Avalanche - connection
The connection of in the avalanche joseki is advised to players who prefer to avoid the complexities of the large and small avalanche josekis.
It is, however, also an excellent joseki in its own right. Players of any level of knowledge can play this move whenever they feel that taking territory in the corner in exchange for giving White influence in the center is not disadvantageous.
is more or less the only move, and is the most usual continuation [1]. After that, White will usually fix up her shape with a. Other plays for White are: lengthen the wall with b, play tenuki, or play at c to try to force Black.
is not absolutely sente, but if black does not answer, white forces with to to take control of the corner.
An important variation in this joseki is here. In this diagram, Black takes even more territory and gives White even more thickness.
If Black omits , White might play there, and Black is more or less obliged to play a, which is painful. can also be played at b.
If white plays tenuki, is a tasking move. It is not the most common one, but we are going to gloss over at a, which leads to complicated fighting needing many diagrams and , which reverts to the joseki shown above. White keeps black separated, then pushes against the black corner group. This gives black territory, but white makes strength, thus weakening the -- stones. A white counterattack against these is likely to follow soon.
Katago evaluation of this variation
Rather than playing at a, Katago wants to hane on the second line and crawl again with . jumps to invite the wedge and the variation ends with the firm connection at .
Black has territory and sente. White has influence towards top (albeit with an open skirt) and centre, plus the potential to turn and build influence to the left side with b. This move is gote for both.
It's interesting to note that Black can next cut at c but White needn't respond. It seems that the -- structure is already good enough to allow for two Black moves, also given -- being low.
If , then gives White strong influence. This result is slightly inferior for Black, compared to the above variation.
However, if the left side has a particular interest, then can be preferred. Then again, White would probably not have played the avalanche in the first place, if she wanted to influence the left side, rather than the top.