Back to the "averaged die", I found, just for fun, this schema for a
d20:
1 face showing "1"
2 faces showing "2"
3 faces showing "3"
4 faces showing "4"
4 faces showing "5"
3 faces showing "6"
2 faces showing "7"
1 face showing "8"
that, is, more graphically:
1
22
333
4444
4444
333
22
1
this would be the choice to go when you feel that the
d6' outcomes universe of just 4 results is too limited for your game model, and you would benefit from improving them to as much as 8, at the price of having a dice type that may be unfamiliar to some players and harder to manufacture.
But this is just a mental excercise, as with the classical
2d6 you would have even more averaged outcomes with two very obvious kind of dice