A narrator might choose to use a different set
of dice to make skill use more or less
predictible.  The narrator might even decide
to use different sets of dice for different
skills.  The following guidelines tell how
to compute the standard deviation, which
is a good guide to how predictible the
results will be.  The smaller the standard
deviation, the more predictible the results. 
<P>
The expectation of a set of dice can be computed by
averaging the highest  and lowest possible outcomes.
For example, with three six sided dice, the 
result is in the range 3 to 18, averaging to 10.5.  Rounding
down gives the alternative of 10.  
Since this expectation also modifies  
the difficulty factor, using different sets of dice
does not change the average level of success.
However, it can change the likelihood and degree of
results very different from the average.
Generally, a wider range of possible values will
mean less predictible results, while a narrower
range means more predictible results.  However,
the more dice used to achieve the same range, the
more predictible the outcome.  Statisticians
measure this predictibility using the standard
deviation; roughly, the amount by which a 
typical result differs from an average result.
<P>
To compute the standard deviation for a set of
dice, follow the following steps:
<OL>
<LI>
For each die, square the number of sides,
subtract 1, and divide by 12.  
</LI>
<LI>
Add all the results  
from the first step.
</LI>
<LI>
Take the square root of the result.
</LI>
</OL>
Note that this calculation 
is not necessary during play. The Narrator
can do it
before play to pick the set of dice that
corresponds to her intended level of
unpredictibility.  
 
As an example of the calculation,
for two six sided dice, we would
square 6 to get 36, subtract 1, giving 35, and
divide by 12, to get 2 11/12.  Doubling (for
two dice) gives
us 5 5/6.  The sqare root of this number
is around 2.3.  For a single 10 sided die, we
get a standard deviation around 2.8.  Both
have about the same range, but the single
die is more likely to be at its extremes
than the pair.  Some common choices might be:
<OL>
<LI>
No dice.  0 Expectation, 0 Standard deviation.
(Subtract 10 from difficulty levels on charts.)
</LI>
<LI>
1 six-sided die.  Range: 6 outcomes.  Expectation 3.5, standard
deviation 1.7. (Subtract 7 from difficulty
levels on charts) 
</LI> 
<LI>2 six sided dice, Range: 11 outcomes. Expectation 7, standard
deviation 2.3,  (Subtract 3 from difficulty
levels on charts)</LI>
<LI>
1 ten-sided die, Range: 10 outcomes. Expectation: 5.5, standard
deviation: 2.8 (Subtract 5 from difficutly
levels on charts.)
</LI>
<LI>
3 six-sided dice.  Range: 16 outcomes. Expectation: 10.5 
standard deviation: 2.9
No change to charts; default set. 
</LI>
<LI>
4 six-sided dice. Range: 21 outcomes. Expectation: 14.
Standard deviation: 3.4.
Add 4 to difficulty levels in charts. 
</LI>
<LI>
2 ten-sided dice. Range: 19 outcomes.  Expectation: 11.
Standard deviation: 4.1 
Add 1 to difficulty levels on charts. 
</LI>
<LI> 
1 twenty-sided die.  Range: 20 outcomes.  Expectation: 10.5.
Standard deviation: 5.7.  No
adjustment to charts.    
</LI>
</OL>