And the catch is the first die has $x$ sides, while the second die has $y$ sides, where $x\neq y$
I had this figured out several years ago, but apparently have forgotten both the answer and too much math since then to either work it out or figure it out from Googling.
Similar questions have been asked before, but all the answers are simplified to two dice with the same number of sides on the symmetry that $P(A>B) = P(B>A)$, which does not hold true for my case. What I need to know is:
Given two discrete, uniform distributions, what is the probability that a sample from the first is strictly greater than a sample from the second?
Given $X$ distributed uniformly in $\lbrace0,1,2,3,...,x\rbrace$ and
Given $Y$ distributed uniformly in $\lbrace0,1,2,3,...,y\rbrace$
How can I find $P(X>Y)$?