> Infinite sums are rather inconvenient to calculate in finite time, although this one does converge to a finite value since the terms become exponentially smaller. We could compute until the terms because small enough for an approximation, but that would be unsatisfactory when an exact solution is possible. The key insight is that it doesn’t matter how many times a given item has already been through the loop, only what quality tier it has now.
Isn't the matrix
...? L isn't invertible, but 1 - L is.