Probability of cumulative dice rolls hitting a number Is there a general formula to determine the probability of unbounded, cumulative dice rolls hitting a specified number? 
For Example, with a D6 and 14:
5 + 2 + 3 + 4 = 14 : success
1 + 1 + 1 + 6 + 5 + 4 = 17 : failure 

Assuming the order matters (i,e 1+2 is a different outcome from 2+1)
The probability of getting the sum $n$ with dice numbered $1,2,\dots,6$ is the coefficient of $x^n$ in
$$\sum_{j=0}^{\infty}(\frac{x+x^2+x^3+x^4+x^5+x^6}{6})^j = \frac{6}{6-x-x^2-x^3-x^4-x^5-x^6}$$
Writing it as partial fractions (using roots of $6-x-x^2-x^3-x^4-x^5-x^6=0$)  or using Cauchy's integral formula to find the coefficient of $x^n$, Taylor series, etc should work.
