[soVeryTired]

> What is expectation?

There is a formal mathematical definition:

Let (\Omega, \mathcal{F}, P) be a probability space, and let X: \Omega -> S be a random variable taking values in some measurable space (S, \mathcal{S}).

Then the expectation is \int X(\omegs)dP

In computer science terms, do an experiment with every possible random seed and average the outcome (set \Omega to be the set of all seeds, and set P to be the uniform measure on them).