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Co-ordination between Adjacent Corners
Path: StatisticalAnalysis   · Prev: WhereIsGoGoing   · Next: PreventingShimariFromGrowingInFusekiStatistics
    Keywords: Opening

[Diagram]
Diag.: Formation A

This is a fairly unpopular formation in professional games, though like everything else it is tried.


[Diagram]
Diag.: Formation B

This is somewhat more attractive.

What's the specific difference here?


[Diagram]
Diag.: Formation B developed

From Formation B, Black can enclose the left-hand corner with the marked stone, and then play a pincer when White approaches the other corner. The pincer does co-ordinate with the enclosure.


[Diagram]
Diag.: A future for Formation A?

It is harder to see into the future for Formation A. Suppose White approaches high in the left-hand corner, like this.


[Diagram]
Diag.: A future for Formation A? (continued)

And suppose also that White later approaches the right-hand corner as shown. Then Black 2 is an ideal pincer, to co-ordinate with the marked stone (played high, deliberately).

The fact is that this type of good development from Formation A is quite remote. White could approach the left-hand corner low, instead. Black cannot develop an ideal position quickly, so it ought to be enough for White to live on the edge of Black's side.

Charles Matthews



Dave Sigaty: Charles, you keep raising interesting points that beg to be tested with the databases. However, it always seems to be like peeling onions - layer after layer and the results make you want to weep! :-)

To take formation B first...

[Diagram]
Diag.: Formation B developed

In the GoGoD CD collection, this formation develops via 1, 3, 5 about 10% of the time and via 1, 5, 3 about 90% of the time. In total, however, this is an unsatisfactory development for Black (in 180 games Black wins 47% and White wins 53%). There are only 8 games where White allows Black to play next here but White wins 5 of them.

The natural comparison is to this formation


[Diagram]
Diag.: Comparison for formation B developed

Here the experience with Black is reversed. In 766 games Black wins 55% and White wins 44%. There are 37 games where White allows Black to continue here. Black wins 26 of them. I think that we can reasonably describe this as one of the basic positive examples of coordination between the corners. From this we can easily see why the previous development from formation B is less successful.

An interesting example comes from the career of Kato Masao. He is a proponent of formation "B developed". Of the 180 examples cited above, 46 are from Kato's games as Black. Some stats for Kato as Black as shown in the July 2002 GoGoD CD:

  • 499 even games as Black: 61.3% winning percentage
  • 293 games with first play on 3-4 point: 60.4% wins
  • 75 games with first two plays on 3-4, 5-3 (formation b) or 3-4, 3-4 (alternate path to the "b developed" formation): 50.7% wins. Note that these have been played throughout his career from 1969 to 1999.
  • 46 games with "B developed" formation: 47.8% wins
  • 27 games with "comparison" formation above: 66.7% wins

Charles Matthews I don't think there's any big secret about coming up with points, on opening (fuseki) theory. I spent much time classifying fuseki patterns a few years ago, and there is no shortage of phenomena that at least raise questions. I find the Chinese and sanrensei relatively dull in a 'high-concept' way - the strategy is accessible to a five-year-old, though the techniques are interesting. Therefore I've looked around at what else there is. Some patterns go to make satisfactory magazine articles; for others, the material is sparse, or harder to interpret, and can make up a 'conversation piece' here in a natural way. I'd normally tend to present such things without trying to prove any case, though I mostly check conclusions with a database.

By the way, for Formation A, the striking example as far as I'm concerned is Takagawa-Sugiuchi Masao in the first game of the 1954 Honinbo match.


Dave Sigaty: First, in terms of this page I think that this game has to stand out. Shuei sets up both Formation A and Formation B with his first 3 moves in a game against Shuho. Needless to say, he loses the game. :-)

[Diagram]
Diag.: 1885-02-26 10-game match, game 4


HA, HA, HA! Eh? Hmmm... So my little joke says more about the shallowness of my research than it does about the issues in coordinating corners you say? :-(

[Diagram]
Diag.: White avoids "Regulation Fuseki"

This diagram shows a related formation with 2 on the 3-4 point instead of the [4-4] above. If White 4 is played at b we have the Regulation Fuseki (honpou no fuseki in Rin Kai Ho's Fuseki Dictionary; the English name is from Appreciating Famous Games, game 5).

Although the regulation fuseki gave good results for White historically, in 15-20 percent of the games White avoided it, mainly by playing at 4 here. This left Black with the question of whether to take the empty corner and, if so, how best to exploit it. Up to 1850 Black most often played 5 at a seemingly in order to avoid allowing White too much initiative on the lower side. The second most frequent choice was this 5, transposing into Shuei's 1, 3, 5 above. After 1850 Black began to play 5 at b transposing into the Shusaku Fuseki. Nevertheless 5 continued to be played occasionally. In a total of seven games in the GoGoD CD where this pattern arose as shown here, Black scored 6 wins and 1 jigo!

