Game Development Reference
In-Depth Information
Laying the two curves over each other (Figure 11.10) makes it easier to see the
differences between them. The first thing we notice is that the 5d7 curve is taller
than the 3d11 distribution. The reason is that the combination of five dice makes
for more possibilities for the middle numbers than 3d11 makes. Specifically, when
using 5d7, 1,451 out of the 16,807 possible combinations (8.63%) yield our median
value of 15. With 3d11, only 91 out of the 1,331 combinations (6.84%) give 15.
FIGURE 11.10
The distribution of numbers generated by 5d7 is narrower and taller
than the one generated by 3d11. Accordingly, the tails of the curve are flatter.
On the other hand, with more dice involved, it is significantly harder to get
them all to play nicely together and roll extreme numbers such as 1 or 30. For
example, to roll a 1 with 3d11, you would need any one of your dice to come up a
1 and the other two dice to show 0. With 5d7, you need to show a 1 on one die…
and then get
four
other dice to cooperate and show a 0 as well. It is my experience
that dice simply don't work well together when you want them to be all nice and
synchronized.
This dynamic is not only what causes the 5d7 curve to be taller in the middle,
but explains why the “bulge� is narrower. The additional probability of the middle
numbers comes at the expense of the extreme numbers. After all, the area under the
two curves is identical. Both of them represent 100% of the possible outcomes. If
we add somewhere, we need to take away from somewhere else. We can see evidence
of this in the difference between the two standard deviations. The 5d7 curve has a
narrower range for its standard deviation because more of the population is com-
pressed in the middle.
