Thinking back on what I learned as a 4 kyu, I realized that I could give a name to one of those "unnamed go skills" that we develop. I had learned to count dame. That's not an advanced skill, but there you go.
Still it provided a heuristic that helped me tactically. It also led me astray at times. Here is an example.
$$Bc A fight
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . . W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X , . . . . . ,
$$ | . . . . . . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc A fight
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . . W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X , . . . . . ,
$$ | . . . . . . . . . . . . . . . .[/go]
Black (moi) has decided to sacrifice the

stone. The question is Black's next move. There is a small contest between the

stone and the

stones.
The

stone has two dame, the

stones have three. No question about which will win, it seems.
$$Bc Gote
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 2 W 1 . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 3 . . . . . ,
$$ | . . . . . . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Gote
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 2 W 1 . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 3 . . . . . ,
$$ | . . . . . . . . . . . . . . . .[/go]
To me, at the time, the right play was

, which reduced the

dame to two and forced

. OC, then I came back and protected with

.
$$Bc Sente
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 2 W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 1 . . . . . ,
$$ | . . . . . . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Sente
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 2 W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 1 . . . . . ,
$$ | . . . . . . . . . . . . . . . .[/go]
But what I learned, to my astonishment, was that the solid connection,

, also threatens the

stones, despite the fact that they have one more dame than the

stone.

How could that be?
$$Bc Threat
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 3 W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 1 . . . . . ,
$$ | . . . . . . . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Threat
$$ --------------------------------
$$ | . . . . . . . . . . . . . . . .
$$ | . . . . . . . 3 W . . . . . . .
$$ | . . . . . . . B W X . . . X . .
$$ | . . . O . O O O X 1 . . . . . ,
$$ | . . . . . . . . . . . . . . . .[/go]
If White plays elsewhere,

fills a shared dame (

) to take away a dame from the

stones while adding a dame to the

stone. Now Black is ahead in the fight and there is no way that White can take the lead again. Remarkable!
It is not that counting dame is useless, but to advance I had to go beyond it.
