OK, I recommend you read an endgame theory book before going further with this line of study. (And I remember earlier in this thread wondering if this level of detail on endgames is useful for you just yet.)
My current favourite is Antti Tormanenās āRational Endgameā. The old Ogawa/Davies book āThe Endgameā has a lot of good material, although you might want to skip the more advanced parts on a first reading. And thereās Robert Jasiekās books, if they suit your style. Or maybe thereās good YouTube videos for these topics nowadays; I wouldnāt know.
My analysis:
A6 is gote. If black plays first, thereās no territory at the top left. If white plays first, then white has 7 points at the top left (three prisoners plus one empty point). So itās a 7 point swing. Older books will describe this as ā7 points in goteā. Newer books say ā3.5 points by miai countingā: for gote, you divide by 2, because the difference between black going first or white going first is 2 moves. It doesnāt matter too much which system you use, as long as youāre consistent.
By similar reasoning, F9 is 1.5 points by miai counting (3 point swing, gote) and F4 is 1 point miai (2 point swing, gote).
The other two positions are a little more complicated.
If black plays F1, then the local position is 6 points of territory (two prisoners, and two empty points at D1, E1). If white plays F1, then black will block at E1, and the two white stones are captured by snapback, so black has 5 points of territory. This is a 1 point swing. In the old style, we say 1 point, whiteās sente. And in the old style, āsente counts doubleā: a 1 point sente is about as important as a 2 point gote.
For F1, the difference between black first (black plays one stone) or white first (white plays and black replies) is only 1 move not 2, so for miai counting, itās still 1 point. (When itās sente for one side, you donāt divide by 2 any more.)
For J5, you need to read a bit more. Black first is easy: black plays J5, thereās no followup moves, black has 6 points at the top right. If white first, then white J5, black will block at J6, and the white J7 stone is captured because of shortage of liberties. If white J5, black J6, white H6, black J8, then white canāt connect at J6. So a more realistic sequence is white J5, black J6, white J4 (threatening to rescue the stone), black J8, and black now has 5 points at the top right.
So J5 is the same as F1, 1 point sente for white, or 1 point by miai counting.
Before you try solving full-board problems like this, I think youāll be much better off finding a bunch of examples and practising this sort of counting until it becomes second nature. And in my opinion, thereās not much value in doing this work until youāre at least a solid 5k. Does HJJ give you an option to skip these problems for now?
