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Counterintuitive Ko Play
This situation occurred to me at 3AM 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 4 points. You start the ko and your opponent makes a KoThreat worth 8 points. You should respond to it, right? Maybe not!
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.)
Without the outside liberties, this is seki. Black cannot leave a dead shape, and white cannot capture.
Therefore, a play at either 'a' threatens to make seki. That's an 8-point threat, since it would deny white 4 points of territory and 4 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 10 points (not 8, since he has to add one stone to his sacrifice) which is still more than adequate compensation for white. But if white answers...
Suppose white goes on to win the 4-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 4 points territory and 4 prisoners, and loses an additional 11 of each. White captures at 2.
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 VitalPoints 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 8-point seki for a 4-point ko rather than answering the threat and losing the ko would be repaid with (lots of) interest later on. Just an example :) This is a copy of the living page "Counterintuitive Ko Play" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |