Game Development Reference
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offer a justification that shows they aren't acting in an entirely random fashion…
they are simply wrong in their logic. Thankfully, plenty of studies have been done
on Mr. Hall's challenge. Science has seemed to nail down exactly where people go
wrong. Before I give away the answer, however, it is educational to approach the
problem blindly.
The actual scenario presented predates
Let's Make a Deal
significantly.
Variations on it can be traced back over 100 years. Joseph Bertrand proposed a
similar question now known as “Bertrand's Box Paradox� in his book,
Calcul des
Probabilités
in 1889. Another version is known as “The Three Prisoners.� The Monty
Hall version is a little easier to relate to, however, so we will use that as our example.
In the classic version of the problem, we (as the contestant) are presented with
three doors. We are told that behind one of the doors is a valuable prize such as a
car. Behind the other two doors are gag prizes such as a goat. We are asked by the
host to select one of the doors behind which we believe is the car. Prior to opening
the door, the host opens one of the two doors that we did
not
choose and reveals
what is behind it. At this point, we are now asked if we want to stay with the door
that we chose or if we would like to switch and take what is behind the
other
door
instead. What should we do?
I really have to point out here that when I presented this question to my wife,
she responded, quite genuinely, “But what if I want the goat instead of the
car?� I think it had something to do with not having to mow the lawn. Believe
it or not, her comment was actually more helpful than you may think. We will
cover the very important concept of the relative subjective worth later on in
Chapter 9.
For now, let's work from the premise that: car = cool; goat = lame.
An overwhelming number of people to whom this problem is presented will
stick with their original choice. Usually, the percentage is up around 80%-90%.
Some people will switch, but the reasons they do so are based more on a “what the
heck� attitude more than from any sort of logical deduction. The tragic thing about
this is that, when presented with this problem, the best option is to
always
switch.
It doesn't guarantee you the car, but it increases your odds of doing so.
“But how can that be?� we may ask. After all, with two doors left, we know
there is a goat behind one and a car behind the other. Our odds of having already
selected the door with the car are 50/50, right? This is the logic that is presented by
the people who
do
switch as well. They figure that, with the even odds, switching
makes as much sense as staying. Right answer, wrong reason.
