The number of different major histocompatibility (MHC) molecules expressed per individual is widely believed to represent a trade-off between maximizing the detection of foreign antigens, and minimizing the loss of T cell clones due to self-tolerance induction. Using a mathematical model we here show that this argument fails to explain why individuals typically express of the order of 1020 different MHC molecules. Expression of extra MHC types decreases the number of clones surviving negative selection, but increases the number of positively selected clones. Based on experimental parameter estimates, we show that the number of clones in the functional T cell repertoire would in fact increase if the MHC diversity within an individual were to exceed its normal value, until more than one hundred different MHC molecules would be expressed. Since additional MHC types also increase the number of presented pathogen peptides, resistance against pathogens only decreases at unrealistically high MHC diversities exceeding 1,500 different MHC molecules per individual.