Game Development Reference
In-Depth Information
In these examples, the math may seem somewhat redundant or excessive. For
example, when buying a warranty, in all three cases the cost is 300. Multiplying
300 by 0.7, 0.2, and 0.1 only to add them back together to arrive at 300 may
seem a little silly. The reason that I do this is to keep in mind that we
do
have
three possible outcomes that we may need to treat separately. While in this case
those three outcomes were the same (i.e., paying $300), in other examples that
we will use shortly, this will not be the case. Please bear with me until then.
The expected values for the two actions are:
In English, the expected utility of purchasing the warranty is to lose $300 over
the course of that year, which is the cost of the warranty no matter what happens.
In the case of not purchasing the warranty:
Again, in more readable terms, the expected utility of
not
purchasing the war-
ranty is a cost of $180 for the year. This reflects the 20% chance of needing a $200
repair and the 10% chance of replacing the $1,400 computer.
Because
E
(¬
W
) >
E
(
W
), this means that the value of
not
purchasing the war-
ranty is greater than the value of purchasing it. However, the result of -180 leads us
to expect that we will have to pay about $180 on repairs over the course of the year.
Different Inputs, Different Outputs
The example above is not a proof that
all
warranties are rip-offs. Given that we per-
formed a mathematical analysis of the problem, our solution is only as good as the
numbers we used. Some of the figures were established in a concrete fashion. For
example, the price of the computer and the price of the warranty are values that we
can point to as being known quantities. Other figures in the example were estimates.
We would have to estimate the likelihood that the computer we are purchasing is
going to need repair work or be cast into the bowels of hell. The question then
arises: What happens when those estimates change?
