KarlKnechtel/Counterintuitive Ko Play

Sub-page of KarlKnechtel

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[1]!

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.)

Black gains eight points

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

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.

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.

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 :)

[1] Bill: Karl, the way you are counting the threat appears to be deiri, taking the swing between results. If you measure the ko that way, the swing between White's winning the ko and Black's winning it is 4 points. In that case, ignoring an 8 point threat entails a 4 point loss plus the loss of the miai value of tenuki, since you get to play somewhere else in exchange for losing the ko (assuming you do lose it). Ignoring the threat is a loser.

Also, such a small ko should be fought late in the game, not early.

Response: Er... yes, quite right. I wrote this a long time ago I think ^^; The key idea I had is that the second and third ko threats are larger than the first, and ignoring the first prevents the second and third from coming about (assuming black follows through). The strategy behind that is poorly thought out though, it seems. Presumably if both players are any good, then the value of kos fought, at the times they are fought, will decrease uniformly. Thus the second and third threats are only relevant to the same ko that the first was used for.

In that case, the increasing value of the threats buys nothing, yes, if the first threat is "too big to ignore". And if the ko is such that an 8-point threat is too small but a 30-point threat isn't, then white can still ignore - it becomes more pressing to ignore it, actually. Maybe white should re-evaluate who if anyone is komaster/komonster :)

KarlKnechtel/Counterintuitive Ko Play last edited by KarlKnechtel on August 3, 2003 - 07:08