Need help with concept of expectation! I have been reading blogs on Expectation. I am quite familiar with what it is but still don't understand what do we infer from it, what does it tell us about the experiment?
For eg: expected number of coin flips for two consecutive heads is 6. So what does this "6" say...are these the most probable coin flips that would get me two consecutive heads? but again most probable value is different from expected value...
Can someone please explain it? 
PS: please refer some good book/blog that covers expectation to the depth.

Intuitively, the expectation is the average of a random variable for an infinite number of drawings. E.g. with a fair coin, exactly $\dfrac12$ heads. It is the "real" average.

The Law of Large Numbers tells that the average computed on an increasing number of drawings does converge to the expectation.
