Dice Mechanics: Examples

Silhouette

         Silhouette is the name of the system used in Dream Pod 9's games: "Heavy Gear", "Jovian Chronicles", "Tribe 8", and "Gear Krieg". The die scheme is to roll a number of d6s and take the highest. If you roll more than one 6, you add +1 to the total for each additional 6. Thus, rolling three 6's nets you a total roll of 8.

         The probabilities for the basic roll are given in the table below. The primary thing to note is that, like most highest-roll systems, there are diminishing benefits to additional dice. From 1d to 2d adds +1 to the average. The next die adds only around 1/2, the next die around 1/3, the next die around 1/4. The rule that adds from tied sixes offsets this tendency compared to a straight highest-die scheme, but the tendency is still marked.

         Within RPGs, this means that specialization is less well rewarded compared to fixed-dice systems where you add skill plus a die roll (such as skill + 1d20 or skill + 1d10).

Dice Result Average
1 2 3 4 5 6 7 8 9 10 11 12
1d 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 3.500
2d 2.78% 8.33% 13.89% 19.44% 25.00% 27.78% 2.78% 0.00% 0.00% 0.00% 0.00% 0.00% 4.500
3d 0.46% 3.24% 8.80% 17.13% 28.24% 34.72% 6.94% 0.46% 0.00% 0.00% 0.00% 0.00% 5.037
4d 0.08% 1.16% 5.02% 13.50% 28.47% 38.58% 11.57% 1.54% 0.08% 0.00% 0.00% 0.00% 5.394
5d 0.01% 0.40% 2.71% 10.04% 27.02% 40.19% 16.08% 3.22% 0.32% 0.01% 0.00% 0.00% 5.666
6d 0.00% 0.14% 1.43% 7.22% 24.71% 40.19% 20.09% 5.36% 0.80% 0.06% 0.00% 0.00% 5.895
7d 0.00% 0.05% 0.74% 5.07% 22.06% 39.07% 23.44% 7.81% 1.56% 0.19% 0.01% 0.00% 6.100
8d 0.00% 0.02% 0.38% 3.51% 19.35% 37.21% 26.05% 10.42% 2.60% 0.42% 0.04% 0.00% 6.290
9d 0.00% 0.01% 0.19% 2.41% 16.78% 34.89% 27.91% 13.02% 3.91% 0.78% 0.10% 0.01% 6.472
10d 0.00% 0.00% 0.10% 1.64% 14.42% 32.30% 29.07% 15.50% 5.43% 1.30% 0.22% 0.02% 6.648

         The following is a listing of the probability distributions for Margins of Success for skill contests. This lists a contest of base, unmodified skills -- add in the total difference of the two characters' situational and attribute modifiers to the MoS column to figure out the probability of a real skill contest.

Skill Contest Margin of Success
-9 -8 -7 -6 -5 -4 -3 -2 -1 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9
1d vs. 1d  0.00%  0.00%  0.00% 2.78% 2.78% 5.56% 8.33% 11.11% 11.11% 16.67% 11.11% 11.11% 8.33% 5.56% 2.78% 2.78%  0.00%  0.00%  0.00%
2d vs. 1d  0.00%  0.00%  0.00% 0.46% 0.46% 1.85% 4.17% 7.41% 11.11% 16.20% 14.81% 13.89% 11.57% 8.33% 4.63% 4.63% 0.46%  0.00%  0.00%
2d vs. 2d  0.00%  0.00% 0.08% 0.77% 0.93% 3.24% 6.87% 11.42% 16.44% 20.52% 16.44% 11.42% 6.87% 3.24% 0.93% 0.77% 0.08%  0.00%  0.00%
3d vs. 1d  0.00%  0.00%  0.00% 0.08% 0.08% 0.62% 2.08% 4.94% 9.57% 15.43% 15.97% 15.12% 13.19% 9.88% 5.94% 5.86% 1.16% 0.08%  0.00%
3d vs. 2d  0.00%  0.00% 0.01% 0.13% 0.21% 1.23% 3.79% 8.41% 15.25% 21.73% 19.23% 14.06% 8.89% 4.42% 1.43% 1.00% 0.19% 0.01%  0.00%
3d vs. 3d  0.00%  0.00% 0.03% 0.18% 0.40% 1.89% 5.33% 11.12% 18.88% 24.33% 18.88% 11.12% 5.33% 1.89% 0.40% 0.18% 0.03%  0.00%  0.00%
4d vs. 1d  0.00%  0.00%  0.00% 0.01% 0.01% 0.21% 1.04% 3.29% 8.02% 14.47% 16.19% 15.81% 14.21% 10.88% 6.94% 6.70% 1.94% 0.26% 0.01%
4d vs. 2d  0.00%  0.00%  0.00% 0.02% 0.05% 0.48% 2.07% 6.03% 13.49% 21.58% 20.73% 15.94% 10.53% 5.52% 1.98% 1.21% 0.33% 0.04%  0.00%
4d vs. 3d  0.00%  0.00% 0.01% 0.03% 0.13% 0.83% 3.14% 8.46% 17.39% 25.04% 21.25% 13.37% 6.78% 2.62% 0.66% 0.24% 0.06% 0.01%  0.00%
4d vs. 4d  0.00%  0.00% 0.01% 0.05% 0.24% 1.27% 4.30% 10.69% 20.21% 26.44% 20.21% 10.69% 4.30% 1.27% 0.24% 0.05% 0.01%  0.00%  0.00%

John H. Kim <jhkim-at-darkshire-dot-net>
Last modified: Wed Jan 3 17:19:26 2007