Game Development Reference
In-Depth Information
Therefore, if we
always
switch, we win two-thirds of the time. The only time we
would lose is if we had originally picked correctly—and that only happens one-
third of the time. Notice how this is different from our original 50/50 premise?
What Did We Miss?
The question is, what information did we miss the first time that led us to the
wrong conclusion? Research has shown that, for whatever reason, people seem to
dismiss the host's selection of doors to reveal. They are so caught up in the random-
ness of their initial selection and the subsequent, seemingly random selection of
whether to keep or switch that they neglect to consider the thought process that
went into the host's decision. People seem to ascribe a similar random nature to the
host's decision. They don't take into account the fact that the host
knows
where the
car is. His decision is
not
random; he is trying to make you choose. After all, Monty
Hall's game was not titled
Guess the Right Door
; it was called
Let's Make a Deal
. The
attraction to the game was not seeing whether or not you got the car on the first se-
lection. It was in the tension surrounding the decision of whether or not to switch.
For that scenario to arrive, the host could
not
show you the car—and in doing so,
tip his hand.
If we think back to the examples in Chapter 1, Monty was not the Blackjack
dealer mindlessly dealing out random cards and following prewritten rules. Monty
was in the role of the Poker player from Chapter 1, making his own decisions that
directly affected yours. (Ironically, on any given show, he may have been the only
person in the studio to
not
wear a stupid hat.)
So, it turns out that a puzzle that is certainly solvable from a logical, rational,
mathematical standpoint fools most people to whom it is presented. Even people
who get it right often do so for the wrong reason. Looking back at our normative
decision theory criteria:
Has
all
of the relevant information available
Is able to
perceive
the information with the accuracy needed
Is able to perfectly
perform
all the calculations necessary to apply those facts
Is perfectly
rational
We had all the relevant information
available
to make a decision. We were able
to
perceive
the information accurately enough. Most people would be able to
perform
the very simple probability calculations with all the accuracy needed. And, with all
of the above, we seemed to be acting in a perfectly rational fashion. The problem
that slipped through was that, while we were
able
to perceive all the information, we
