Game Development Reference
In-Depth Information
Compare this to the estimated utility of
not
building a tower.
Again, we find that
E
(¬
T
) >
E
(
T
). Therefore, the estimated utility of
not
build-
ing the tower is greater than that of building it.
Many factors go into this determination, so the decision is rather tenuous.
Certainly, the building costs of the barracks and the tower have a lot to do with the
determination. However, one of the major components is our
assumptions
about
the likelihood of attack. In this example, we are using what is probably a rather
naïve assumption that there is a 30% chance that our barracks won't be attacked at
all. Likewise, we are assuming only a 20% chance that it will suffer a large attack.
This may be the case if the barracks is well back behind our lines deep in our city.
In that case, by simply using some nonmathematical reflection, we could agree that
not having a tower over the barracks would be justified.
However, if we were to change these assumptions about the susceptibility to at-
tack—perhaps by assuming the barracks would be along the front lines—we would
expect the utility of an accompanying tower to shift as well. For instance, let's use
the same costs for the buildings and the damage estimates but change the attack
probability figures to something that is more in line with a typical “in the thick of
things� RTS scenario.
No Attack:
5%
Small Attack:
60%
Large Attack:
35%
As we can see by the updated figures in Figure 7.8, by simply changing the ex-
pected percentages of attack, the utility functions have swung significantly in favor
of building a tower. The equations themselves would now be as follows:
