Game Development Reference
In-Depth Information
FIGURE 7.6
By reducing the price of the warranty, the expected utility of purchasing
the warranty is better than what we can expect by not purchasing it.
The math works out to:
Now, with our half-price warranty in hand, the expected value of the whole
shebang is a negative $150. However, as we saw before,
not
purchasing the warranty
will cost us about $180. This time, despite the fact that the computer is just as reli-
able as it was in the first example in Figure 7.6 (for whatever
that's
worth), we see
that
E
(
W
) >
E
(¬
W
). The difference in the price of the warranty made it more
worthwhile to purchase. More accurately, it made it less of a drain than the
poten-
tial
of the computer breaking and us
not
having the warranty.
Generalizing the Formulas
Remember, however, that we are assuming that the failure rates are static and ac-
curate. We have only “solved� the situation for those figures. It would behoove us
to formalize the formula (so to speak) so that we can apply it to all combinations of
parameters just by plugging in the numbers.
The above equations show that this is actually a simple process. Once we have
the different variables that we need laid out in the proper arrangement, calculating
the two utility values is rather straightforward.
