'Perfect information' in this context means that the player has full knowledge of the current game state. There is no information about the game that is hidden from the player.

An example of a game with perfect information is chess. In chess, both players know position of every piece on the board and all the possible moves for both sides.
An example of a game with imperfect information is poker. In poker, the players do not know the cards in other players' hands or in the deck. Therefore the players cannot make fully informed decisions and have to rely on probabilities.
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