Game Development Reference
In-Depth Information
Given our vast experience with technology, we could apply what we believe are
reasonable probability figures on this. We believe the odds of the computer contin-
uing to work for the entire year are 70%. (Again, give me a break… it's a hypothet-
ical.) We give it a 20% chance of needing a minor repair and a 10% chance of
becoming a proverbial doorstop.
By applying the percentages and the associated costs for the various events, we
achieve the figures shown in Figure 7.4. No matter what happens during the dura-
tion of the warranty, we are out the $300 we paid for it. If we
don't
buy the warranty
and nothing goes wrong, then we don't lose anything. If the computer requires
fixing, we have to pay $200 for the repair job. If something goes amiss and we must
toss it on our ever-growing pile of defunct electronic equipment, we are out the
entire $1,400 we paid for it. (May I suggest at this point that we
don't
replace it with
a computer of the same model?)
FIGURE 7.4
The prices for the computer and the warranty can be combined
with the expected percentages of needing repair or replacement to
determine whether or not to purchase a warranty for a new computer.
Similar to what we did with previous examples, we are going to attempt to
calculate our expected utility for the prospective warranty. For a change, we now have
solid numbers with which to work. As much as I don't want to make this a formula-
laden book, I want to walk through the mathematics of this particular example.
For those of you not familiar with reading statistical and logical notation, I will
explain a bit of terminology. First, we will define
W
as meaning the purchasing the
warranty. The symbol “¬� means “not.� So ¬
W
would mean “not
W
�—or in this
case, “not purchasing the warranty.�
To calculate the relative benefits of each of those two paths, we need to calculate
the
expected utility
(
E
) of each of either purchasing (
E(W)
) or not purchasing
(
E(
¬
W)
) the warranty. This involves taking into account the cost of the three
possible outcomes in a manner that also respects the likelihood of those outcomes
occurring.
