Ok, I'll bite. He certainly has something prepared for this cut, otherwise he wouldn't have played elsewhere, but I can't see how white can get a bad result out of this. My guess is that he'll tenuki again to extend on the right side, aiming to counter white's solid profit with black's speed. If I get thick in the upper right, I'll be able to easily invade / reduce whatever he builds in the upper left or on the right side, so I'm not concerned.
It was a hard decision to come to this move. I expected him to play on the bottom, because this seemed to be the biggest area - expanding his development in a primary way with his bottom left, and hindering my development in a secondary way with my bottom right. But tenuki is still a good choice, though aji remains for me to take advantage of.
I see the bottom still as being a huge place to play, but now that he's breaking up the top right, the right side is also appealing.
In short, I feel that I must decide between a play on the bottom:
These areas are somewhat miai, so I could let him decide. But I don't see a bigger area on the board to play than these two spots. So I must select the biggest of the two.
So the ultimate question becomes, which is biggest?
Initial Analysis A 3-4 enclosure is very nice, because it has power to extend influence to each side. The so-called double wing formation is valuable, and worth quite a bit if I can achieve it, for example, considering only the bottom half of the board:
Now with a 3-4 enclosure, the area around "a" is the primary mode of development for the (black) enclosure. If you can pick only one direction, this direction will yield the most points, because the influence is more box-like:
In contrast, "b" is secondary. It's less box-like, so it yields less influence for black.
Since go is a game of balance, restricting the opponent's development is equal to expanding your own (at least early in the game). Therefore, while "a", above, is the greatest area of development for black, "b" is the greatest area for white.
In addition, I already have a stone placed where white would like to extend on the left - this was the result of my tenuki.
Therefore, at first thought, the bottom seems ideal. Suppose the value of "a" is X for black, and the value of "b" is Y for black's development. Since "a" is primary direction, X > Y. Since the formation is the same shape, just rotated, the same position "b" would be X for white, since that's white's main area of development.
Considering only these factors, a play at "b" is worth (X + Y), as it is a dual-purpose move, both enhancing black's development and restricting white's. "a", on the other hand, only develops black by looking at this half of the board, and is only worth X.
This was the line of thought that I had in considering the bottom to be the biggest area of the board.
Playing From the Heart
Being convinced by my analysis, when he decided to cut, I felt almost immediately, "OK, then I'll play the bottom if you don't", which would have given us this diagram:
But from my heart, this didn't feel right. Yes, there is aji in the top right. Yes, black can still invade the right side later in the game. But white has potential there, which could become large. Perhaps he can play in a way to eliminate the aji of the two black stones, rendering them inefficient.
Was this diagram truly better than the other way around?
Above, black still has aji in the top right, and white's corner seems in-check. White has invested four stones in the area, but nothing has gotten out of hand.
On the other hand, using my previous equation, now white has gained X and black has also gained X, for an equal result. If the bottom half of the board is equal, then is the top equal as well?
Surely, white has an advantage considering only these stones (of course, he has 4 stones to black's three). So if the bottom half is equal for black and white, overall black is behind?
It was at this point that I realized that my equation from before, was too simplistic. Yes, by playing on the right side and white playing on the bottom, both of us get our "primary directions" satisfied by our extensions.
But I missed the important variable of "Z", the value of countering the influence of the top right. The values I made up for X and Y were values associated with playing the primary and secondary extensions for the 3-4 enclosure. It did not consider the value associated with playing in a spot that hindered the development of the top right, which I'll call Z.
To think of it in another way, if we were playing on an 11x19 sized board, and we had something like this:
then the value of "a" has little effect on any influence toward the non-existent top right. In this case, perhaps the analysis could be performed the way I did it - "b" has dual purpose value of (X + Y), with "a" having single purpose value of X. (Note: Maybe on this size of board, the extension lengths are not ideal )
But this is *not* the case. We have a 19x19-sized board, and the value of playing "a" very much has an effect on the top right.
The question then becomes, is Z > Y? That is to say, is the value of having a supporting black stone greater in relation to the top right, or is it greater in terms of the secondary direction of the 3-4 enclosure?
I think the answer is aligned with what I felt in my heart when I considered playing to the contrary: It is bigger to have a supporting stone for the top right corner: I will have two tenukis in this top right corner, so it would be great to have support nearby.
Having another stone nearby will make it easier to exploit aji in the area, and also hinders white from profiting from my tenuki.
I should put greater faith into that which I feel in my heart.
With his playing on the bottom, I feel the biggest area is on the top, now. I already have an extension on the left, so it would have been desirable if he got the chance, to approach the top left 4-4 from the right.
My playing here gives a balanced shape with the left extension, and helps the corner.
