Ko fight Example

  Difficulty: Intermediate   Keywords: Ko

Here is an example of a simple ko fight. We will calculate the values of winning the ko versus executing the ko threat.

Table of contents Table of diagrams
A ko for life.
Life
White's ko threat
White takes the ko, Black plays a threat
Ko fight
Ko fight (ii)

The ko position

[Diagram]
A ko for life.  

Black has just taken a white stone at a. If Black manages to connect at a, his bottom group will live



Calculations

Calculating the size of the ko

[Diagram]
Life  

Black lives after filling at B3, with two points of territory. If his group dies, then White will gain 25 points, so the difference between winning and losing the ko is 27 points.

White knows this as well so she tries to play a ko-threat.



Calculating the size of the threat

[Diagram]
White's ko threat  

This move threatens to make the white bottom left group alive again (making two eyes at B2) and make two points of territory. The group being dead, Black gains 20 points, so the ko threat is worth 22 points. Now the question is whether Black should answer the threat or not.



Decision making for this threat

  1. If Black fills the ko and White lives, Black gets two points, minus two points for White, net 0.
  2. If Black answers the threat and lets White take and win the ko, Black gets to play one move elsewhere. Locally Black gets 20 points in the bottom left corner minus 25 points for losing the ko, a loss of 5 points. However, if the move elsewhere is worth more than 5 points by miai counting, Black does better (as a rule) than by winning the ko.

Local threats

Sometimes, local threats exist, which continue the ko fight, because filling the ko would not resolve the situation:

[Diagram]
White takes the ko, Black plays a threat  

Here, Black plays B4 as a threat to connect his group and capture the marked stones, so that White's filling the ko would not affect the group's life. White should therefore answer this local ko threat at W5, and let Black retake the ko. Later, Black has another local ko threat at a.



The fight continues

If Black wins the ko, thanks to his local threats, White gets something in exchange.

This ko is worth nine points [1]. Suppose that the ko arises when other plays are worth around seven points. Then we might get this kind of ko fight.

[Diagram]
Ko fight  

W4 takes ko. B7 ditto. W8, B9 elsewhere. W10 takes ko. Then

[Diagram]
Ko fight (ii)  

W4 elsewhere. B5 fills ko. W6 elsewhere.


Black takes and wins the ko, and gets one move elsewhere, while White gets three moves elsewhere. If these moves are worth around seven points, White gains 14 points in exchange for the ko.

But if White does not fight the ko, but just plays elsewhere after Black takes the ko, leaving the ko until the end of the game, then she will get only seven points in exchange for the ko. At the end she will just fill dame or pass while Black fills the ko.

(Actually, B5 above is a losing ko threat, so White's compensation for losing the ko is somewhat greater.)


[1] The value is 27 and the local tally = 3

  • Black ignores a threat: (B1 + B3) = 2 black moves
  • Black answers a threat the White ignores: B1 + (W2 - B3) - (W4 + W6) = 1 white mov

Ko fight Example last edited by TheBigH on June 11, 2012 - 13:55
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