Probability

I need a formula to determine the following:

A deck of 56 cards exists, with 4 sets of numbers 1-14;

Given a hand of (X) cards, randomly distributed;

And the ability to combine 3 of them through addition or subtraction in any order you choose;

What are the odds of being able to create (Y) through that combination?

The goal of this formula is, for a range of 0-22 for the value of (Y), to show what the odds are of each being possible, and how a change in (X) - probably within the range of 1-7, but might go higher - effects those odds.

When I was younger I liked to play games with cards. Every suit was a nation with the numbered cards being regular soldiers and the pictured cards were nobility. They would fight against each (I held the cards against each other and the one that would tear the most lost the battle). My favourite part was sending out the queen with a small escort resulting in an enemy ambush. When the queen's guard were captured, I would make small tears in the queen's card and slide the hostile king/jack into it repeatedly to simulate rape. This ofcourse upset the other king, leading to a big war between all the suits with only a few survivors.

thank you - reflecting on your post, I realized that there's nothing quite like sitting back and sipping on a can of swine.

>>1
Given a hand of (X) cards, randomly distributed
I'm afraid you won't be able to determine any probabilities for a random distribution.

>>1
Probabilities are often ugly. This one looks that way as well. Just make a program to brute force it. Functional is good for this sort of task.

Also, do they have to use three cards? For instance, a hand of 1,1,1, may or may not be able to combine to form 2 depending on the interpretation.

Also, your use of effects could have possibly not been a typo, but I'm betting you meant affects.