FYI, a play like this is not as good, because it leaves the 3-3 more open:
This is a critical point in the opening, so I have to be very careful. If I misjudge the direction of play, black will grab the initiative and the game will suddenly become difficult. Here are the moves I'm considering :
They're basically divided in 3 groups : - a and b are slow, tenacious moves, grabbing profit while aiming at an invasion of their respective side. Out of these two, I prefer a. - c and d are stubborn moves, treating the right side and the upper left as miai. c looks a bit too slow now, so I think d is better. - e and f deal directly with the upper left before black gets to play c15. e is like smashing through the front door, f is sneaking from the back door. I'm not sure which one I prefer.
Instinctively, I'd want to play either a or f, but I'll think a bit more about it.
The optimal result for this move would be to split off c10, but black can just enclose white in the corner and this is basically the same as move b above.
I said earlier that go was about forcing your opponent to make decisions. Probing is very valuable, even early in the game. When you force your opponent to make a decision, you can have a better idea of what to do next. If you make the decision first, then he can react. If he makes the decision first, you can react.
His last move is a good one, in that it's difficult for me to decide on the best strategy.
Already, it starts to become a question of, "Who is really doing the attacking here? Yes, I pincered his single stone, but black's two single stones are in the midst of 6 white stones. It's not clear if I'll profit from this attack.
Note that the cut at the marked intersection would not work, because the ladder isn't working for black. Black could atari the marked stone in the diagram above to help with the ladder, but there's no guarantee that white would answer, given the action that's happening on the side.
Are the black stones doing much? It's possible that I might be able to build a wall and later invade the bottom. But it's not clear to me how the attack will develop.
I feel a little uncertain about a battle in the center, so I could decide not to defend the corner first. Perhaps I can jump out to begin with and get the party started!
So this brings me to a crossroad: * Do I jump out first to get a head start on white? * Do I defend the corner first to secure points, then follow white out into the center? * Do I try to simply settle immediately with the left side stone, and then defend the corner?
The second option seems possible, but I don't want my side stones to become a burden.
This brings us to the probe that I played: I want to see how white will respond here to assess how easy it will be to settle my stones, if I do jump out from behind black. I don't want these stones to become a burden, but I also want corner points. Based on his answer to my probe, I will decide if it's more important to jump out first, take the corner, or perhaps settle the stones immediately.
So let's see how he answers this, then I can consider the three options I've been contemplating so far.
If he plays d4, it's possible that b5 could aid in settling c10. Based on what he selects, I'll decide whether to act upon this now, or just let it linger.
Mostly, I don't want c10 to become a burden, but I also don't want to give up points submissively.
If I was white, I'd be glad to respond to this move. It makes an invasion on the bottom markedly more difficult is aji keshi against other invasion moves. like the common probe at D2.
Also, if I was black, I'd feel glad to have finished the corner and make white jump up into the center of the board. Black is more comfortable here because he still has room for a two space extension while white will have to mind his group for the rest of the game.
Black has to crawl on the second line, but this is too easy on him. He reduces the corner while making a base for his stone. So looks questionable. Let's look at another possibility :
This is the best case scenario for this move. It's similar to the first variation above, but I think it's slightly better for white. However, it probably won't be so easy :
In the first variation, the loss on the bottom side is too big. In the second one, black easily makes sabaki for his stone.
This finally leads us to the move I played, d5. It puts emphasis on the outside, allowing black to live in the corner. Of course, he certainly won't do so right now, but it gives him good aji. Let's see how it goes from here .
His move gives me aji to work with on the bottom, which is a plus. However, it also puts more pressure on c10 than some of the alternatives.
I am still weighing the consequences of the three options I was considering earlier. Defending the corner immediately will give white chance to pressure c10 - it's easier now with his last move in place.
I could opt for settling by contact, or by jumping out like discussed earlier, at risk of losing points in the corner.
It still comes down to a question of which is more important: securing corner points, or helping c10 first (and if so, which way to help is best)?
I feel that just going for points is the wrong attitude at this point in the game. On the other hand, it is a lot of points, and how much can I really expect to gain from c10?
Due to his response to my last move, I was somewhat inclined to help out my weak stone on the left (c10), using one of the alternatives discussed in my earlier post - the attachment to settle, or jumping out into the center.
But I realized that by defending the corner like this, I not only gain points, but he also becomes weak. Since he is weak, C10 is not so weak.
Further, if the battle runs to the center, it becomes easier and easier to exploit the aji on the bottom:
Since I have more space with my C10 stone than his stone on left, I should be safe. Furthermore, it should make his last move somewhat ineffective, since the two stone wall in the bottom left corner will be facing a living black group.
We are slowly moving into the middle game. Even though there are big moves left, there is nothing to consider but the left side. First of all, I have to assess the relative strength of black and white. Am I in a position to fight strongly or should I make sabaki instead? Depending on that judgement, there are many possible moves. I will list a few variations that come to mind.
Considering the marked black stone and the forcing moves starting with 'a' in the upper right, this feels heavy, so it's probably not good. Next, the keima.
