@Riot Compatibility Testing

So I'm in school for Programming, I have a particular fascination with creative and compelling interfaces.. Anywho my project group had a discussion about testing for Compatibility, when we were trying out some Web UI Elements that had different issues depending on the browser the user was using.

Anywho during my regular LoL forum troll during lunch, I read a few posts talking about League compatibility and I'd never really thought about League actually having the issues we learn about in school. I mean how often do you REALLY use school knowledge?

Back to the point, the thread was about how the minspec for LoL in theory would creep up with every patch release. But that Riot works hard to keep the minimum spec constant. I think @Riot Baconhawk mentioned that they do their best working with some minspec testing but that all the possible combinations and configurations just are impossible to completely test.

In class we were mapping out our plans for testing coverage in different browsers with different versions of a variety of different things, and there's a bit of a debate of how best to approach it. I'm curious if I could get some opinion or input.

At first, the obvious solution, seemed to be a Matrix. With an array of configurations and mark everything off as we tested. However the quickly proved highly inefficient...

Our theory for now is to use a combination of a linear plan for coverage and a matrix for visualization. The linear plan individually tracking everything that must be tested, and then the matrix tracking the various combinations. With high-risk combinations, MinSpec, MaxSpec, and AvgSpec all highlighted.

Anywho some input on how to efficiently test and track impossibly large combinations would be insightful. At what point do you say "We've tested enough".

Much appreciate :)