Perl: the Markov chain saw PerlMonks

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A sum of random numbers will be more bell-shaped than a single random number. Hence, rolling 2 6-sided dice will yield more sevens on average than rolling an 11-sided die numbered from 2 to 12. The more dice, the more heavily weighted toward the center of the range you'll be.

For your 6-21 example, there are 16 numbers that need to be covered. You could roll two 16-sided dice, add them together, and divide by two to get a center-weighted result in the desired range.

Here's a little program to demonstrate the distribution:

```my \$range=16;
my \$low_end=6;
my %freq = ();
for (1..1000) {
my \$result = int((rand(\$range)+rand(\$range))/2)+\$low_end;
++\$freq{\$result};
}
print "\$_: \$freq{\$_}\n" for (sort {\$a<=>\$b} keys %freq);
__END__
6: 10
7: 35
8: 44
9: 52
10: 61
11: 77
12: 107
13: 109
14: 118
15: 111
16: 95
17: 46
18: 49
19: 57
20: 24
21: 5

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