to estimate the number and distribution of all MHC binding peptides. We show that the number of self-peptides with a high affinity to a given human MHC-I molecule is between 200 and almost 200,000 and is much less than the estimated total number of peptide sequences. This result suggests that MHC molecules are selected through evolution in order to reduce the number of self-peptides presented. The number of viral peptides presented is also low and varies between zero and a few hundred per virus for a given HLA allele. These low numbers explain the need for multiple alleles within an individual. We show that six codominantly expressed MHC-I alleles are sufficient to present at least one or two peptides per virus for the vast majority of viruses. Viruses can escape detection either by using peptides that cannot be presented on MHC molecules or by using peptides whose presented segments overlap significantly with self. Most viral families (such as influenza, HIV, Hepatitis and HPV) present as many peptides as predicted from their genome length, and overlap minimally with the human self-peptide repertoire. However, a few latent viruses, such as herpes and adenovirus share considerable peptide sequence homology with their human hosts.