It always works that way. Just has to be the right protein, with the right mutation. Most of those mutations are not viable.
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Well if you have hundreds of thousands of viruses (or is it millions) spreading inside of each infected human, and you have hundreds of thousands (or is it millions?) of infected humans, even a low rate of mutation will relatively quickly yield the virus with the mutated protein, and once the mutation is given the chance to spread, your vaccine will become useless.
Again, that applies to all organisms. This one doesn’t know to speed up or become more inaccurate because you are thinking about it.