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Games of Perfect Information

Started by Russell Oct 16, 2004 at 8:38 PM 5 replies 2.2k views

Original Post

Oct 16, 2004 at 8:38 PM

I have two questions about what a "game of perfect information" is, and what it is not. Several times in the past few days I have read a definition for a "game of perfect information" that doesn't sound correct. Here is one of them.

Quote:
A game has perfect information when at any point in time only one player makes a move, and knows all the actions that have been made until then.

Using that definition, poker is a game of perfect information, but I have never seen poker described this way. First question: Is poker a game of perfect information, or is this definition incomplete? Second question: If every player could see all other players' cards in a poker game, would the game then be considered a game of perfect information? There is still a random component of the future cards to be dealt. You may initially be dealt the best hand, but since players get more cards in most forms of poker (draw poker, community cards Hold'Em, 7-stud, etc.), you can't determine who will win. If a game has perfect information, it seems like you should be able to calculate who will win (at least in theory).

Extrarius

Oct 17, 2004 at 1:18 AM

I think a 'game of perfect information' would probably mean a game where the game's current state is known entirely, so a poker game where the players were keeping track of the deck AND saw all players' cards would be one of perfect information.

Of course, this is just a guess.

The Reindeer Effect

Oct 17, 2004 at 1:55 AM

Yea, game of perfect information is, as Extrarius put, a game in which the entire state is known to both players. An example being Chess.

An RTS is not a game of perfect information if it has a fog of war, because this prevents the player from seeing outside the line of sight of his units.

IADaveMark

Oct 17, 2004 at 2:58 PM

In theory, each card dealt to each player is an action. It those actions were known, then each player would know each other player's hand.

Russell

Oct 23, 2004 at 3:43 AM

What if you knew the cards which your opponent's held, but not the cards which would be dealt next? Would such a game be a game of perfect information?

stevie56

Oct 23, 2004 at 4:41 AM

As I understood the definition, a ‘State of Perfect Information’ is one where all the facts regarding the current state are known to everyone involved in deciding on next moves.

This fits chess and draughts, obviously. But not Scrabble.

For this to apply to cards, you will need either all the cards in the deck be dealt, face up, to each player; or a shorter hand dealt, face up to each player, from a deck that is placed face up and spread out on the table, so the further cards to be dealt are known beforehand.

As this only applies to a few card games, I’d suggest most are not ‘Information Perfect’.

lucky_monkey

Oct 23, 2004 at 8:53 PM

Quote:
Original post by Russell
What if you knew the cards which your opponent's held, but not the cards which would be dealt next? Would such a game be a game of perfect information?

Technically yes. A sequential game is a game of perfect information if the players move one at a time and if, when it is my turn to play, I know every action that every other player has made up to now.

The "information" in "perfect information game" is more about having seen your opponent's actions/strategy rather than having seen the state of the game.

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