Ko fight example from a pro game - 5
White has just forced Black to play inside his own territory with . According to commentator An Younggil from gogameguru, White should now fill at a which would lead to a half point win. See 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.
After taking the ko with , 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.
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 here, allowing to start the ko fight. - is an ordinary threat, but launches another ko as a threat. It's all about calculating values now.
If White filled the ko at the bottom upon , Black would capture at a, making two points (a captured stone and a point at ) 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 , 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.
resolves the upper ko, so that proceeds with the second stage of the bottom ko.
In this second stage, both parties produce ordinary threats, thankfully so for us, mortal spectators.
Black's ko threat at loses a point: White would need to play after all outside liberties have been filled. However, it turns out to be just enough to force White and answer at .
In the end, Black has gained five points from the ko, while White has gained two from the ko at and one by getting 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 http://gogameguru.com/commentary-cho-hanseung-choi-cheolhan-55th-kuksu/.
Bill: There is one more point at stake in the ko.
If White fills the ko at or a, then - is a one point ambiguous play. Black connects at , getting one point less territory there, . . .