[Jazza]

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Neither player really has an advantage either way even if the numbers are picked non-randomly. Another way to rephrase the game is that if both players guess the same number, B wins; If the numbers are different, A wins. B may be able to catch a pattern of what numbers A is guessing, but A also can find a pattern of what B guesses. Neither player is at a disadvantage.

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yes i'm aware of the symmetry, but i'm interested in the case where one suspects the other of playing non-optimally