Perfect Information is a term from game theory, the mathematical field concerned with modelling strategic decision making, ingames as well as in other situations. I’ll try to write more about game theory soon.
The term Perfect Information has been adopted by non-mathematicians interested in games (i.e. us), and – quite unusual when a technical term finds wider use – is usually used in the same meaning: a Perfect Information Game is a game where, on every move a player makes, he knows the complete state of the game, including the history of all previous moves. This excludes, quite obviously, every game that deals a hand of cards to each player: other players cards are hidden from you, so you have imperfect information. However, games where every player plays with an identical set of cards can still be perfect information games: since you have knowledge of all previous moves and knowledge of the cards in each set you can easily infer a player’s remaining cards.
Slightly less obviously, a perfect information game has to be sequential: players have to take turns. Any game where players act simultaneously is not a perfect information game. Think about it like this: the other players’ move is part of the game state. When you make your move, theirs is not known to you (or it wouldn’t be simultaneous), so you have imperfect information.
Surprisingly perfect information games may contain random elements. Surely the outcome of the dice roll is information that is hidden from me? Game theory circumvents this problem by declaring the random element – be it a dice roll, a card draw or something else – as something that occurs outside of your turn and is thus part of the game state. Games without any kind of random element are known as deterministic.
So, enough of the theory, everything is easier with some examples: Chess, Go, Quarto and tic-tac-toe are all deterministic perfect information games. There is no randomness involved and the whole game state is visible. As an example for a non-deterministic perfect information game, take Backgammon (or take Senet from last week): there is an element of chance, but all information about the game is visible to you. As a more modern example, take Macao: there is dice and cards involved, but when you make your turn no information is hidden from you. As for games of imperfect information, those are easy to find: start with anything that deals cards to people, like Poker, Tichu, Haggis and millions of others all over the world.
And that’s the very short – and probably incorrect, if you ask a mathematician, explanation of perfect information games.
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Photos in the banner: Tic Tac Toe by Flickr user downing.amanda (CC-BY-SA), Chess by Romain Guy (CC-BY-SA) and Backgammon by Adrienne Bassett (CC-BY). Thank you all so much for sharing your photos.