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 | 9 | 10 | 11 | 12 | ||
| 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.