Game Development Reference
In-Depth Information
For instance, in Chapter 6, in my introduction to the Monty Hall Problem, I
mentioned that my wife suggested that getting the goat instead of the car wouldn't
be too bad. I disagreed. She and I have a differing opinion on the relative merits of
goats and cars. We put different utilities on them.
As a slightly less bizarre example, I put a differing value on a decent steak than
does my wife. She, on the other hand will pay massive amounts of money for her
particular favorite latte—which I view as paying money for coffee-flavored milk. I
just don't get it. The technical restatement would be,
I have a different utility for
lattes than does my wife
. It costs the same no matter which one of us buys it, so the
value
of the latte is the same regardless. This is something that we accept as part of
human nature (and something we will attempt to quantify later).
To some extent, these differences can be modeled mathematically. While not
accounting for everything, it gives us a starting point from which we can grow,
tweak, and massage.
Probably one of the easier ways to examine utility is to do so in the realm of com-
parative values. By using ordinal rankings, we are able to achieve a sense of relation
between objects or thoughts—that is, “This is
more
important to me than that.� At
that point, we can then begin the process of scaling things in a way that provides not
only quantification but direct comparison—for example, “This is
twice
as impor-
tant to me as that.�
Blaise Pascal was one of the 17th century's more amazing minds. His contribution
to mathematics came by way of trying to help out a French aristocrat kick his gambling
habit. Despite Pascal's religiosity, he did not preach to his friend about the evils of gam-
bling. Instead, he provided mathematical advice on how to win at gambling.
He took up the question with Pierre Fermat, the wellspring of what we now
know as modern calculus. In what was likely a series of conversations that included
more numbers and symbols than actual words, it is likely that Pascal invented prob-
ability theory—and set in stone the underpinnings of today's casinos.
Pascal stated that when it comes to making bets, it is not enough to know the
odds of winning or losing. You need to know what is at stake. For example, you
might want to jump into a bet despite unfavorable odds if the payoff for winning
would be really huge. (Which explains today's multi-million dollar lotteries.)
Conversely, you might consider playing conservatively by betting on a sure thing
even if the payoff is small. Of course, betting on a long shot wouldn't be terribly
wise if the payoff is small. You might as well hand your money out.
