Bell Dice
Dice whose distribution is a descrete integer value aproximation of a bell curve. Bell dice designed to closely match the mean and standard deviation of a flat distribution polyhedral die, commonly designated Dn, and with m sides, may be designated as a Belln:m. While the mean and standard deviation may be a close match, the min and max may vary from the base Dn. Where a smooth distribution is desired larger number of side is desirable.
Curiously, Belln:n, where n <= 10, has the same distribution as a Dn.
Bell dice may be used to obtain the randomness of a difficult to obtain or physically impossible die size. They are not suitable where a uniform distribution is specifically desired, such as a die roll to look up an entry in a generator table. A sampling of Belln:6 :
1d4 |
1d6 |
1d8 |
1d10 |
1d12 |
1d14 |
1d16 |
1d18 |
1d20 |
1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
3 |
3 |
4 |
5 |
5 |
6 |
7 |
2 |
3 |
4 |
5 |
6 |
7 |
7 |
8 |
9 |
3 |
4 |
5 |
6 |
7 |
8 |
10 |
11 |
12 |
3 |
5 |
6 |
8 |
9 |
10 |
12 |
13 |
14 |
4 |
6 |
8 |
10 |
11 |
13 |
15 |
17 |
19 |
Should it be necessary to preserve the min and max, the following Bell dice work:
Bell2:4 through Bell6:4
Bell3:5 through Bell9:5
Bell2:6 through Bell11:6
Bell3:7 through Bell15:7
Bell4:8 through Bell21:8
Bell6:9 through Bell30:9
Bell10:10 through Bell49:10
Bell21:11 through at least Bell100:11