Game Development Reference
In-Depth Information
Thankfully, we have plenty of techniques at our disposal for generating normal
distributions of all sorts of sizes and shapes. Interestingly, many of us “older folks�
were introduced to these techniques in the form of hunks of acrylic or hardened
plastic—dice.
A Fantasy RPG Introduction to Real Statistics
The pen-and-paper role-playing games (RPGs) in the mold of Dungeons & Dragons
(D&D) were many people's unwitting introduction to probability and statistics.
This phenomenon became so ingrained in the gaming culture that many people
still refer to probability curves in terms of combinations of dice. If I write terms
such as “2d8� and “3d6,� there is no shortage of people that recognize them as “the
sum of the rolls of two eight-sided dice� and “the sum of the rolls of three six-sided
dice,� respectively. In fact, the latter was a D&D staple for generating the six char-
acter “ability scores� —strength, intelligence, wisdom, dexterity, constitution, and
charisma. This is not a coincidence.
As we mentioned before, we often find normal distributions in nature. Traits
such as the six listed above are natural candidates for us to plot on normal distrib-
utions. Using strength as an example, most people are going to have a strength that
is near a concept of “average� strength. The farther away from that average we go,
the fewer people we will find who fit the description. There will be a very select few
who are at the extremes—those who can barely lift their own hands and those that
can heft small planetoids. This fits with what we know of the characteristics of a
normal distribution. The same can be said for intelligence; most people are fairly
close to average, with very few at the extremes. These characteristics of population
distribution are why the creators of D&D elected to generate ability scores in the
fashion that they did: “Roll 3d6� (Figure 11.7).
Perusing the D&D literature, there is a veritable cornucopia of die-roll combi-
nations in evidence. Although I am not willing to invest the time to prove it, I believe
the creators used every possible combination of dice at least once. (That is not a
small number, either.) Die-roll instructions have their own formalized protocol
that is very expressive. Using simple operators, you can instruct someone on exactly
the way to use those tumbling tools to generate the distribution that you are trying
to achieve. Some examples are:
1. d20
2. 3d4
3. 2d6 + 1
4. d6 + d10
5. 3d8 + 2d4 + 10
6. d10
Ă—
10 + d10 (for generating numbers from 0 to 99)
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