To recap the definition in (link), a game consists of rules and elements. I will define what rules and elements are, then I’ll take chess, baseball, and the Kirby Kid’s favorite example, Super Mario Bros., as examples illustrating what elements and rules are. First, elements and rules are an equilibrium; it is impossible to speak strictly of one without speaking of the other. The rules of the game define every possible combination of “properties” for elements and possible properties for an element, where elements exist to be placeholders with certain combinations of properties. Properties will be clearer with examples, but the important thing about a given property is that it can be evalutated from the player’s (or the software’s/referee’s) point of view. The upshot is that properties will be required to apply rules of the game’s motion.
The point of elements is that they are placeholders for properties. In chess, the board is initially set so that pieces like pawns are put on different squares, which is to say that there are multiple pawn elements in different positions (where position is a property). For the white player to arrange his side of the board for the purposes of chess at a table, he needs 8 little markers that the white and black sides know to be pawns as opposed to any other piece and which unambiguously indicate the positions of the pawns. Regardless of whether the game is being played on the board, on a computer, or in the mind, the concept of the pawn is a useful identity that allows the system to tell that it is not any other piece. An element is an abstraction that can be represented in many ways, it is only required that someone involved in the game (a human, computer, or the laws of physics) knows that the element is there (otherwise, how can it affect play?).
Given that we have defined the elements that we are interested in, rules of mechanics and interplay (as Kirby Kid sets them out) will follow, the rules of the game’s motion. Essentially, these rules determine how the properties of elements change.
Elements are a nexus for understanding what is going on in the game’s proceeding. As such, as a practical matter, it helps if elements are represented as impressions in perceptible media that have a changing representation as properties of the element change. At the very least, it is important to understand the consequences of mapping properties of elements to their representation. This doesn’t apply to human beings alone, as a computer that does not understand a representation of an element and its properties as binary data will just stop working, assuming that this isn’t some intended “feature.” For example, many chess sets incorporate a few essential properties in a matter that is readily apparent. By color, we can tell if one piece can take another (and which pieces are moveable by which players). By shape, we assign rules of motion and capture. By placement, we know the position of the piece. In Super Mario Bros., the man in the red overalls has what we could evaluate as dimensions of speed, acceleration, position, volume, and possession of the ability to spew fire, all of which are discernible by shape, color, and motion on the screen (and indeed, reinforced with sound effects). In baseball, players are kept track of by their uniforms and by virtue of the fact that they are unique human beings, and an umpire keeps track of action by use of these visible element labels.
There is a lot of work dedicated to the representation of elements and their properties. Jesper Juul and Kirby Kid both dedicate a lot of space to effective representation of gameplay in terms of intuitive experiences. Indeed, a human will likely find the visual output of Super Mario Bros. more effective feedback than reading the game’s hexadecimal memory under most circumstances. Even speedrunners who take advantage of the machine’s particular view of the action still have to interface directly with the feedback intended for the human player. In general, it is easiest to speak of the game’s elements and rules in terms of the intuitive objects that they appear as when we see the feedback, so we’ll do that when we can, because effective analysis and game design do not need to be expressed in low-level code to be precise.
The foremost “problem” with defining a gamespace is that a representation will not be unique, a problem for all modelers. What is the problem here? Well, when we are getting feedback from a game, what elements of the game are going to be considered to be under the player’s direct control? This is important if we want to divide a game into aspects like Kirby Kid’s interplay and mechanics. Does the player just control Mario, or is the Goomba and the pipe an extension of Mario’s being? Furthermore, how does one tell one element from another? Are all Goombas appendages of one composite Goomba being? Quite frankly, such a distinction is not worth stressing over provided that one clearly defines where the player begins and ends or where an element begins and ends. Ultimately, elements and rules are tools of expression, and their utility comes from effective analysis and game design. As we will see, when we define elements and rules, we can swap out the rules and change properties of elements to create new experiences or ponder why a different set of rules wasn’t picked.
As such, in chess, each piece can be treated as a separate element. This follows easily from the observation that pieces mostly move one at a time (castling being a notable exception). Each one has a position, color, and rules defining motion, capture and transformation (in the case of the pawn). In chess, the colors are assigned to two separate sides who have agreed to vie in checkmating the king of the opposite color, so every piece of a player’s color could be treated as an extension of that player. Despite the natural characterization of individual pieces as elements, nothing stops chess analysts from evaluating a formation of pawns as a useful element in itself, where each pawn is an appendage of the whole. The same distinction exists between a baseball player and the team, or Bowser alone compared with Bowser and hammer projectiles.
Of course, an analyst might be most interested in the “smallest” elements, which is associated with minimal amount of impact that a player can have on a system. In chess, this is naturally the individual piece. There are smallest elements for Mario, but this is harder to gauge. The discrete space in Super Mario Bros. is so fine that what we consider a single element covers many squares at once, so there’s an ambiguity that isn’t present in chess. What keeps Mario as a single element is that his whole volume with its pixels move together. There is a continuity to Mario’s appearance that keeps him looking like one element. Furthermore, certain projectiles will “kill” the player by touching any part of Mario, so the application of some rules to all pixels of Mario defines his element in a way.
And what is a natural suggestion for the player’s element? We suggest an idea: Mario’s presence on screen in whatever form is necessary for player action; in mathspeak, the player’s elements are the ones so defined that the intersection of all possible player experiences involves those elements, so Mario would have to be more generally defined so his form with a mushroom or fire flower or star was a dimension of his being. Such a definition gives new insight to chess, where the white player elements would be the set of white pieces including the king: it’s impossible for the player to play regular chess without the king, whereas good players might decide to start a game where they give up a rook.