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Perfect information, in game theory, means that each player has the same information for every move in the game: for instance, in Chess or Go. Contrast this with imperfect information, a common characteristic of card games, where players do not have information about each other's hands.

Further details:
"Such games have perfect information: each player, when deciding his move, must have complete information about the current position of the board (I include in 'position' qualities that may be physically undetectable, such as whether a player may castle), or equivalently, about the original position of the board and all moves made so far. Examples of perfect information games would include Chess and Backgammon; games like Stratego, Kriegspiel, or the recent Stealth Chess are not perfect information games." - J. Mark Thompson, Defining the Abstract,

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