[Welcome to Sensei's Library!]

StartingPoints
ReferenceSection
About


Paths
SecondCourseOnKo

Homepages
KarlKnechtel

 

Counterintuitive Ko Play
Path: SecondCourseOnKo   · Prev: KoSituation1   · Next: CountingProblem01
    Keywords: Ko

This situation occurred to me at 3 a.m. last night while I was unable to sleep due to trying to think about go problems that I might actually be able to program a computer to solve, and how to do it. :)

Suppose there is a ko on the board, relatively early in the game worth four points. You start the ko and your opponent makes a ko threat worth eight points. You should respond to it, right? Maybe not!

[Diagram]
Diag.: What is the aji here?

Right now, White is alive and the marked black group is dead. White can capture safely because there are outside liberties. White can remove (nearly) all her bad aji from the situation by starting the capture at either a; Black needs two moves to make a ko threat then. (Black will still have one large ko threat after the capture is done, as seen below, but that's unavoidable if White wants to prevent seki.)


[Diagram]
Diag.: Black gains eight points

Without the outside liberties, this is seki. Black cannot leave a dead shape, and White cannot capture.


[Diagram]
Diag.: An eight-point ko threat

Therefore, a play at either point a threatens to make seki. That's an eight-point threat, since it would deny White four points of territory and four prisoners. White answers this threat by starting the capture with either b.

But is that wise? If White just goes and connects a ko, Black makes his seki and that's the end of it. Oops - that's not quite right. Black can still make the ko threats shown below later, by sacrificing the seki. But in that case, the first threat will cost him ten points (not eight, since he has to add one stone to his sacrifice) which is still more than adequate compensation for White.

But if White answers...


[Diagram]
Diag.: A 30-point ko threat.

Suppose White goes on to win the four-point ko. Later on, a ko worth 20 points breaks out, and Black needs to find threats. Black can now threaten again by putting white into atari with 1, an option not previously available. And this threat is worth 30 points by my count - by not answering, White is deprived of the initial four points territory and four prisoners, and loses an additional 11 of each. White captures at 2.


[Diagram]
Diag.: Another 30-point ko threat

And if that's not enough for Black to win the bigger ko, Black gets a second 30-point ko threat by threatening to take both vital points of White's straight four. Of course, White cannot reasonably be expected to have known (in general) that a larger ko would break out; but with that sort of insight, sacrificing the eight-point seki for a four-point ko rather than answering the threat and losing the ko would be repaid with (lots of) interest later on.

Just an example :)



Path: SecondCourseOnKo   · Prev: KoSituation1   · Next: CountingProblem01
This is a copy of the living page "Counterintuitive Ko Play" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.