In stark contrast there are four games in the collection where White played 4 at c in the opposite corner (a much rarer move than White 4 shown) and Black replied with 5. White won all four games. Are these results essentially random? This is always possible with so few games. Are there relationships between the sides after 1, 3, 5 that are sufficient to overcome the issues between 1, 5 and 3, 5? Are the relationships such that they work better against White 4 above than they do against White c instead?


[Diagram]
Diag.: Shusaku Fuseki Variant

There is another set of games where Black sets up formation A along the bottom by playing Black 5 in the Shusaku Fuseki to this 5-3 point (there are a number of variations in the placement of White 2 in the actual practice with this Black 5). We can imagine that this is basically aimed at limiting White's (enhancing Black's) options in the upper left. The question then becomes the relative improvement in the left side potential versus the cost along the bottom side. In the collection this was a relatively successful though rare strategy with Black winning 9 of 13 games.



Dave Sigaty: While looking at the page on the Mark II Kobayashi Formation with GoGoD CD and Kombilo, I was startled to find the information below. It challenges a lot of what I thought I knew about fuseki and the coordination between corners.

Consider the following two side patterns:

[Diagram]
Diag.: Orthodox Fuseki

See Orthodox Fuseki. Normal considerations of coordination tell us that the shimari on the right coordinates well with the 4-4 stone on the left.


[Diagram]
Diag.: Mark II Kobayashi

See Mark II Kobayashi Formation. Black lacks a good follow-up move here because the left and right corners do not really coordinate.

But there is a problem with this simple analysis:
Search Results from July 2002 GoGoD CD

Orthodox Fuseki:
Games: 689
Black winning percentage: 51.2
White winning percentage: 48.6

Mark II Kobayashi:
Games: 307
Black winning percentage: 55.0
White winning percentage: 45.0

So why does the pattern that lacks proper coordination have the better winning percentage?

You might think, "Hold on, this is the Kobayashi formation so maybe it the results are biased by his results!" Good thought, here are his results:

Kobayashi Koichi
Orthodox Fuseki:
Games: 27
Black winning percentage: 48.1
White winning percentage: 51.9

Mark II Kobayashi:
Games: 52
Black winning percentage: 53.8
White winning percentage: 46.2

Well, yes he did better with his namesake. But on the other hand he didn't even score as well as the average result for Black. He even managed to drag down the overall results for the Orthodox but played only about 4% of the games.

What about somebody else? Here is another familiar player famous for his "no nonsense" style.

Yi Ch'ang-ho
Orthodox Fuseki:
Games: 29
Black winning percentage: 72.4
White winning percentage: 27.6

Mark II Kobayashi:
Games: 24
Black winning percentage: 79.2
White winning percentage: 20.2

Again we see the same pattern, less coordination makes better results. So dear readers tell me, should I throw away those dusty fuseki books and use the space for my growing manga collection instead? :-)


Charles No, don't do that. Mail them to me ....

In one sentence, my theory. You can play in a less co-ordinated way, but it implies you are going to fight harder.

DaveSigaty: I am wondering about something a little different. I believe that we think a lot about the importance of coordinating our own corners. In the competitive struggle, however, it may be more important to strike the right balance between coordinating our own and limiting the coordination of our opponent's corners. Therefore the value of outward facing formations such as Mark II Kobayashi may indeed exceed that of well coordinated but inward facing formations. This isn't too hard to grasp. What really has me wondering is whether or not Go books (and fuseki theory itself) are biased toward coordinating our own corners simply because it is easier to describe. We can more easily control our own formations than the combined formations between Black and White. The named fuseki are normally derived from the Black stones only (in some cases the White stones but normally they are receiving the same name that arose from a Black formation). So to what extent are our preconceptions based on the preponderance of material that we read, where that preponderance may reflect factors other than actual success rates?
Charles There are several reasons for treating a fuseki book as something to argue with. There is is a relatively new Kato book on the Chinese from the Nihon Ki-in - I started to want to debate it, just turning over the pages. But to pick up Dave's point: it is good to learn co-ordination (which is an aspect of strategic connection) because the stronger your opponent, the more you need to have it. I'm sure the very top players are well aware of all that, but you can't win big titles just with good orthodox play. That only takes you to pro 9 dan level. I might settle for that, though.

General discussion on statistics moved to database search.



Path: StatisticalAnalysis   · Prev: WhereIsGoGoing   · Next: PreventingShimariFromGrowingInFusekiStatistics
This is a copy of the living page "Co-ordination between Adjacent Corners" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.