Well, Odin, seems my friend Source kinda answered my question already.
Anyway, yes, there's a shortcut, like I already wrote in my message.
From any die you simply take the lowest value and the highest value, add them, and divide by two. Add to this a possible '+' and you have the average for that particular roll.
If you have more dice (2D6, 3D6, etc...) simply multiply the average of a single die by the amount of dice.
In other words:
1D6: min = 1, max = 6, so average = (1+6)/2 = 3.5.
1D8: min = 1, max = 8, so average = (1+8)/2 = 4.5.
1D4+3: min = 1, max = 4, so average is (1+4)/2 = 2.5. Add to this the +3, and you get 5.5 as an average for this roll.
An alternate way is to say the following: min = (1+3) = 4, max = (4+3) = 7, so the average is (4+7)/2 = 5.5. Note that now you don't include the +3, since you already used it to modify the lower and upper limit.
2D12: min = 2, max = 24, so the average is (2+24)/2 = 13.
Alternately, 1D12 has a min of 1, and a max of 12, so the average is (1+12)/2 = 6.5 - for two such dice the average is then 2x 6.5 = 13 (which is correct accoring to what we just saw).
3D20: min = 3, max = 60, so the average is 63/2 = 31.5. Again, this can be computed by taking the average of 1D20 (which is 10.5 as you can check for yourself) and then multiply it by 3.
Okay, this is where I will end the lesson for now. Questions anyone?