Perfect Infomation

Interestingly, there hasn't been much of an attempt to formalize the definition of the most common selling point of abstract strategy games: 'perfect information.' Maybe it's just me, but there seems to be some argument over what counts as perfect or imperfect information, but where there's agreement, it's just some vague concept.

According to Wikipedia, a game has perfect information if "each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the 'initialization event' of the game." While this definition is nearly acceptable, there are some factors that put this into a bit of a debate.

Whether the definition needs changing is still open to discussion, this piece is concerned with where information within a game is not obtained.

For this to make sense, let us look into some factors that some people might agree are not accessible to a player's knowledge:

Things beyond our control

Chance and Randomness are rather interchangeable, but they define cases where scenarios can or fail to happen if random factors beyond the capabilities of the player are met. From the creation of starting setup to determining possible moves or circumstances, chance is determined through generators and sometimes a means to interpret its results.

The former is seen as more incompatible to perfect information while the latter is accepted as long as it doesn't include anything beyond the player's control happening outside the game. Some games use random starting states as a feature to create unique games without compromising on rules of play or other relevant information.

Backgammon can be a game of intelligence but plays are determined by the roll of the dice, which can drastically change one's strategy, a common contrast from Chess. Some simulator-type games use some type of randomness to imitate outside factors or the aleatory nature of environments or situations one can encounter. 

In some cases, chance is usually augmented by either choice or advantage. Choice is where players can choose how these random factors, usually from rolling dice or drawing cards, will be used in a turn. Advantage is where a player has an additional, usually permanent factor that is always added to a random one. The two can also come before the roll, e.g. a choice to do which roll or an advantage that is added based on the result of the roll. 

Generally, the point of contention is whether having some random initial setup should be included in context of perfect information or outside it.

Things one does not know

When a player does not fully know all the relevant information of the opponent, yourself or even around the game, then there is obviously no perfect information. This usually creates a sort of necessity to deduce the unknown from what is more or less known, 

Unknown opponent information exists where the statement "My opponent is currently in this state" cannot be immediately answered. Bridge perfectly sets an example as to how unknown opponent information is deduced through bidding and sometimes card play.

Any game that involves drawing from a deck or hidden stock is also unknown information. In this game, any statement about the state of the game as it happens is indeterminate.

Facts about a game that are not explicitly obvious do not count. This type of information is still open and depending on the rule you may be able to ask for it.

Things that might happen

Foresight is an aspect of gameplay that we can consider to be beyond the limit of player information and so does not usually count. After all, much of game strategy is planning ahead, and therefore taking into account possible and probable events.