  In a game where both contestants have perfect information, there is a strict
limit on how perfect that information can be. By contrast, when one player is
deprived of all information, the limit on the other player's information
disappears, admitting a hierarchy of levels of lopsided perfection of
information. We turn toward the question of when the player with super-perfect
information has a winning strategy, and we exactly answer this question for a
specific family of lopsided-information games which we call guessing games.
