Retooled dice mechanic (probability issue)

[Sarcose]

There's a question at the end of this exposition.

So my friends and I started up GURPS and have played for a few months. We are a crunchy group but also a minimalist group, and GURPS' rolling gets a little too complicated at times. To that end, I am attempting to compound multiple rolls into single rolls by adapting a strategy from O.R.E. : a dice pool that generates separate probability curves - that is, I could technically pull three separate outputs (or more if I wanted to get complicated) from a single roll of multiple dice: the number of matching dice (preferring the highest number on matches), the total score of the roll, and a single score on a dedicated die and/or the number shown on the matched set. O.R.E. does not bother with the second output - the total shown on the whole roll, but this is because it uses a variable dice pool.

I was thinking I would go from 3d6 to 6d6, so I could use a very similar probability curve to the one that GURPS already uses and it would not be difficult to adapt the system. By making it a static number of dice, I could pull the total in addition to the outputs that O.R.E. uses.

The most immediate feature of this would be the ability to pull to-hit and hit location from one single roll, rather than two. Granted, this is only using two of my three proposed outputs, but I was also going to use this system to run a horror game with nested outputs of unknown quantity (let's say, any IQ roll would be done 6d6 and the player would only know what the total roll would mean, but not the width or height, and I would use it to determine, for instance, a hidden measure of sanity effects or corruption or something similar).

That all was both background and discussion fuel. I don't know how partial the GURPS forum is to maintaining the purity of its mechanics, but I feel the community is flexible enough for my needs and I thought this would make for an interesting thought process.

My question is this: I don't know much about probability. I know that 3d6 is a bell curve whereas 1d20 is linear. I know, too, that the Height of the roll (the number shown on the matching set) would therefore be linear as far as I know (since there is equal chance of 1-6 being the result)(although perhaps the chance of a given match set beating another match set would factor into the probability interestingly). What I do not know is how to find a probability calculation for finding different match sets from a roll of XdY - save that the distribution of matches in 3d6 would not yield many positive results for my purposes, which is why I'm doubling the number of dice. That is, I don't know what the chances of, in a roll of 6d6, for there to be a matching set of two, a matching set of three, four, five, six. My question is, can anyone teach me in very lay terms, or better yet just direct me to a probability calculator for my purposes? I can find calculators for any number of any type of dice -- but these lay out tables for given sums, not for given match sets. I am not sure how to relate the two.