Ko fight example from a pro game - 5

  Difficulty: Advanced   Keywords: EndGame, Ko

Table of contents Table of diagrams
Position at move 247
Sente ko - white wins
Sente ko - black sente
Moves 248 to 257 (8 at 2) (9 at 6)
Moves 258 to 267 (9 at 3)
Moves 268 to 277 (8 at 2)
The end - Moves 278 to 282
One point ambiguous play
One point sente

Introduction

[Diagram]
Position at move 247  

This ko fight is the deciding fight in the endgame of the 5th and decisive game of the 2011 Kuksu title match between Choi Cheolhan (White) and Cho Hanseung.

White has just forced Black to play inside his own territory with black+circle. According to commentator An Younggil from gogameguru, White should now fill at a which would lead to a half point win. See [ext] his game commentary for reference. On this page we'll dig further into the calculations of the ko exchange.

The ko is a sente ko for Black. Filling the ko gains 1 2/3 points.



Demonstration of the sente ko

[Diagram]
Sente ko - white wins  

White would make one point if he fills the ko at white+circle.

[Diagram]
Sente ko - black sente  

After taking the ko with B1, W2 fills. By contrast with the previous diagram, White has 1 less point of territory, Black has 1 prisoner, and the ko stone is worth 1/3 point for White, in total a difference of 1 2/3 points.



The ko fight in the game

[Diagram]
Moves 248 to 257 (8 at 2) (9 at 6)  

In fact there needn't be a ko fight: White could simply have filled it at his turn. But according to An, Choi was under time pressure and made some calculation mistakes. He must have thought he had enough ko threats and not enough points, so he played W1 here, allowing B2 to start the ko fight. W3-B4 is an ordinary threat, but B6 launches another ko as a threat. It's all about calculating values now.

If White filled the ko at the bottom upon W7, Black would capture at a, making two points (a captured stone and a point at W7) while White loses two points (a and b) or three (if Black can continue at b). We can say this ko is worth 4,5 points.

It looks natural to capture at W7, since we all learned to capture the ko first, but according to An, White would win (by 0,5 points) if he now connects at a. Clearly, these pro commentaries do not suffice with heuristics but simply read the rest of the game.

W9 resolves the upper ko, so that B10 proceeds with the second stage of the bottom ko.

[Diagram]
Moves 258 to 267 (9 at 3)  

In this second stage, both parties produce ordinary threats, thankfully so for us, mortal spectators.

[Diagram]
Moves 268 to 277 (8 at 2)  

Both continue to consume their threats in the respective areas.

[Diagram]
The end - Moves 278 to 282  

Black's ko threat at B2 loses a point: White would need to play W3 after all outside liberties have been filled. However, it turns out to be just enough to force White and answer at W5.

In the end, Black has gained five points from the ko, while White has gained two from the ko at white+circle and one by getting W3 for free, compared to if White had connected the ko immediately at move 248 (the actual move essentially made one point at a). The net difference is 2 points. Since Black won the game by 1,5 points, we can say Choi's fighting spirit made him lose this game, which could have been a half point win, and hence the title match.

This analysis could not have been produced without An Younggil's great commentary at [ext] http://gogameguru.com/commentary-cho-hanseung-choi-cheolhan-55th-kuksu/.


Bill: There is one more point at stake in the ko.

[Diagram]
One point ambiguous play  

If White fills the ko at white+circle or a, then W1 - W3 is a one point ambiguous play. Black connects at B4, getting one point less territory there, . . .

[Diagram]
One point sente  

Or W1 - W5 is sente, holding Black to 10 points.




Ko fight example from a pro game - 5 last edited by 68.122.10.73 on December 27, 2011 - 10:07
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