Life In 19x19

White can press down Black on the lower side and cut off the stone on the left. On the other hand, 5 stones are not doing a lot in the lower left corner. I go for White but actually I have no idea here.

I'm really not sure. With boards like this, with one side played out and the other untouched, I sometimes try to ask myself whether White got enough out of his two stone advantage on that side. Looking just at secure territory I'd say no, but then again not everything is settled. White has sente, and the fighting might lead to the top left solidifying further. On the other hand, White also has a weak group. I think I'd rather have Black, but not with 94% certainty.

Personnally, I'm unable to say who's better here, so I defer to our Silicium Overlords :

Katago prefer black, giving him around 73% winrate and +11pts (7.5 komi)

One thing it see is that the cut at F9 is not a real problem for black. Black can settle on the side with a push at D10, and if white cut, black can push. Here is what Katago would play if White cut for (each move played on lizzie, with over 10k playouts) :

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[go]$$Wcm30
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O . . . . . . . . . . . . . . |
$$ | . . O . O X 7 . . , . . . . . , . . . |
$$ | . . . X X 1 3 6 . . . . . . . . . . . |
$$ | . . . . . 2 4 5 9 . . . . . . . . . . |
$$ | . X X . . . . 8 0 . . . . . . . . . . |
$$ | . O . X . . . . . . . . . . . . . . . |
$$ | . O . X O O . O . . . . . . . . . . . |
$$ | . . O O X . . . O , . . . . . X . . . |
$$ | . O . . X . X . . . . . . . . . . . . |
$$ | . O X X . . . . X . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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[go]$$Wcm40
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . 8 6 5 O . . . . . . . . . . . . . . |
$$ | . . O 4 O X O 3 . , . . . . . , . . . |
$$ | . . . X X O O X . . . . . . . . . . . |
$$ | . . . . 2 X X O O . . . . . . . . . . |
$$ | . X X . 1 . . X X . . . . . . . . . . |
$$ | . O . X . . . . . . . . . . . . . . . |
$$ | . O . X O O . O . . . . . . . . . . . |
$$ | . . O O X . . . O , . . . . . X . . . |
$$ | . O . . X . X . . . . . . . . . . . . |
$$ | . O X X . . . . X . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This explain Katago move for white :

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[go]$$Wcm30
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 1 . . . . . . . . . . . . . . . . |
$$ | . . . . O . . . . . . . . . . . . . . |
$$ | . . O . O X . . . , . . . . . , . . . |
$$ | . . . X X . . . . . . . . . . . . . . |
$$ | . . . . . . . 4 . . . . . . . . . . . |
$$ | . X X . . . . . . . . . . . . . . . . |
$$ | . O . X . . 2 . . . . . . . . . . . . |
$$ | . O . X O O 3 O . . . . . . . . . . . |
$$ | . . O O X . . . O , . 5 . . . X . . . |
$$ | . O . . X . X . . . . . . . . . . . . |
$$ | . O X X . . . . X . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

BTW, this is not the result of an invasion, but of a 3 space high pincer.

I'd take Black. This time I'm more than 89% certain, which probably means I'm wrong. But White's moyo on the right side doesn't look all that impressive to me, and yet it's a one-basket situation. Black has two shimaris plus territory at the bottom, which looks superior to me.

White, because black's circled empty triangle connection is dumb and becomes really inefficient if he takes the 2 stones. (And the 2nd line square-marked slide is already inefficient). (W 27 just some random move for example). W J4 atari is so nice free kikashi, black presumably played L3 but that was a mistake. In actual practice maybe white plays 28 as k6 nobi but the point remains the same that eventually black will need to capture and the marked stone is retarded. There are some other moves Elf probably doesn't like, such as white's s4 descent in reply to attach being somewhat generous, right side move, probably several mistakes in this distant approach joseki, but they are minor compared to these 2 inefficient black stones.

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[go]$$Wcm27 White to play.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X 1 . . . . . . . X . . . . . |
$$ | . . X , . O . . . , . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . 3 . O . . . . . . |
$$ | . . . . . . . . . O 2 X O . . . . . . |
$$ | . . . O . . . . O X O O X O O , O O . |
$$ | . . . . . . . . . B X 4 X X . . X . . |
$$ | . . . . . . . . . . # . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . X . . . . . |
$$ | . . X , . O . . . , . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . 3 5 O . . . . . . |
$$ | . . . . . . . . 1 O 2 X O . . . . . . |
$$ | . . . O . . . . O X O O X O O , O O . |
$$ | . . . . . . . . . X X 4 X X . . X . . |
$$ | . . . . . . . . a . X . . . . X . b . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The connection at looks huge. If we assume 2-3-4-5, White's influence should really be superior to Black's territory, even if "bots dislike influence". White's lower left 4-4 benefits from this connection, and together with komi, should match Black's two corner enclosures. The top right likes an extension, but White's already there.

