Kenny vs. David Part 2: A San-San Invasion, and a Slight Mistake (Maybe?)

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The sequence I predicted in Part 1 panned out, and Kenny used sente (the initiative) to approach my bottomright corner with move 11. Taking into account my stone at 10, I felt comfortable playing a tight pincer attack two spaces to the left of 11, at 12. Kenny then used his approach stone to assist in an invasion of the san-san (3-3 point), with move 13.

After a 3-3 invasion, the owner of the 4-4 stone typically has a choice as to which side to block on. If the surrounding situation is symmetrical, then it doesn't matter which side, and in fact it may pay to delay the decision until you have more information. On the other hand, if the situation is assymetrical, it is not always obvious which side you should block on. To understand how to make that decision, it's first important to understand what happens when there are no stones around at all.

Diagram A

After white invades with 1 in Diagram A, black blocks above 1 at 2, and pushes white down to the second line from 3 to 8. White then pushes out with 9, and both players protect their shape with 10 through 12.

You may say that white has taken black's corner, so white is better off, but the reality is anything but. In exchange for white getting roughly 10 points of territory, black has gotten a powerful outer wall which is worth much more than 10 points. It can be hard to determine the value of a wall, and harder still to utilize a wall to get your rightful value from it, but both are vital skills in the game of Go.

So what exactly is a wall like this for? For starters, it's not for making territory. If you try to start building the three other edges to complete an enclosure of some area, you will end up spending many moves for a relatively small profit. It is much more efficient to make your territory against the edges and corners of the board, as you already have natural foundations to build against there. It is rare in Go for a substantial amount of territory to be made above the fourth line.

Diagram B

The best analogy is perhaps to a minefield. If your opponent's weak groups end up near a wall, they will have to run the other direction to live. As I've remarked before, you probably won't kill, but you will have a favorable fight. Power limits your opponent's options, and when your opponent's options are limited, you can profit.

In fact, that is the very purpose of playing on the 4-4 point to begin with. If black wanted the corner as territory, he would play the 3-3 point. A play at the 4-4 point is not intended to make immediate territory, but rather to create a dominant presence in the corner, so that the fights which follow are favorable to your side. If white is going to demand the corner from black, he will get it, but he will pay a high price.

Now let's take a look at another symmetrical situation. The butterfly formation in Diagram B is a great target for a 3-3 invasion, because black already has a substantial amount of outward influence. There is no way in which black can attack the invading white stone to build up a substantial amount of power that it does not already have. Sure, it'll get a little bit of additional outward strength, but much less than the territory white will gain. As such, the 3-3 point in Diagram B is a big point for whoever takes it first.

Diagram C

However, if white were to try the 3-3 invasion in Diagram C, black invites the opportunity to block to the left of 1, at 2, cutting off 1 from the nearby white stones. After white lives in the corner, black has a destructive invasion at a, assisted by the firmness created by 2. Without 2, an invasion at a isn't so appealing, so white has created problems for himself by allowing black to get thickness exactly where it's useful.

On the other hand, if white already had a stone at b, then its group to the left would be strong enough not to have to worry about a black invasion at a. In that case, if white plays 1, black would do better to block at c, letting white connect his groups by playing at 2 himself. After this exchange, black feels somewhat clumped up and inefficient, with his two-stone wall so close to the marked black stone above, but at least he gets something out of it. If he blocks to the left, at 2, then white gets more of the corner, and black gets a completely useless wall, because of white's stone at b.

Kenny vs. David (14 - 20)

Thus was my reasoning when I played 14. My intention was to separate white's two unsettled stones. Because of my stone at 12, 11 was already weakened somewhat, and could be treated by white as a sacrifice stone (with a bit of leftover potential even after it's sacrificed). So, after 14, it's perfectly reasonable for white to push upward with 15 at 16, instead of playing 15 where he did. However, white chose to first threaten the connection to 11, by playing 15. At this point, I decided that a connection to 11 is rather unimportant, so I blocked at 16.

This is where I believe Kenny made a mistake. The normal response to 16 is to play at 17 in Diagram D, which serves to both connect to 11, and to threaten to move into the right side somewhat. If black were to try to cut at a now, white could safely play b, which would leave black's cutting stone no room to escape. Without 17 in Diagram D, black could play c after white b, capturing 15, and white would be devastated.

Diagram D

Instead, Kenny played 17 directly to the right of 13, allowing me to cut off 11 with 18. White had no choice but to protect 15 with 19 (otherwise his corner would die), allowing me to link up to 12 by playing 20. White's 17 and 19 are an inefficient combination, serving somewhat redundant purposes, whereas a play at 17 in Diagram D would have most of the same benefits, in addition to linking up 11.

As a result of this exchange, I got the best of both worlds. I effectively managed to block white off on both sides, and connect to 12, leading to a position qualitatively similar to Diagram A, which heavily favors black. In this case, white's territory in the corner is a bit smaller than in Diagram A, but the power black receives is a bit looser. On the whole, I am very happy with this result, and I believe this game is looking up for me.

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