3-4 point, high approach, inside contact, solid connection
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The canonical joseki for the solid connection at is as shown, with making a three-space extension from two stones, "completing" the joseki. Here the low extension is shown, may also be played at the high extension at a. The low extension emphasizes territory, while the high extension emphasizes influence. See fourth line vs. third line for more discussion on this aspect.
Depending on the left side, may also be played at b or c, each with its pros and cons. The advantage of here is that it finishes the position in one move.
In older days, at d is also seen (Takahashi Shigeyuki (B) vs. Go Seigen 1936-04-14), but presently it is no longer considered to be joseki. See 3-4 point, high approach, inside contact / discussion about why d is considered to be too wide.
In special cases, may also be played as a pincer at or around . See the section on "Black pincer variant" below for more.
Black's alternatives for the extension
The one-space jump of finishes the joseki in one move, with no intention of further expansion along the left side.
As Black's position is low, subsequently and can expand the top side. Incidentally, Leela Zero suggests may be more efficient at a.
The diagonal move at implies an interest in further expanding the left side with a move at . Later, Black can play at a for further expansion.
As the stones form diagonals that are compromised by , in this variation is a common probing move, which aims at Black's cutting points at a and b. As Black can only defend only one of them, White can then decide a suitable follow-up. Note that the timing of and its follow-up moves is important for achieving the best effect.
If Black defends on the 3-3 point, then the and exchange allows White to profit in sente, as is weakened.
The knight's move of also aims at further expansion near . Without , a move at White a will expose the weakness of the knight's move.
When Black ignores , strikes at the waist and cuts Black off.
Black's pincer variant
Black can play at or a if White's extension frustrates Black plans at the top. (This is bad locally, but may be playable overall.) White's compensation is to fence in Black and create substantial thickness. For both players, knowing how to handle White's thickness is key to playing this variation.
A word about : the connection can also be at b. is a little better than c. (Compare with getting ahead with a one-point jump.)
If Black plays atari at instead ...
... and capture a big corner. at a would be soft. The stone loses half its purpose.
here is also soft. Black plays a good empty triangle and White has either a cutting point (after White a) or bad shape (after White b).
Another option that came to the surface in the AI revolution is here. After , White can take sente and play elsewhere.
In the opening or early middle game, it may be slow for White to defend at a if Black checks? at . This means Black can invade at .
One possible continuation is that Black connects back with , while White has a wall. provides breathing room for the resulting influence in the center. Given that White has ignored to take a big point elsewhere, the loss of territory is acceptable.
White can also resist with . After , Black needs to connect at . White has influence and sente but the stones are now without a base.
Black can also fight with , leading to a whole board fight.
White's choices depend on the rest of the board. After , it looks natural to play a but Leela Zero suggests that b is superior.
When blocks firmly, Black can play - in sente. White needs to cover the cutting point with .
surrounds more loosely and treats the original solid connection more lightly, giving more importance to overall influence in this variation with . After connects, White has sente, which is the major advantage over the previous diagram. Leela Zero gives this a 10% difference.
is very effective. It threatens to link up at a. If White prevents this with , the fight can become very difficult for White after . Often, White just defends with at b. After that, Black can treat as kikashi if he likes.
So White will, in absence of supporting stones, likely choose to take influence with and subsequent moves.
Faster development - no extension
One novel understanding coming from the AI revolution is that the solid connection doesn't need an urgent extension. It has more thickness than previously thought. In this early board position for example, Black may choose to enclose the upper right. If then takes away Black's base, defends and Black doesn't seem to be off badly.
If he wants to play on the lower side, ...
White can resist with this pincer, leading to a double approach pattern in the corner. Again, taking away Black's base doesn't seem as troublesome as previously thought, due to a and the forcing moves of b or c available.