Game Development Reference
In-Depth Information
To artificially model a population, we need to identify the key components of that
population. We need to make some broad assumptions about the decision that the
population faces and use those conjectures as both building blocks and constraints
as appropriate. Much like setting out stakes and lines defines where we will build a
house, identifying, measuring out, and fixing in position the important features of
our population is a necessary step in the process of constructing an accurate model
of a population. From that model, we can then make the assumption that any one
sample drawn from that population is representative of a randomly selected mem-
ber of that population. The
law of large numbers
suggests that the more samples
we draw from that model, the more the aggregate of our selections begins to mimic
the population as a whole.
For example, if we fill a bag with five red balls, three blue balls, and two green
balls, and then select randomly from the balls in the bag, we have no idea which
color ball we are going to select on any given draw. We can say nothing about the
individual selection. While we can suggest that we may select a red ball about as
often as a non-red ball, we can't exactly predict which color we are going to select
next
. We also can't say
why
we picked the color we just did. We didn't follow a rule
that said, “You will pick a green ball this time.� However, over time (and assuming
that we replace the selected ball each time), we will find that we are selecting red
balls 50% of the time, blue balls 30% of the time, and green balls for the remaining
20% of the time.
By artificially defining a distribution of colored balls, we can model an eventual
distribution of those colors without necessarily prescribing the color of any individ-
ual draw. Similarly, by defining a distribution of any behavioral trait or decision, we
can model an eventual distribution of these traits or decisions without prescribing
any individual event or agent.
In Chapter 4, we glibly recalled the marketing staple “four out of five dentists
surveyed recommended sugarless gum….� This does not mean that any given den-
tist recommends sugarless gum to 80% of his patients. This means that if we were
to select a random dentist, we are 80% likely to have selected one who recommends
sugarless gum. The statistic as a whole tells us nothing about any individual dentist.
However, if we were to attempt to model that population in a game, we could
leverage that one number. It wouldn't be difficult to create a game (“Dental
Prophylaxis Simulator�) wherein the player would discover that 80% of the dentists
he encounters recommend sugarless gum. That experience would mesh with what
we know of the real world (or at least what the marketing folks have told us about
the real world).
