I'm not a statistics genius but I think if you do a search on 3d6 it should turn up a probability distribution for each value from 3-18...it's been done and posted a thousand times. Besides doing single or multiple added dice you should also look into "dice pools", where you roll a number of dice (with the number generally higher or lower based on a given attribute) and then either look for a success, or count successes, or add them together for a success.

In Deadlands, for instance, each "attribute" has a die type and a base value. Under that, you have skills that derive from it that you can buy up. Say you have Agility at d10 and a value of 3 and, under that, you might have Shootin' at 5. When you try to shoot somebody you'll roll five d10s and take the highest result on a single die and compare it to a target number. I think the target number is generally 6 to hit a human-sized target with no modifiers - so, if you rolled 2, 4, 5, 7, and 8 then you hit, because 7 and 8 beat your target number.

Deadlands also has "exploding dice" where, if you roll the top number on the die you get to pick it up and roll it again, adding the new score to the previous value. If you hit the top number again you roll and add again. It gives additional benefits for every 5 points by which you beat your target number. It also has the concept of "going bust"...if more than half of the dice come up 1s then you fail and something bad happens.

There are many variations on the dice pool concept - worth checking some of them out.
M