An experience can be abstractly represented as a set of possibilities (a "possibility space"). These are all the possible events and/or goals that could occur during the experience. Each icon on the diagram to the right represents one of those possibilities. A given experience might have anywhere from a very small possibility space to a practically infinite possibility space, and the diagrams here are generally much smaller than most experiences would be in reality. The point of these diagrams is not to accurately map out the possibility space of real experiences, but to give an abstract visualization of experiences in general.
At any given time during the experience, the audience can only perceive some of the possibilities. The diagram to the left shows a snapshot where the audience can see most of the possibilities, but there are still additional possibilities that they do not yet perceive. Which possibilities the audience perceives is a combination of what they have experienced so far and the model they have developed of the experience. In reality, the non-perceptible possibilities are generally much more numerous than these diagrams imply.
Some of the possibilities in the space may be perceived, but are not actually possible. The diagram to the right shows an example of how this might look. Generally, these perceived possibilities that are not actually possible represent ways a story could have gone, but in the end did not, or a goal that ends up being unattainable (due to the way the experience works, lack of skill, etc.), or similar situations in other media forms. These are not automatically bad, although they can be frustrating if the audience really thought it was possible and was really anticipating it happening. These types of "false" possibilities are often critical to surprising the audience and making an experience interesting.
Meaningful Possibility Space
The size of a possibility space alone doesn't matter very much until the "quality" of each possibility is considered. Possibilities that are meaningful to the audience are much more important than ones that are not. A particular possibility (for a particular audience) could range from meaningless to deeply meaningful. A story that is very obvious and just follows standard tropes has little meaning, while a story filled with emotionally resonant choices and clever twists has a lot of meaning. A game that has a single dominant strategy has almost no meaningful possibilities, while a game that has hundreds of interesting and viable strategies has many meaningful possibilities. Depth can come from any type of element, not just interactive or narrative elements.
The diagram on the right represents how meaningful a given possibility is through the size of the icons. This gives an abstract way of visualizing the meaningful possibility space of an experience, which is what matters when creating engaging experiences.
While the amount of meaning each possibility has is subjective depending on the audience, it is not arbitrary. Possibilities that satisfy one or more of the core psychological motivations of the audience (autonomy, mastery, connection, novelty, and safety) will be meaningful, while those that don't will not be meaningful.
Interactive, Directed, and Undirected
The diagram to the right shows an abstract representation of a typical interactive possibility space. The various possibilities of the experience (represented by the icons in the grid) have been carefully constructed by the designer, but anyone engaging with the experience can make various choices about how they go through it. In this case, the designer builds and releases tension by presenting the audience with interesting goals to pursue (which builds tension) and obtain (which releases tension). The audience has some control, but is being guided through the experience by the designer. Note that in this case, not all possibilities were explored, but the audience generally followed a path where the meaning of each possibility (represented by the size of the icons) increased over time (as the designer intended).
In a non-interactive experience, such as a book or a movie, the writer or director will directly dictate the audience's path through the possibility space, as shown in the diagram to the left. The possibility space is generally much smaller in these experiences, but it can still be very engaging because the path through that space is so skillfully crafted and controlled, with very finely tuned building and release of tension. (In this case, the red icons are possibilities that the audience thought might occur, but were not actually part of the directed experience.) If the experience is primarily a narrative one, tension is built through story and character conflict (and released when those conflicts are resolved). In a visual or musical experience, tension is built through contrast of visual or audio elements. Even experiences build on kinesthetics, smell, or taste will use contrasting elements to build tension.
On the far extreme in the other direction is the undirected interactive experience. This type of experience general presents the audience with a large world of possibilities to explore, but doesn't really attempt to guide the audience through it (or does so only to a small degree). Here the audience chooses their own goals; it is the designer's job to just make sure the possibility space is so interesting that it is easy for the audience to choose goals that build and release tension in an effective way. The diagram to the right shows how this might look, with the possibility space being much more chaotic and the path through that space being much more haphazard. Despite the unstructured nature of an undirected experience, it can still be deeply engaging because the chosen goals can be exactly what is most meaningful to the specific person going through it, instead of having goals that must appeal to a much wider audience.
Increasing the size of the meaningful possibility space (i.e., the potential depth of the experience) is a very different task than guiding the audience through that space in a skillful way. Some creators are much better at creating possibilities, while others are much better at guiding the audience through those possibilities. Different experiences rely on different blends of these two things.
The total "amount" of meaning of the entire possibility space is referred to as the depth of the experience (obviously, this cannot really be measured accurately). Most of the time, however, we have to be concerned with the perceived depth, not just the potential depth. If the audience cannot perceive enough meaningful possibility, they will leave the experience before getting to the depth that is actually there. Of course, increasing the depth of an experience through increased complexity will not work if the audience's mental model becomes too complex, as they will either be unwilling to continue the experience or unable to perceive the depth that is there.