Counting problem 5 / Discussion

Sub-page of CountingProblem5
White's follow-up  

Dieter's analysis: White has the follow-up of 1 and 3. Black can either play ko (but it's a flower-viewing ko for White), or defend as in the next diagrams.

Diagram 1: Defend  

Later Black will have to answer a at b.

Bill: I believe that Black 4 is better at 7. Later Black will have to make a protective play.
Diagram 2 :Black first  

This is the result if Black plays first: no big follow-ups, just the small endgame at a and b.

Dieter: Now I will try to count this position, assuming the ko is too large for Black to bear. I am bred with deiri counting and I'd much appreciate Bill and others providing the miai counting analysis.

Minimal position  

Let's take this as the expected territory for both players. We count 9 points for Black.

Diagram 1: White first  

Compared to the neutral position, White has made three points. Black has six points. White has gained 6 points over the neutral position..

Diagram 2: Black first  

Here, Black gains 7,5 points (one for the circled point, half a point for the ko at b).

Sente or gote:

If White 1 is sente, its value is 7,5 x 2 = 15.
If White 1 is gote, we add the sente follow up of 6 points to the 7,5 = 13,5.

I understand the flaw of estimating the value here. W1 is sente, if the next biggest play x < 6. White's next play y = min(x,6), so 15 is an overestimate.


White's follow-up (var. 1)  

Bill: White 1 - 6 is sente. Later Black has to make a protective play, say at a.

Counting the marked points, the local score is +1.

Black first  

The question then becomes how to count this position. (Three white stones have been captured at the marked points.)
I get 12+ points, the exact value depending on komaster.
That makes the original position worth 6.5+ points, and the miai value of taking or saving the three white stones 5.5+ points.

Counting problem 5 / Discussion last edited by CharlesMatthews on January 15, 2003 - 11:29
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