This is a simplified dice mechanic using standard d6 dice to balance 5 unique weighted distributions.
Define the following events:
A = {6,5,4,3,2}
B = {6,5,4,3}
C = {6,5,4}
D = {6,5}
E = {6}
Meaning event B is rolling a 3 or better. The probability of event B is 4:6
Weight each event as:
A(12) B(15) C(20) D(30) E(60)
The weighted events have an average value of 10. If multiple dice are thrown, the weighted average will be 10 times the number of dice: