There is a problem with "doch". doch (1) is a shortened form of jedoch and introduces a clause containing a contrary idea.
doch (2) is an adverb, a filling word, often called modality adverb as it marks a special attitude of the speaker towards what he says.
Das weiß ich doch! marks some annoyance about being told things that are general knowledge for the speaker. This "doch" is placed after the verb.
Ich bin doch nicht blöd! marks a statement as something self-evident.
Das ist doch nicht zu glauben/unglaublich! marks a very strong emotion.
I haven't studied all the things "doch" can express but I am sure there are still some other "modalities".
There is even a "doch"(3). As an answer you can say: Ja/Nein/Doch - as Daniel has already pointed out in his post.