The player operates under the knowledge that there is information, that is fixed in a particular game representation (yet varies over different game instances), and is not known to him or her. The game may involve revealing or obtaining this information in order to make better decisions or may be part of the instrinsic nature of the game (to make decisions without having all the information).
It is important to make the distinction between information that is initially unknown and can be learned, from that which can be learned from one game playing session to another. The latter is not considered incomplete information because it can be learned independently from a game session.
In the card game Poker, each player does not know the exact cards that the other players have. Each time the game is played the players have different cards, so there is no way to anticipate other players hands based on previous games. Information gathered about other players mannerisms and betting styles while playing the game can possibly increase the amount of information known about other players' cards. However, final knowledge of the cards in the other player's hand can only come after the round is over.
In WarCraft there is an option called Fog-of-War in which the exact location of enemy units is obscured from view unless they are within the line of sight of player controlled units.
In the MMO Ultima Online, players could wear a special robe (a grey robe refered to as a "Death Robe") that could hide most items the player wears and would seem to indicate that the player recently died, and does not have any posessions and cannot fight or defend themself. This player would appear harmless, but could effectively combat other players with a calm trigger-finger style of play, knowing that they have little to lose and everything to gain, should they defeat their opponent. Conversly, an opponent wearing a full set of high quality armor would often panic, knowing they have much to lose and not knowing if they have anything at all to gain. This panic would be the cause of their downfall.
In the turn-based strategy game Advance Wars the fog-of-war option disguises not only the movement of units but also the opponent's choice of production of units.
In Guild Wars, you do not know which of the hundreds of skills your opponent has brought into the match until they use those skills against you. This has been used by some teams (most notably, Idiot Savants in the Guild Wars Factions Championship) to create suprise tactics and plays when the time is right. However, since the opponent can see any skill you use and unused skills are pointless, this is not a generally used tactic or focal point of the game.
In Myst you are trapped in a strange world. You complete puzzles that give you pages to books that give you information on how to leave, Depending on which books you add pages to you get different information that lead you towards different endings, one of which is winning.
Soul Calibur 2
Soul Calibur 2, a fighting game, allows special move inputs to be entered while doing other things (pre-buffered), meaning a powerful move could be executed with a button press under certain circumstances. Guessing and counter-guessing regarding which move that will be creates a hidden weapon and a rock-paper-scissors sort of strategy in a game that provides otherwise completely information.
Player vs. player combat in Ultima Online involves a great deal of bluffing, guesswork, and missing information. Spells that reflect attacks can be cast before combat. Poisons can be applied to weapons and items can be trapped. Players typically go through a series of non-damaging disarming moves at the onset of combat. Also, a unique set of words of power are spoken while any particular spell is cast, announcing your intent. Players would create macros that would rapidly say a slew of different spell words while they cast to disguise the nature of their next move.