In my board game, I am using a 3 parameter dice system like in the white wolf RPG. While playtesting, sombody was not sure if he really had more change to hit. So two of my friends, who made more intensive probability maths than me, have found the formulas to compute the probabilities. Then I decided to make a computer program that generated the probabilities.
The probabilities are calculated on 6 sided dices. Since this is the most common dices used by board games, it should be useful for everybody. For 10 sided dices, the probability distribution should look alike. The tables cover up to the rolling of 10d6.
I placed all the probabilities in a pdf document and upload it on this forum. I don't mind if you want to place it on the future wiki or anywhere else on the forum. Here is the link :
http://www.bgdf.com/files/My_Uploads/Larienna/diceprob.pdf
I now realise that this probability table is essential for balancing the game. So if you use this kind of roll in your game, I strongly suggest you take a look at it.
Happy analysis!
I made some modification for the D6 chart. There was an error somewhere.
Since I am currently having problem with the probabilities of the dice system in my game, I am thinking to switch to D10 to increase the value range. This is why I generated a d10 probability table which can be downloaded here :
http://www.bgdf.com/files/My_Uploads/Larienna/d10prob.pdf
It also mean that it can be used in white wolf RPG ( Vampire, Mage ).