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Player Agency, Critical States, and Games as Formal Systems

In which Joey expounds at length about player agency in games, using standard Chess as an example.

Joey Gibbs

July 13, 2011

5 Min Read

Hello again true believers, and welcome to another of Joey's (pen)weekly blog posts! Joey here, reporting live from FS's UXL. The post is a little early this week - because I'll be out of town for the weekend and likely will have little desire to compose - but hey, I'll chalk it up to being slightly more proactive than is my usual modus operandi.

True as ever to my word, today's topic will be player agency - that mystical force that is the hallmark of interactive media everywhere.

So what is player agency, exactly?

Well, player agency describes the ability of a player to interact meaningfully with gameworld. More than simple action/feedback interactivity, agency refers to knowing actions taken by the player that result in significant changes within the world.

So let me toss this idea to the audience: If we consider games to be closed, formal systems, then a given game will have as one of its characterisitcs a theoretically finite number of potential game states. For example, in the game of Chess the white player might lead off by moving any of their pawns forward one space. This movement of a single peice illustrates a very simple state change: The Chess system has gone from its initial starting state (with the pieces of both armies arranged at the beginning of the game according to the rules of Chess) to a new state in which one white pawn now occupies a square that is one forward of its initial starting point. Together, these two states make up a small fraction of the state space complexity of Chess - that is, the total number of possible states legally reachable within a given match that is being played under the auspices of standardize rules.

In my thesis, I am currently defining interactivity as the ability of a player to alter the state of a game system. Agency I define as the ability of a player to knowingly make irreversible alterations to the state of a game system.

Going back to the example of Chess, because Chess pawns cannot move backwards, it is impossible once a single pawn has been moved for the system of Chess to revert back to its initial state assuming that standard rules are upheld. This means that the single pawn move is one of many possible irreversible, or critical, states that the player may choose to take. Limiting ourselves to an examination of only the game states that arise from the first move by the white player in a game of Standard Chess, from the initial state of the game the white player may then force one (1) of twenty (20) possible state changes:

Pawns at A2-H2 may all be moved either one (1) or two (2) spaces directly forward. Eight (8) pawns at two (2) possible moves apiece yields 8 x 2 = 16 possible states.

Knights at B1 and G1 may be moved as well - B1 can be moved to either A3 or C3 and G1 can be moved to either F3 or H3. That's two (2) knights at two (2) moves apiece, yielding 2 x 2 = 4 possible states.

Combining these move sets yields 4 + 16 = 20 possible opening moves for white, which correspond to twenty (20) possible game state changes.

Of these 20 possible new states, 4 are considered to be neutral and 16 are considered to be critical:

A neutral state is one that can be undone. Because knights can move both forwards and backwards in their characteristic L-path, a knight that has been moved from G1 to H3 may, for example, by summarily returned to G1 on the next white turn. Assuming for the moment that black has made no move, the white player can return the game to its initial state by moving the G1 knight back to its starting position.

A critical state, on the other hand, cannot be undone once it has been reached. For example, if any one of the eight (8) pawns is moved, the move cannot be undone in the next turn because, by the rules of standard Chess, pawns cannot move backward. The movement is so permanent, in fact, that the game can never again be returned to its initial state while played by standard rules. This triggering of an elimination of states that were previously available within the game system is the hallmark of a critical state. Critical states can sometimes make additional states accessible, but they will always eliminate states that were previously available when reached. This idea of critical game states is essential to a further discussion of player, agency, game space, and the effect that they have on the type of narrative experience that a game can provide for its players.

Wow. That got pretty serious in there, didn't it? Gimme a break - I've been so busy lately that I haven't been able to do formal work on my thesis. I'm pleasantly surprised with this blog though - It's giving me occasion to go back over my theory and re-organize things in my head.

I think next week I'll talk a little about indirect control and maybe start in on how the organization of space affects player agency. This Chess example is working out pretty well so far - so much so that I might have to use it in the paper... We'll see once August rolls around. By then I should be done with my CAPM exam and I'll have more time to write.

That's all for now true believers! If anybody actually reads these things, feel free to write a (preferably constructive) comment. I'm always on the hunt for feedback.



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