I tried writing down a few reponses and ideas, none of which really made sense in the end. Probably to get to the bottom of it, it makes sense to just take final positions of a game, where one knows what the winner should be, and then try to extrapolate from there.

Let’s say this was a game, where both players have played 20 moves each (which they have), only black played in white’s area a lot, before playing twice in their own, and white removed all the prisoners. There have been no passes. White has 10 more prisoners, and no komi.

Territory scoring would say 19 points to white, and 12 to black. If they play it out with stone scoring and prisoner return, then white does win by 7.

We expect the score with area scoring to be the same, since both played the same number of stones, 28 to 21. I think then to make it combinatorial, you need to some how turn that score of 1 point per stone, and 1 point per area, into moves (ignoring prisoners).

Maybe when it comes to filling in territory you can think of it like each player takes turns placing a neutral (red/grey) stone into each point of their territory, and when they’ve finished doing that, they take turns removing their stones from the board.

The reason is to come up with rules of a game, which is effectively just the counting process.

That way the numbers kind of make sense, if we modify them to the above.

On the left, Black and white would take turns removing stones, and white would have two extra left over.

On the right, White would first place a netural coloured stone (red or grey or something) into the open area, while black removes a stone. Then both continue to remove stones and White has 6 extra left.

At least the result of the game then is the actual area score?