Game Development Reference
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middle. There are 216 possible combinations, producing 12 possible values from 3
(1 + 1 + 1) to 18 (6 + 6 + 6). There are 27 ways to throw a 10 or an 11, but again, only
one way to throw a 3 or an 18. In other words, you're 27 times as likely to roll a 10
as you are an 18.
The Gaussian Curve
When you add dice together like this, the probability of each possible result forms a
bell-shaped, or Gaussian , curve, a phenomenon familiar to mathematicians. Figure
10.6 shows a graph of all the possible results when rolling three six-sided dice and
adding the resulting numbers.
It's important that you realize what this means for your game. If you use this addi-
tive dice mechanism and you specify that a player must roll an 18 to succeed at a
task, he has only one chance in 216 of actually rolling it. That's less than one-half
of 1 percent. In other words, it will almost never happen. This system is not the
same as rolling one die with 16 faces numbered from 3 to 18. With one such die,
the chance of rolling an 18 is identical to the chance of rolling any other face, one
in 16, or 6.25 percent. That's far more than one chance in 216.
FIGURE 10.6
The Gaussian curve
produced by rolling
three six-sided dice
and adding the result-
ing numbers
30
25
20
15
10
5
0
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Added Values of Three Six-Sided Dice
These curves describe many phenomena in the universe, from the pattern of water
droplets falling from a central point to the intelligence levels of animals (and
humans). To put it succinctly, most things lie somewhere in the middle of the
curve; rare things lie in the extremes. When that's the sort of effect you want in
your game design, use a Gaussian distribution.
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