How big is the 6 point double sente

    Keywords: EndGame
How big is it?  

This kosumi is the prototypical Double Sente. It is also large: 6 points.

Or is it?

I have discussed a similar example of this play, where its potential was obviously small. But here it certainly looks big, with wide-open spaces on either side. :-) However, pros frequently do not reply. Some double sente!

How large is it? Well, we really do not have enough evidence to say. The diagram is faulty. It does not show us enough of the surroundings. I frequently criticize such endgame diagrams.

I used it for 3 reasons. First, if I gave a diagram with enough information to compute the size of the plays, I would have to do it, and I do not want to go to the trouble. ;-) Second, at the time this play is made, there often is not enough information to make precise calculation feasible. Third, there is, even so, enough information here to say something about the size of this play.

White gote  

B7 = tenuki

If White responds, W2 - W6 is gote. Later, W8 - B9 is sente.

If we compare this with its mirror image, we see that the difference between the result when Black plays with sente and when White plays with sente is 6 points. Hence, a 6-point double sente.

Since the position is symmetrical, we figure that each player gains 3 points by comparison with the original position. I have marked the 3 points that Black would lose in the mirror image if White played first with sente.

The fact that the position is symmetrical tells us that, unless there is something that breaks the symmetry, this is a gote play. Why? Because sente gains nothing. But the kosumi gains at least 3 points for each player, so it is gote.

Furthermore, we know that B1 is 3 points bigger than W2. Why? Let's say that B1 gains x points and W2 gains y points. If White replies immediately, then B1 - W2 gains 3 points, so x - y = 3, and x = y + 3. B1 is 3 points larger than W2.

Charles Matthews did a database check and found that pros responded to the kosumi about half the time. 3 points is a large drop in temperature. Normally there will be several plays that are smaller than B1 and larger than W2. The question becomes, why did they reply so often? The answer, I expect, is that in those cases it was sente, because of the weakness of the opponent's stones. In other words, it was not really an endgame play. (And the position may often have been asymmetrical, so it was not a double sente, either.)

Can we say anything more about the size of this kosumi? Based upon my experience, I am going to offer a guess. I have to make some assumptions. First, that neither player threatens anything more than to intrude into the other's territory. Second, that that territory is large enough that it is not obvious how much of it is at stake. Third, that the kosumi is the correct local play for each player. (This third assumption reduces my estimate somewhat, because, if there are no better plays, the territory is not that big or insecure.)

Steve Kroon Under these assumptions, how should the player making the kosumi follow it up if he is ignored. i.e. how does he get the 8 points mentioned below?

Bill: Usual continuations are the large monkey jump and the one space jump.

Based upon my experience, I am going to guess that the incursion threatened by B1 is worth about 8 points. That makes B1 worth about 11 points by miai counting. That is right at the upper end of the large yose. That means that it will probably be played when the opponent's stones are not so secure, that its threat will be bigger, and so it will be worth even more: maybe 12 points or so.

What if it is large enough to be sente? Then we have to add 3 points, which the reverse sente player can no longer claim, as they belong to the sente player. That kicks the value up to around 14 points, which is about the size of the first play or a shimari. It may even be bigger than that. Big!

-- Bill Spight

How big is the 6 point double sente last edited by BillSpight on June 9, 2005 - 15:42
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