3-4 approach, high or low

Fig. 1 Which approach move?  

SnotNose What factors apply when considering whether to approach the 3-4 black stone at a or b? Presumably the stones in the lower left corner matter. Perhaps those in the upper right do as well. Finally, perhaps there are issues of territory and influence. However, with so many possible continuations (think of all the possible pincers alone!!!), I don't know how to make this decision. Does anyone? Or is it a matter of style? Contributions welcome.

Effect of thickness

Fig. 2 Low approach idea  

SnotNose One idea that occurs to me is that if white has a thick position in the lower left corner, facing upward toward the upper left, perhaps a play at is good since if black ignores it a press at a developes white's moyo. Or, white can play b and hope for a Taisha fight.

More generally, if white wants to develop the left, the low approach move might help.

Of course, if black doesn't tenuki, white won't get to play a or b. One thing is certain, black won't pincer here so that cuts down the possible joseki to consider.

Fig. 3 Low approach perhaps bad now  

SnotNose But, if we add some more stones to the board, giving black a moyo in the upper right, perhaps is now bad since that permits (or black can play a himself), squashing white's moyo and expanding black's. Perhaps in this case a is better (let's leave out the idea of approaching from the other side for now).

Fig. 4 High approach  

SnotNose I can't resist giving this high approach example. Black can still develop the top with the attachment . Black and white then push along the line between the moyos. Next black plays a. Later black can play b to take more corner profit. So, white has less to hope for in the corner this way.

High approach unusual  

This is quite a rare combination ( high, low) in pro games. The other three possible types are more common.

In this case one can give this rationale:

After standard joseki  

Assuming a white 4-4 stone lower left, as we look at it, this is reasonable for White on the left side.

But you could say that the stone stops White doing anything very effective with , now. Black can probably take sente to play elsewhere.

From The Direction of Play

Evand: Consider also the following position, taken from The Direction of Play.

Where should Black approach?  

If Black at b, then the following is natural:

Black's high approach  

However, Kajiwara explains that has little effect on the 3-3 stone, and so is not a very good move. Therefore, Black approaches low. This would suggest to me that a large piece of the high/low decision is based on the same principles as all of the rest of joseki choice, namely whether at the end the stones are in good places. Since is not well placed, Black chooses a different variation.

Charles Well, it can't be that simple.

Single side  

Look at this side pattern alone, and ask a crude statistical question: is White's next play here at a or b?

Then quite convincing numbers come up in a database search: a and b are equally likely.

There is certainly more to be said about that result.

But reverting to the previous diagram, you can say that there contradicts Black's choice of the small high enclosure in the upper right. Given that context, I see the reasoning.

Side with enclosure  

There are few enough examples of this side from recent times in pro games - a small sample only from the last 25 years. When Black does approach in the upper left, is preferred.

Simple sides

Dave: Once the stones start growing this is a very complex question. On the other hand, in the beginning, the issue seems to be dominated by who holds the opposing corner. If White approaches from a her own position, she prefers the low approach. If her approach wedges between two Black corners, she tends to play high. This tendency is pretty clear in professional games since the 90's.

White tends to play low (1)  

In my data, White prefers to the high approach at a by about 4 to 1 over the period 1990 - 2004.

White tends to play low (2)  

Here the difference is less, about 2 to 1.

White tends to play low (2)  

Here the difference is more, over 5 to 1. This is not surprising, see opposing 3-4 points.

White tends to play high (1)  

When the opposing corner is Black, White approaches high at about 4 times more often than the low play at a. In addition, White is as likely to use the far approach at b as the play at a.

White tends to play high (2)  

Here White is actually much more likely to approach the upper left (normally from a White position in the lower left) than the upper right. However, in cases where White chooses to approach the upper right first, the high play at is more than twice as frequent as the low play at a.

White tends to play high (3)  

Here White is more than 5 times more likely to approach high at .

White tends to play high (4)  

With the shimari in the upper left the case is more extreme. White is 10 times more likely to approach at than at a. The distant approach at b is also twice as likely as a.