I was wondering how professionals count during their games. Do they count in pairs, in groups of fives or do they simply see "those are 5 points, plus those 8 plus those 3 plus those 13..." ?

I don't know, though I expect they know at a glance how many points a large number of common shapes are worth (e.g. L+2 group in corner is 6 points).

We know that Cho Chikun suggested counting (the already identified intersections' points) in pairs of 2, but there is no reason why every professional should do likewise. It is pretty much possible that other professionals use (also) other methods such as counting rectangles, subtracting friendly stones but adding opposing dead stones inside a rectangle, counting multiples of 10, 5 or any other convenient number fitting the given intersections, first counting empty then occupied intersections etc. Why should one count in pairs of 2 when one can identify a big rectangle much faster?:)

The much more demanding question is: how do different professionals correctly identify the intersections to be in-/excluded from a count? Cho: reductions of either the black or the white territory regions to their minima, then compare. Michael Redmond: read ahead the endgame until the game end. IMO, the latter is much more difficult than using reduction sequences.

Influence? According to Go World 41, Takagawa imagined sample global best use sequences for using influence for making / reducing territories apparently before then doing positional judgement.

I think the most important difference isn't on the counting method itself but on the ability to count as a local situation develops and then just remember that count while playing somewhere else. After that, it's just a matter of adding and subtracting points as each local situation evolves.

What I mean is: I don't think professionals recount the entire board from scratch very often during the game.

I wonder how accurate pro's count. I could imagine they just roughly guess the score in fuseki and middlegame, it's just that their estimation is better due to more and precise experience. Because some intersecions you just can't evaluate early enough, so therefore I'd say a win by 0.5 is luck like in any amateuer game^^.

Strong amateurs having thinking time and used to positional judgement make their estimates during opening and middle game with numerical 0.5 significance and an error of less than 1 or 2 points, if the position is quiet. Why should professionals make less accurate estimates? If the position is hot, then greater judgement mistakes can occur more easily.