Earlier I considered the question of what game design was. This was partially in regard to the Situation Model, but it also branched out more into the relationship between what the player sees (the set of possible inputs for a given Situation) and what the game designer creates (a list of rules and so forth that determines what a given Situation is and how the player can act therein).
The secret of game design, the purpose of having a coherent theory of game design in the first place is to answer the following question: how does a particular set of rules create a specific set of Situations that the designer would feel that a player considers interesting and potentially entertaining? That is, a full theory of game design answers the vital question of Chess. How do these seemingly simple rules create such a degree of complexity, depth, and challenge?
However, we may not want to use game design to create "complexity, depth, and challenge." We may want to do something else. Game design can be used to create other emotional reactions (fear, suspense, etc) or to do things we haven't really thought of yet. So a greater, more general formulation of the question is this:
Given a specific goal for a game's design, how do you create the appropriate elements to achieve this goal?
One problem with this question: it may not be answerable.
That being said, the Situation Model is a good tool for answering this question. Using it as a model, a game designer can test bits of gameplay (whether as a thought experiment or as a live prototype) and attempt to experience the game using particular bits of Knowledge and/or Experience. As a design tool, its most useful purpose is making sure that the decision making portion of the game is without pathologies, difficult to the specific degree the designer wants, and has the specific pacing and advancement that the game designer wants.
The Situation Model is a priori knowledge. That is, it is derived entirely from logic based on premises. You could derive the Situation Model before there were videogames, or even before there were games.
As we come to understand the decision making process, we can also see how certain aspects of game design work to create Situations. For example, the primary difference between Chess and Tic-Tac-Toe with regard to decision making depth is that Chess is, thus far, not solved. That is, we do not know the single path that leads to complete victory (or guaranteed stalemate). Tic-Tac-Toe is solved; there is a single best answer which, if taken by both parties, is guaranteed to lead to a tie game.
One of the principle differences is that Chess has a wealth of decisions available to the player from the start. Tic-Tac-Toe, even in its opening move, only really has three (corner, center, side). So, as an ad-hoc rule, one could say that the number of decisions available increases the depth of the game.
Of course, looking at other games can show that this only holds when those decisions are actually important. If some decisions are clearly wrong, then there are fewer actually viable decisions.
This kind of information is an example of a posteriori knowledge. That is, it requires evidence from the world to understand. It requires a degree of experimentation, rather than purely bound to logic.
Until we find an a priori mechanism that can directly answer the fundamental question of game design, until we have a way to know the unknowable, we are going to have to develop rules based on a posteriori knowledge. We're going to have to look at specific instances and develop a theory of how game design becomes what the player plays.
Articles in the "Design Details" section will explore this kind of a posteriori knowledge in an attempt to deduce some kind of theory of game design.