Black will probably not go for right away but then a White play here turns his lower side into a liability, with A and B as pressure points. So Black's sente will only be temporary and he also still needs to respond to the shoulder hit at the top.

Taking all this into consideration, I go for the "locked up" argument, rather than the "territory" one.

I think I'm 0/2 on the ones I've posted responses so far - I didn't know that the attach underneath was unfavored by the AI! And while I did see the tewari-ish argument Uberdude suggested when I liked the color with the sides, I thought that the jump in the top left corner activated the weakness significantly more than it did. It's fun to play out the positions that I like but the AI doesn't against the AI - shows me how it converts positions I would find uncomfortable to positions I would find winning.
Anyway, time to try to redeem myself. My first instinct is white, because I really like having active influence in the opening. On second consideration, I see the merits of black's position, where we can expect maybe 12 points from the bottom, maybe 10 points from each of the top two corners, and the cutting aji around K5 is really annoying for white. So if my investigation of the present board state is inconclusive, I need to look into either the future or the past. Let's start with the future; below I show my 5 candidate moves from W's next move.

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[go]$$Wcm27 Which should white play?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . X . . . . . |
$$ | . . X , . O . . . , . . . . . S X . . |
$$ | . . . . . . . . . . . . . . S . . . . |
$$ | . . . . . . . . . . . . . . . . S . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . M . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . O . . . . . . |
$$ | . . . . . . . . S O S X O . . . . . . |
$$ | . . . O . . . . O X O O X O O , O O . |
$$ | . . . . . . . . . X X . X X . . X . . |
$$ | . . . . . . . . . . X . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

My first instinct was to fix the weaknesses around K5 with a full move, but on my read of B's best local move, it doesn't seem 100% urgent (still quite urgent though). The problem is that if B takes sente to approach the play at X, it will be very difficult for W to use the influence. So my second candidate area is to make it difficult for black to take X by starting with either Q16, P15, or R14. The problem is that losing sente would allow black to come back to make the first move somewhere in the K5 area, which gets very painful for white. White can't even really take the left side, and seems to be the struggling side in most variations I'm looking at. So my analysis of the future seems to put black ahead, as there are two areas that are too good for black to take.
So let's look at the past. My guess is that Black 2-space approached a 3-4 white stone in the bottom right corner, and W shoulder hit it.

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[go]$$Wcm13 Without the fighting on the bottom.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . X . . . . . |
$$ | . . X , . O . . . , . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . O , O O . |
$$ | . . . . . . . . . . . . . X . . X . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Note that there are 7 black stones and 6 white stones on this board. I think AI's would slightly prefer black in this position, as W played a side move, and B got to make pretty decent shape in the bottom right. All the other stones do is have W push over the top of W's bottom. So let's compare the game with a simple variation:

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[go]$$Wcm13 White pushes B down.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . . . . . X . . . . . |
$$ | . . X , . O . . . , . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . 7 5 3 1 O , O O . |
$$ | . . . . . . . . . 8 6 4 2 X . . X . . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This variation would be again questionable for W, pushing from behind without great reason. But even this is not actually clearly better for W than the game, where W does basically the same thing but has holes in his shape. The only way the you could claim the game is better is the nearly useless black stone at L2, but I would tend to think that what white owes in the center is worth a move at least. Thus, my analysis of the past seems to concur with my analysis of the future that white's wall is just too thin, and B is ahead.

I've never lost a game nor seen someone else lose a game because of committing efficiently to one particular area, so I don't actually agree with the one-basket argument. Uberdude's argument that L2 really is just that bad is tempting, because none of W's stones are so obviously out of place. Admittedly, I don't know just how lopsided Elf likes to evaluate, but my impression is that passing (basically what playing L2 is) would drop you from 50% to maybe 80%. I don't think W has other great advantages, so I'd give an upper bound of W's winrate at around 80% - so knowing that the winrate is 89% makes me want to double down on black. But who knows? I'm getting a feeling I've just gone 0/3