Game Development Reference
In-Depth Information
Checking Our Premises
To find out what the actual probabilities are given our remaining two doors, we
need to walk through the problem. When our decision time comes, there are two
possible scenarios.
1. We picked correctly.
2. We did not pick correctly.
Before we let our 50/50 mentality lead us forward, we need to check the premises
on which that 50/50 mentality is based. To do that, we have to understand what
happened
prior
to the “keep or switch� decision. Somewhere between our initial
choice of which door we wanted and our
second
choice of whether to keep or switch,
something very relevant happened—but we have to know where to look for it.
As we know, the only event that happens in that time frame is that the host opens
a door for us, showing us what is behind one of the doors that we did
not
select. As
we have done before in Chapter 5, we need to now put ourselves in the role of the
host. What decision is he making in that time? What information is he using to
make that decision? And most importantly, what information does that convey
to us for our keep or switch evaluation?
First, let us analyze what happens if we had picked correctly to begin with
(Figure 6.4). At this point, the host is faced with two doors behind which are goats.
It doesn't matter which one he elects to reveal to us. He could pick either one and
it doesn't change the end result. We are, indeed, faced with a car (our door) and a
goat (the door he left for us).
FIGURE 6.4
In the Monty Hall Problem, because the host knows where the car is,
his selection of which door to reveal is more important than our initial, blind selection.
Always switching doors nets us a two-thirds chance of winning the car rather
than the expected one-half chance.
