The Concept of Utility - Behavioral Mathematics for Game AI - page 121

or the roll of a die, the amount of the wager (in this case, the team members com-
mitted to offense) actually changes the odds of success… again, for better or worse.
Of course, our next question—indeed, our next challenge—becomes determin-
ing the answers to those “how much� questions. And for that, we need more than
vague ideas of none, some, more, or all. It's time to start putting values on the util-
ity of our playing pieces.
U TILITY OF M ONEY
Part of our difficulty with Pascal's Wager was the inability to quantify the inputs. In
fact, it was even made worse by using dissimilar measures such as Heaven and Hell
vs. lifestyle. How do those compare? Is cheating on my wife or coveting my neigh-
bor's ox worth even 20% of the value of the Heaven we may give up? Is telling the
truth to my wife about how her new hairstyle makes her look like our neighbor's ox
worth more than 14% of Hell? These are calculations that are near impossible to
make because the comparisons themselves are so vague. (We'll give it a shot
nonetheless a little later on.)
However, by making sure all measures are of the same type, our calculation
process gets much easier. For the moment, let's follow a more intuitive approach by
employing something that we use all the time as a universal quantifier—money.
Money has value that is hard to argue with. Most of the time, the actual value
of any given item of currency is emblazoned right on it for all to see. A $20 bill is
worth… 20 dollars. After all, it says so. The value of that currency relative to other
currencies may change—that's what gives us fluctuating exchange rates. The value
of a currency compared to what it can buy may even change—which gives us infla-
tion and deflation. At that point all we are doing is comparing the value of that cur-
rency with the value of something else.
V ALUE VS . U TILITY
Value is different from utility , however. As we mentioned at the beginning of this
chapter, utility represents the relative satisfaction that we get out of something.
Satisfaction, in this case, can also represent more than just happiness or pleasure. It
can represent the usefulness of an item in achieving a goal.
In the case of Marci holding Marvin Gardens, the original value was represented
by what she paid for it in the first place. As she held it, that value changed as
people were willing to pay more and more for it. The reason for that shift is that
Marvin Gardens had a utility over and beyond the face value of the property—other
people needed it to improve their positions. For Marci, the utility of Marvin