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By the Minimax Theorem of von Neumann and Morgenstern, Zero-Sum games are known to have a value, the expected value to one of the players when both play an optimal strategy. In the following we model Zero-Sum games where players face a hard information/entropy constraint as in the work of Christopher Sims (2003). The resulting game reveals an enlarged set of optimal randomized mixed strategies and can be shown to have an Informational Value which is a measure of the informational robustness of the game. In an example the randomized equilibria (which do not exist when information/entropy constraints are ignored) are derived, the geometric properties of the Shannon/Stratonovich Value of information investigated, and the Informational Value calculated.