Is Karger's algorithm guaranteed to do better than random guessing in terms of expectation?

We can obtain a lower bound of Karger's algorithm of finding the optimal solution by running it once, and in terms of this it is much better than a random guessing. However, this should not mean if you run the algorithm on a large number of graphs, once for every graph, then you will have more chance of getting a smaller cut than do random guessing once, right? (i.e. I think this means the expectation of the rank of the cut the algorithm finds is not guaranteed to be better than (2^n-2)/2, e.g. 2^n-2 is the number of cut of a graph and hence this is the expectation of the rank of the cut given by one random guessing).

Is there any theory on karger's algorithm from this perspective?