Game Development Reference
In-Depth Information
Reconstructing a Guesser
In the case of the Denmark experiment, each possible selection from 0 to 100 has a
number of people who selected it. Focusing only on the segment of semi-logical
guessers again, we don't care why they selected the number that they did. After all,
there are probably 15,000 of the initial 19,000+ respondents in that category. However,
by analyzing how many picked each number, we can remix those exact figures and
turn them into likelihoods that any one person would pick those numbers.
For example, if 2% of the people picked the number 29, we could assume that
any random person had a 2% chance of picking 29. If 1.3% of the people picked 15,
we could assume that any random person had a 1.3% chance of picking 15. If 0.3%
picked the number 70, we can assume that any given person has a 0.3% chance of
picking 70 as well.
Selecting the Proper Tool
While the curve that defined the dentist's recommendations was relatively simplistic,
and the curve that resulted from the respondents in the Guess Two-Thirds Game
was slightly more involved, there are plenty of standard curves that fit many situa-
tions. Additionally, we can tweak, adjust, and even combine each of the standard
curves with each other to build in subtle nuances. We can use these results just as
we did above—to model the likelihood of any given person from a population in
proportion to that type of person's occurrence in the population. If we do this
process carefully and correctly, we can model a startlingly deep array of behaviors.
But first, we must learn about some of the common tools of the trade. At the
end of this chapter, we will use some of the tools to address the Guess Two-Thirds
population problem above.
U NIFORM D ISTRIBUTIONS
For the sake of completeness and of setting a base from which to work, we must
first at least pay a passing recognition to uniform distribution . As the name im-
plies, it is a probability distribution that is… well… uniform . Every item in the pop-
ulation has an equal chance of being selected. Examples are not hard to come by. If
we were to flip a coin, the odds of heads or tails showing would be uniformly dis-
tributed between the two options. If we roll a fair die numerous times, we would
find the result of the rolls to be uniformly distributed among all the sides. Each of
the 52 cards in a deck has an equal opportunity to be picked; therefore, the proba-
bilities of each card being selected would be uniform. When we ask the computer
for random numbers (yes, I know they are actually pseudo -random numbers), we
 
 
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