FUNDAMENTALS OF GAME DESIGN, SECOND EDITION
Numeric and Symbolic Relationships
This section discusses the differences between the numeric and symbolic relationships and how you may combine them to achieve your design goals for the core mechanics.
Numeric relationship means a relationship between entities defined in terms of numbers and arithmetic operations. For example, the statement "A bakery can bake 50
loaves of bread from one sack of flour and four buckets of water" specifies a numeric relationship between water, flour, and bread. Here is another example: "The probability of an injury occurring to an athlete in a collision with another athlete is proportional to the weight difference between the two athletes and their relative speeds at the time of the collision." Although this second example leaves the precise details up to the programmer to decide, it does specify a numeric relationship: Weights and speeds, both numeric attributes of the athletes, go into computing the probability of an injury, a numeric entity. (Remember that an attribute is just an entity that belongs to another entity.)
Defining numeric relationships precisely requires some familiarity with algebra and arithmetic. First, you must ensure that you use meaningful equations; if you write that the speed the convoy will travel is in part a function of the quantity defined by (the weight of supplies) v (number of pack horses - number of camp followers), you may very well end up with a divide-by-zero error. Because the resulting value interacts with other parts of the mechanics, changes in the way you calculate that value will have a domino effect, ultimately influencing the gameplay itself, and you must be able to understand and predict these effects. Chris Crawford's Balance of Power: International Politics as the Ultimate Global Game (Crawford, 1986) remains one of the best books ever written on numeric relationships in the core mechanics. Although it is out of print, used copies are still available from online bookstores. The text is also available in ASCII form at www. erasmatazz. com/library/ Balance%20of%20Power. txt.
Numeric relationships lie at the heart of internal economies, and the later section "The Internal Economy" discusses them further.
The values of symbolic entities—red, on, empty, found, and the like—cannot be added together or otherwise manipulated mathematically. You must specify all the states that a symbolic entity may represent, and the relationships among them, without equations. For instance, the red, yellow, and green states of a traffic light are not related to each other numerically; they're simply different. To use a traffic light, you must document how it gets into each of its possible states and how the light in each of those states affects the behavior of other entities. To define the behavior of an NPC driver who sees a traffic light, you would write three separate mechanics into his AI, one for each state of the light, to say how the driver reacts to seeing a red light, a yellow light, or a green light. When any entity in the game (such as a driver) interacts with a symbolic entity (such as a traffic light), you must state exactly what happens for each possible symbolic state of the entity. If you leave one state out, no interaction will occur with that state.
A binary (two-state) entity is sometimes called a flag. You will often create flags in your game to document whether the avatar has entered locations, overcome specific obstacles, and so on.
This chapter doesn't discuss symbolic relationships much further because they are relatively easy to define and their results are easier to predict; numeric relationships are harder to create and tune. Although it is possible to create extremely complicated symbolic relationships (think about Rubik's Cube), most of the symbolic relationships in games tend to be rather simple.
INTEGRATING SYMBOLIC AND NUMERIC RELATIONSHIPS
A symbolic entity can contribute to a mathematical function if you have a mechanic that associates a symbolic entity into number. For example, the state of a car's transmission is symbolic; the transmission is either in one gear or another, and you can't add gears together. But you can make a table that shows the gear ratio of each gear, and use the results to make computations about the speed of the driveshafts. For example you can specify, "In first gear, the ratio is 3.83 to 1. In second gear, the ratio is 2.01 to 1. In third gear, the ratio is 1.46 to 1. In reverse gear, the ratio is 4 to -1. The negative value causes the driveshaft to turn backwards."
This mechanic converts a symbolic entity (transmission state) into a numeric entity (gear ratio).
