How big is the 6 point double sente

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.

= tenuki

If White responds, - is gote. Later, - 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 is 3 points bigger than . Why? Let's say that gains x points and gains y points. If White replies immediately, then - gains 3 points, so x - y = 3, and x = y + 3. is 3 points larger than .

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 and larger than . 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.)