Game Development Reference
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of the guests. Rather than simply guessing (which is not a very suitable task for
computers), we would be tasked with determining what formula(s) we would use
to take into account what the other agents would be doing.
It is in that neutral territory that behavioral mathematics comes into play, and
likewise, where we need to use observation and a little inference to construct those
behavioral algorithms properly to adequately fill that gap.
Q UANTIFYING O BSERVATIONS
Converting ideas into numbers alone might not be as hard as it seems, however.
Quantifying things not just in ordinal terms (e.g., A is greater than B) but in pre-
cisely relative terms (e.g., A is twice as big as B) nudges us closer to the realm that
computers can use to calculate and therefore closer to what we can use in game AI.
In this case, we must ask another question. Just as the prior query was “What is im-
portant?� this one could be phrased, “How much more important is it?�
Counting on the Edge of a Razor
I will illustrate with an example from my own life that came as something of an
epiphany to me—and, given the circumstances, was a sure sign that I needed to step
away from AI development for a day or two. It came while I was shaving.
If you happen to use refillable razor cartridges as I do, they may come in a plas-
tic container of five cartridges (Figure 2.3). If I were to ask you the odds of any of
those particular cartridges being in use, you would likely give the mathematically
simple and straightforward answer of one in five—or 20%. That would certainly be
reasonable to assume. However, there is a subtle difference to be illustrated here. If
you were to randomly select from my five cartridges, each of the five would have a
20% chance of being selected by you. Likewise, if you knew nothing else of the
situation, a random selection that you made would have a 20% chance of being
the correct cartridge. However, that doesn't mean that each cartridge has a 20%
chance of being in use at any given moment.
What if I told you that I always use the cartridges in order, from the top one in
the container down to the bottom one? Would that change your decision? Why?
After all, you were not asked the order in which I use them. You were not asked to
guess which one I would use next based on which one I was currently on. You don't
know how long ago I purchased the refill pack. You don't know for how long I typ-
ically use one blade.
 
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