Here are numbers
And a demo board to play around on
Thank you so much. To me J3 or D3 seem to be the start but both end in gote. Then, I feel like the computer wants me to do something with a possible ko in the center to get around the gote problem.
Yeah, I can’t see anything better than these either 
44+38=82, but 9x9=81. I can give you black winning by 44 points to 37 using Chinese counting.
Hints:
- D3 is bigger than J3. If you use old-style counting then they’re both 2-point moves, but J3 is gote for both sides, while D3 is reverse sente from black’s perspective. Or the modern way, you’d count D3 as a 2-point play but J3 as only a 1-point play by miai counting.
- Next, it’s a tedomari problem. Later, F7 and J3 have the same move value, but depending on the move order and the choice of responses, either player could end up with the last move of the game and the extra point.
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Hi. I’ve tried the following: Black starts
D3. B4. B5. F7. F6. J4. J5. J3
D3. B4. J3. B5. C5. J2. J4. F7. F6
And a few others that don’t work.
I have no further ideas so could someone please tell the first two or 3 moves please. I’ve reduced my percentage success rate on endgame to about 10% thanks to trying a zillion variations on this:)
If White gets B4, then who gets B5 will at least determine whether-or-not
A5 and C5 are Black territory. Furthermore, C5 would be followup for White,
so the difference between whiteB5 and blackB5 would be at least 5/2 points,
which means whiteB4 is sente. (The reverse-sente is 1 point.)
E4 is followup to whiteD3, but there’s no further followup to White getting both.
(See the discussion between hexahedron and shinuito.)
Thus, that region is, Black moves to B+2, White moves
to [Black responds to 0, White follows up to W+2].
The latter is 1+star, so D3 has temperature 3/2.
It seems to me that the hane-connect on the right interacts with
White’s push from the top: However, this interaction can’t matter
more than infinitesimally, since Black can just treat whiteF7 as sente.
Thus, Black starts with D3: Black has no sentes,
and D3 is Black’s only play larger than infinitesimal.
After D3, the temperature is 1, so the game comes
down to who gets the last play at temperature 1.
Black still has no sentes, so the next moves
are whiteB4 and blackB5, leaving just the right.
If White now plays the hane-connect, then Black plays J7 for tedomari, so White
plays J7 instead. If Black responds with J6, then White plays the hane-connect
for tedomari, so Black must make the other 1-point play available to Black.
This is a good start!
The followups are tricky.
- If white plays B4, should black answer at B5, or play elsewhere?
- If white plays F7, should black answer at F6, or play elsewhere?
These two situations are not the same!
- After white F7, if black plays elsewhere, then white F6 only takes away one more point of territory.
- After white B4, if black plays elsewhere, then white B5 takes away two points, because A6 is no longer a point of territory. (Even if you’re using Chinese not Japanese scoring, it’s still useful to think in these terms.)
Therefore on this board, with no big moves remaining, we treat white B4 as sente, while white F7 is ambiguous (maybe you answer, maybe you don’t , still need to analyse a bit more).
Start with black D3, white B4, black B5, white F7. But then black shouldn’t answer, but should play J3 at this point. Spend a bit of time to look at each sequence and see why black gets an extra point that way compared to your first sequence. (hoctaph has said it all, but in much more technical language!)
Generally, one of the most common endgame mistakes is to answer your opponent’s moves when there’s actually a better option elsewhere. You should always take a moment to ask: how does replying to this move compare with a mutual damage strategy?
Move values and sente versus gote are the key to narrowing it down. I quickly identified D3 as the only 2-point move on the board (everything else is smaller), and B4 as sente for white, so D3 must come first, and you may as well analyse as if the B4-B5 exchange happens next (hypothetically, there might be a different sequence giving an equally good result for white, but there’s no chance of white doing any better, so there’s no need to explore other options). This only leaves three variations to analyse (white plays F7 next and black answers, white F7 and black doesn’t answer, or white J4).
I quickly identified D3 as the only 2-point move on the board (everything else is smaller)
How do you get 2 points for D3 but not for the hane-connect?
I get 3/2 points for D3. If you’re using swings instead,
then I’d think you would get that for the hane-connect too.
I made a mistake, that’s how 
I counted D3 as reverse sente for black. Practically speaking, I stopped at “clearly bigger than the other moves” and didn’t carefully assess the value of the followups after white D3.
On this full board position, it is in fact a global sente for white (black doesn’t have any better response than connecting), but considered in isolation it’s local gote with miai value 1.5 as you say. And the hane-connect at J3/J4 is a 2-point swing, gote with miai value 1.
Thanks for the correction!