Endgame Problem 40 / Solution

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Sub-page of EndgameProblem40
[Diagram]
Slightly better  

The atari at B1 is slightly better, on average, than the sagari at a. The sagari leaves Black with 4 points. The position after B1, while still hot, has a count of 4.0375. In a real game, the sagari may be correct.

Of course, now we have the question of how we derived the value of 4.0375.

[Diagram]
White plays first  

If White plays first we have a position with a count of 1.075.

If Black plays at B1 instead, the local score is 7. As these are gote, the average count is 4.0375.

How do we get the count of 1.075?

[Diagram]
White plays first  

After W1 the count is -1.85. (Per convention White scores are negative.) If Black plays B1 the score is 4. The average is 1.075.

How do we get the count of -1.85?

[Diagram]
Black plays first  

After B1 the count is -0.2.

[Diagram]
White plays first  

After W1 the count is -3.5.

The average count is - 1.85.

[Diagram]
Losing sente  

W1 is tempting, but the count after B2 is -1.6, for an average loss of 0.25 point.



[Diagram]
count = -3.5  

After W1 the local score is -5 (counting the Black stone already captured). If B1 instead, the local score is -2. The average is -3.5, as advertized.



The count of the next position is -0.2 (counting the captured Black stone).

[Diagram]
White wins the ko  

B2 elsewhere. W3 fills the ko.

The local score is -3. White has made 2 net plays to get here.

[Diagram]
Black wins the ko  

W2, W4 elsewhere. B5 fills the ko.

The local score is +4. Black has made 3 net plays to get here.

The difference in score between these positions is 7 points. The difference in plays is 5 plays. The miai value of each play is 7/5 = 1.4 points.

So the initial position in the ko has a count of 4 - 3 * 1.4 = -3 + 2 * 1.4 = -0.2.



--Bill Spight


Discussion

Karl Knechtel: b was also proposed in the problem statement; what is the miai value here? Also, what situations would make the sagari correct? (I assume they have to do with the ko threat environment?)

[Diagram]
Ko  

Bill: The sagari may be better if this ko is unfavorable for Black.



The atari at B3 leaves the same count as the sagari, but White can still make the ko.


Paths: <= Endgame =>   ·   <= Endgame Problems
Endgame Problem 40 / Solution last edited by BillSpight on May 4, 2004 - 16:51
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