Game Development Reference
In-Depth Information
Substituting Normal or Triangular Distributions
If the above calculations are prohibitive, we can obtain much the same result by
using a normal distribution. If we set the range to be slightly more than twice what
we would normally be using for
λ
(that is, half of the curve would be on either side
of
, and slightly skew the curve to the right (i.e., make the
positive portion of the tail longer than the negative), we can achieve a similar
distribution. We can even generate very similar results without the skew on the nor-
mal distribution. What we end up with is a normal distribution that amounts to
λ
), position the mode at
λ
λ
,
+/- half of
λ
, centered on
λ
.
To tie off a loose end that we left dangling earlier in the chapter, we will revisit re-
constructing our Guess Two-Thirds participants. We had identified three different
types of guessers. We are going to break that into four types for purposes of this
exercise. We also identified the rough percentages of the whole that each of these
groups of people represented. To recap:
Group
%
“33� guessers
4
“22� guessers
3
Random guessers
30
Semi-logical guessers
63
When generating a random guesser, the first thing we need to determine is
which of the four categories the guesser is in. The result of that will determine our
next course of action. Once we know the
type
of guesser we are working with, we
then select what process we want to use to generate their actual guess. In the case of
the “33� and “22� guessers, the answer is simply 33 and 22, respectively. The ran-
dom guessers (30% of the population), as we determined earlier, would divide their
guesses up across the entire range from 0 through 100.
As we discussed before, the semi-logical bunch requires a bit of special treat-
ment. We noticed that they fall roughly into a normal distribution with a range
from 0 to about 70. The distribution has a slight right skew that shifts the bulge of
the population from its natural center of 35 to a new mode of about 25. However
we construct it, we know that 63% of the time, our guesser needs to pick a guess
from that distribution.
So… let's throw this model into some code using the tools we laid out earlier.
