Game Development Reference
In-Depth Information
FIGURE 8.9
As the value of a prize goes up, the marginal utility of each increase gets
smaller. As the value of a wager goes up, the marginal utility of each increase gets larger.
Of course, as with many of the concepts that we discuss in the topic, trying to
mathematically describe “enough� is a bit more art than science. In the St.
Petersburg paradox, the graphs we used were indistinct in that our scale of value
ran from zero to
n,
infinity, or generally “somewhere over there someplace.� The
utility axis was even more hazy in that it really only expressed “more� or “less� utility.
In a sense, that was by necessity since the entire dilemma dealt with “personal pref-
erence in the space of possible infinity.� If that isn't vague, I don't know what is.
In the examples we have shown so far, some of the thresholds we have set have
been concrete. In the case of declining health, reaching zero health is a fixed point.
There is nothing subjective about it. The same could be said for spending our last
dollar. Some thresholds are defined by the rules of the environment. In Monopoly,
the rules of the game state that three properties of the same group have more util-
ity when combined than they do individually. Therefore, it is an inherent property
of the game that three properties is an important threshold for determining mar-
ginal utility.
On the other hand, some of the thresholds we suggested were somewhat more
flexible. In the case of building soldiers to defend our town, we arbitrarily decided
that four soldiers was enough. We made a design decision. The same could be said
