Dice Mechanics: Examples

ICON

         The ICON system is used in the Star Trek and Dune games from Last Unicorn Games. In it, you roll a number of d6's equal to your attribute and take the highest. The exception to this is that one die is always the Drama Die. If the Drama Die is a 6, you add in the second highest die as well. (If there is only 1 die, you add in a second die in case of a 6.)

# of dice Chance of Result Avg #S
1 2 3 4 5 6 7 8 9101112
1d 16.7% 16.7% 16.7% 16.7% 16.7% 0.0% 2.8% 2.8% 2.8% 2.8% 2.8% 2.8% 4.08
2d 2.8% 8.3% 13.9% 19.4% 25.0% 13.9% 2.8% 2.8% 2.8% 2.8% 2.8% 2.8% 5.06
3d 0.5% 3.2% 8.8% 17.1% 28.2% 25.5% 0.5% 1.4% 2.3% 3.2% 4.2% 5.1% 5.70
4d 0.1% 1.2% 5.0% 13.5% 28.5% 35.1% 0.1% 0.5% 1.5% 2.9% 4.7% 7.0% 6.07
5d 0.0% 0.4% 2.7% 10.0% 27.0% 43.1% 0.0% 0.2% 0.8% 2.3% 4.7% 8.6% 6.31
6d 0.0% 0.1% 1.4% 7.2% 24.7% 49.8% 0.0% 0.1% 0.4% 1.7% 4.5% 10.0% 6.46
7d 0.0% 0.0% 0.7% 5.1% 22.1% 55.4% 0.0% 0.0% 0.2% 1.2% 4.1% 11.1% 6.58

         The interesting thing to note about this distribution is how additional dice have very diminishing returns, and also how everything starts to pile up at 6 and 12. An infinite number of dice would have a distribution: 83.3% chance of 6 and 16.7% chance of 12, for an average of 7.

         My problem with this is that past a certain point, nearly everything rests on getting a 6 on the drama die roll. For example, Deanna Troi (Strength 3d) has a 23% chance to beat Data (Strength 7d) on a straight Strength roll contest.


John H. Kim <jhkim-at-darkshire-dot-net>
Last modified: Fri Feb 7 17:55:36 2003