Black to find the best endgame. Enjoy!
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My first instinct would be G8, to prevent White from taking the corner.
If someone wants to play it out …
To me G8 seems too passive.
White can connect the two white stones with a move around H4.
Not very sneaky.
But how about starting with H8?
Separates the two stones from the other white group and opens possibilities for Black to throw in a stone.
I’m too lazy to read right now, so I’ll just drop the idea of h2 to increase points against the corner, with the idea of cutting white off in sente or killing the whole board if white resists. Wouldn’t that be spectacular? 
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Not only spectacular, but also very sneaky.
I like it.
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H5 just kill the 2 white stones?
If Black H5 then White G8?
Then w gets a ko but has no big threat (just the 3
stones )
Yes, whether and/or how black can avoid white living is part of what makes this position interesting. 
Note that A in jlt’s diagram being sente also helps white’s eyespace…
Also, a note: the correct solution is distinctly better than any alternatives, so you don’t necessarily need to care about the whole board score/komi, but in case you do want to check your work, the solution should result in a Black win at 6.5 komi under Japanese rules, if you assume Black has already captured 3 white stones on the left. Incorrect solutions should result in a White win if white plays correctly.
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One thing is sure: my first instinct (G8) was wrong since this leads to a White victory by 2.5 points (assuming komi is 6.5).
No i was thinking of the ko generated by J8.
And thinking that A wont be a thread enough big.
Sorry I don’t understand which ko you are talking about.
In a real game, I wouldn’t have had a chance of finding this move. It wouldn’t have even crossed my mind, and I would have stopped searching for the best move. I finally stumbled upon the solution move, but only by exploring all possible options. It’s really remarkable because …
It combines miai and preemptive eye-stealing into a single, unintuitive play.
I’m sure that Sakata Eio in particular would have appreciated its brilliance. He was known for such moves.
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Peekabo
J8 seems sufficiently bonkers to warrant a forum post, whilst preparing a good territory close if white backs off vs using the ‘strange things happen at the 1-2 point’ liberty property in the corner to allow cut if white hanes.
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@Groin
I think H8 fails for the same reason as G8: Black doesn’t get enough points to win the game.
So, anyways, yes, this is the unique best move for black!
The basic issue is that black cannot cut white off because white lives unconditionally in the corner.
For example if black hanes, this is a possible sequence and white can connect at A or live at B.
Or in jlt’s variation, there is no ko, white lives unconditionally using the same escape threat.
If black extends then it’s easy life too.
In all of the above, white is relying on J8 to make eyes. What happens if black takes it here? Still doesn’t work right now. White atari and connect and leaves black with a weakness at A. Now if black A next, white B makes enough space. If black B, then white C connects under because black is too short of liberties to cut white off. But this is perhaps the line that is most challenging for white to live.
Other ways of cutting fail, white lives or connects back with very similar variations.
Going back to the start, if black simply draws back, the ordinary-looking move, then it’s not too bad for black.
But white still gets the very big hane at J8, and so black didn’t keep white out of the upper right corner well. Plus black’s shape is awkward and has to soon spend another move filling at A.
Black’s dream would be to never have to play the G8 stone, and to be able to get J8 instead of white getting it, for example like this, hane at H8 and then follow up at J8. This would be very efficient.
But it doesn’t work, because white can get J8 in sente first before connecting back, again because of how white is threatening to live with two eyes in the upper right. So black ends up losing out on J8 again.
J8 was both the key endgame point when white connects back, and the key point that challenged white’s life most, and the solution is for black to play it immediately.
If white links back, black gets the efficient dream result from earlier.
And if white pushes in, now black cuts and there is no way for white to live. Black is already occupying the critical eye point. This is perhaps not the most optimal way to cut for endgame and other ways of cutting work and/or may be better, but it’s good enough.
For example, this is a straightforward kill now. Black might look a little short of liberties if white hanes at A, but black has enough.
The effect of black’s immediate J8 was to add the two marked stones before black cut white off.
If we remove them, then white lives easily by taking this move or A in sente, then playing J8 (B) themselves.
One more example sequence - what happens if at the very start, white tries to link back before living in the corner? It’s very important that black can spend a move to push at 3 to break white’s second-line points on the right. And it works for black too. In this sequence, white dies via bent 4 in the corner.
And there’s a bit of reading, but white’s immediate hane also doesn’t work. There’s a bit of reading from here, but black J8 is on the right spot to win the possible liberty fights from here.
Yay.
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