Game Development Reference
In-Depth Information
If you have any awareness whatsoever of how gambling odds are set up in such
things as horse races, you are familiar with this concept. The “favorite� horse gen-
erally has nothing to do with how congenial said steed is at parties. It is based
entirely on the fact that many people believe he is the most likely to win. Naturally,
if the aggregate opinion of the people can be trusted, we can assume that makes Mr.
Horse a sure bet—and the payoff is low. However, if there is a horse that is consid-
ered a “long shot� in track parlance, the payoff is significantly higher. It can be…
you aren't likely to win anyway. In a way, the excessive payout would be a reward
for your foolhardiness.
Looking at Pascal's observations today, they don't seem terribly spectacular. It
is something that is ingrained in us on many levels and in many areas of our lives.
However, the premise does merit a closer look at some specifics, if only to help us
identify the steps in the process that has become so intuitive. (We may even find
some surprises.)
The essence of these sorts of decisions is that there is no way of knowing what
the outcome is. Regardless, you have something of yours on the line—the wager.
Given no control over the outcome for whatever reason (be it random chance such
as a die roll or not enough knowledge of the situation such as in Matching Pennies),
you are making what is referred to as a “
decision under risk
.� Pascal was attempt-
ing to solve this problem in the realm of gambling, but it could be applied to every-
thing from the stock market to whether or not to ask out a potential date to
consenting to a potentially risky surgical procedure. (“As with any surgery, there is
the risk of death.�) The best you can do is collect knowledge of the situation, ana-
lyze your choices, and determine what the potential payouts might be. This is what
Pascal brought to the table.
P
ASCAL
'
S
W
AGER
After putting all of this thought into the mathematical laws of probability theory
(and I assume passing on the advice to his gambler pal), Pascal applied his new con-
cept back to his religious beliefs. What resulted is now known as “Pascal's Wager.�
Ol' Blaise wanted to justify, to himself mostly, his belief in God. More accurately,
he wanted to justify his living his life
as if
God existed (which, naturally, includes
believing in God).
He knew, as a good scientist, that it was impossible to
prove
the existence of
God. In fact, he allowed that you couldn't even determine the
probability
that God
existed. However, from his beliefs in the religious teachings, he could apply what
was “at stake� in the wager… eternal life.
