We report on a systematic study of Boltzmann entropy as a function of state space size. As the state space, characterized by the number of objects N , is increased we find that identical entropies are shared by many different state space configurations. These degenerate states are called doppelgänger states. A calculus is developed to predict the occurrence of these states. Theoretical and numerical analysis shows that for large N almost all configurations are doppelgängers. Boltzmann entropy is fundamental to disparate disciplines such as statistical mechanics, mixing theory, combinatorics, and information theory. Our analysis then may have some broad interest.

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