This keima is the obvious attacking move, but after , white's shape feel thin and I'm not sure how to fix it. I'm not dismissing this move however, I just need to think about the follow-up. Let's look at the cap.
The cap is a flexible move, keeping open the possibility of sacrificing the left side stone. The second variation is similar to variations I have looked at in other posts. In the first variation, however, the marked stone looks a bit misplaced. Just because of this, I'm not sure the cap is playable. Next are the attachments.
If I attach on the bottom, something like this is likely to happen. I don't think this is a good result for white, because the resulting influence is not very useful.
Attaching on the outside is a sabaki technique. Here it feels too generous even though white will probably end in sente. Last but not least, attaching on top.
Cross-cutting might work, but it's quite complicated. This simple result looks OK for white. It's better than the outside attachment variation above because white is not pressed so low this time.
Here white makes good shape in the middle while black settles on the side. is well positioned to reduce the upper side should black try to build somethink there.
In the end, that gives me 3 moves to think seriously about: the keima, the cap and the attachment on top. I'll do more reading tonight when I get home, all these variations are confusing me .
After the jump, if black makes a two space extension then D5 will look deliberate. Also if white can bring the game closer to the top right I think that's a good thing: If the game focuses on fighting bottom left and top right, I think the game is okay for white.
makes good shape in the middle. Next, white 'a' settles this group. Black can play at 'a' himself to prevent it, but then white can block at 'b', weakening the black group on the side a little bit. Of course, in the above diagrams is not forced.
By the way, I'm really enjoying my first experience in a Malkovich game. I can't wait to read all the comments! Also,
16 diagrams in total for the last move, to play a simple keima in the end Well, I remember reading in a book (I think it was by Hane Naoki) that playing the same move quickly or after a long thought might be the same on the board, but there's a world of difference in terms of content, so...
I'm having a difficult time determining my next move. It was nice to get corner profit, but after my probe in the bottom left, white is somewhat strong in the local area, which makes it somewhat easy to attack my single stone.
For example, following an instinctive response, white can get nice influence, and black doesn't even have eyes in the area:
The wall white is making on the outside will be excellent help for invading on the right side later in the game. In addition, black isn't even alive yet, and there is a lot of white help in the area.
But it's not clear that black will even be able to get enough liberties to live before white protects. Anytime white feels in danger of this cut, he can protect:
Maybe black can bend his head out, but white definitely controls the flow here, and can control the direction of the game with the attack. If white made a misstep in the attack, perhaps black could turn things around, but I can't play hoping for that to happen.
So black could play like a chicken, hoping for a variation like this:
It's good to keep white's group separated here, and white doesn't get the wall he'd get in the earlier variation, but he can still attack these stones.
Additionally, since he played the night's move, simply by playing here now, I remove the aji of the knight's move. For example, with the cut aji still in place, I can extend on the top in sente (later):
The possible benefit of this is that I can avoid inducing him to fix the aji of the knight's move, so I could later, for example, play the ladder breaker in sente - or maybe attack his group in the future.
The plus side of something like this is that his group is not totally safe yet, and my 4th line stone on the right side could be helpful in the future. Additionally, like I originally intended, the marked area might be possible to invade later.
He could defend the bottom, perhaps, by attacking my running group, but he can't play on both sides. If he protects from beneath, I get initiative against his weak group above.
But this isn't totally clear, either. Maybe he'll continue to lean. To give an extreme example:
Both sides have a lot of cutting points, and it's not clear to me if this will end up OK for black. Again, while I'm inclined to attach, I don't really want to here, since he can get a wall to invade the right:
To summarize, I'd like to keep the knight's move aji there, if possible, so it's somewhat undesirable to cut his knight's move to get an attachment in sente. On the other hand, it seems advantageous for white to keep up the attack if I try to run out into the center.
It comes down to this: Will it be a greater loss for black to cut immediately so I can help my single stone, or will white be able to effectively continue the attack and make black lose more when he runs out?
Because black took immediate profit in the corner, rather than helping the side stone, it's clear that white will gain profit here. My goal is to minimize this profit.
P.S. I thought about potentially using aji in the bottom left to try to somehow get the hane to work to help my side stones, but a working sequence isn't coming to me yet.
For example, I tried to think if something along these lines would work, in order to get help for the side stone:
These are just a few of my thoughts right now. I don't feel like I'm at the stage to make a move, yet, because nothing that I've come up with seems really satisfactory for black, yet.
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VincentCB
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or 'a', I'll simply jump out.
seems somewhat natural. The white stone extended close to the strong black corner, so I pincer and attack.
. This is certainly what he's aiming at :
looks questionable. Let's look at another possibility :
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, white's shape feel thin and I'm not sure how to fix it. I'm not dismissing this move however, I just need to think about the follow-up.
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is well positioned to reduce the upper side should black try to build somethink there.
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makes good shape.
is a territorially tight move, securing one eye on the side while opening up play in the corner.
