Table of Contents

What's the Page for
This page is an index of different ways to generate random numbers within a variety of ranges with "common" polyhedral dice. It is thus also (in part) a way to emulate some of the Zocchi "exotic" dice (d3, d5, d7, d14, d16, d24) with gardenvariety dice (d6, d8, d12, d20). This is not to lower the value of a range of polyhedra; rather, it is to emphasize their aesthetic importance by illustrating how strictly unnecessary they are.
Speaking narrowly, you could generate a flat probability range for any number with poker chips and a black marker, marking them up with a zero on one side and a power of two on the other. This would require a hypothetical universe of supernormally long gaming sessions and attention spans. All of the other possibilities are choices we make by preference ease, speed, uniformity, and style. As explained elsewhere better than I could (by James Maliszewski), the last bit is important.
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The charts below are unnecessary, though they save some arithmetic that (though you can become pretty fast at it) can slow things down, especially at first. You can always determine the number by doing the math like so:
d6 as d3 and d20 as d5, base 5
Roll the d6 as if you were generating 13, and subtract 1. This is, in the parlance of elementary school, the "fives" number: Multiply it by 5, and add it to the d20's 15 result. This means the two dice will generate a number from 115. If you only want 114, reroll 15's (ie, 56 on the d6 and 1720 on the d20).
In any case, here are some number generation methods. I've to prefer methods that use fewer dice, that use platonic polyhedra, that skip the d4 (because I don't like how they roll!), and that minimize rerolling. Feel free to critique or elaborate! When dice are described as big/small, it indicates that the number of sides are the same, so you need two different colors.
 Zocchi numbers and aesthetics
 cool dice
 flat distributions
 platonic solids
 die priority
 base 'technique', factoring
The Numbers (1X)
2,3,4,5,6,7,8
2,3,6: d6
4,7,8: d8
5: d20 (to avoid rerolls of 6)
9
2d6 as d3, base 3
Big/Small  12  34  56 

12  1  2  3 
34  4  5  6 
56  7  8  9 
10, 11, 12
10: 1d20 / 2
11,12: 1d12, reroll 12 for 111
13,14,15
d6 as d3 and d20 as d5, base 5
d6/d20  14  58  912  1316  1720 

12  1  2  3  4  5 
34  6  7  8  9  10 
56  11  12  13  14  15 
16
2d8 as d4, base 4
Big/Small  12  34  56  78 

12  1  2  3  4 
34  5  6  7  8 
56  9  10  11  12 
78  13  14  15  16 
17, 18
d6 as d3 and d6, base 6
Big/Small  1  2  3  4  5  6 

12  1  2  3  4  5  6 
34  7  8  9  10  11  12 
56  13  14  15  16  17  18 
19, 20
magic!
21, 22, 23, 24
d8 as d4 and d6, base 6
d8/d6  1  2  3  4  5  6 

12  1  2  3  4  5  6 
34  7  8  9  10  11  12 
56  13  14  15  16  17  18 
78  19  20  21  22  23  24 
or d6 as d3 and d8, base 8
or d12 and d6 as d2, base 2
25
2d20 as d5, base 5
big/small  14  58  912  1316  1720 

14  1  2  3  4  5 
58  6  7  8  9  10 
912  11  12  13  14  15 
1316  16  17  18  19  20 
1720  21  22  23  24  25 
30
d20 as d5 and d6, base 6
d20/d6  1  2  3  4  5  6 

14  1  2  3  4  5  6 
58  7  8  9  10  11  12 
912  13  14  15  16  17  18 
1316  19  20  21  22  23  24 
1720  25  26  27  28  29  30 