Slicing graphs

We define a slice in a graph $$G=(V,E)$$ as a partition of $$V$$ into two non-intersecting sets $$A$$ and $$B$$. An edge of $$G$$ is said to be sliced if one of its ends is in $$A$$ and the other is in $$B$$. Suppose that we want to maximize the number of edges that have been sliced. We use the following approximation algorithm :

Assign every vertex $$v \in V$$ to $$A$$, $$B$$ uniformly at random.

The randomized algorithm has no more than $$n$$ times worse than the optimum in expectation. What is $$n$$?

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