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Points Or Ko Threats 1at B
Difficulty: Advanced
Keywords: Problem
Black has gone the way of the Monty Python parrot. KarlKnechtel: (I'm putting in some "Advanced" level concepts here, but trying to explain them at a "Beginner" level. :) ) This is rather a sort of perverse case of ThereIsDeathInTheHane, I suppose. ;) Black expects to make a slight gain by pushing into white's territory along the side, winning one point basically. White surprises by making a hane as well, even though it's in atari! Actually, this is a throw-in tesuji. Black captures, but when white plays at 4, it's all over. There is nowhere for black to make eyes. So what went wrong? The mistake in black 1 is that it lets white play 2 in sente. As seen on PointsOrKoThreatsDiscussion where this diagram originally appeared, playing first at either 2 or 4 by black will be enough to make two eyes. (The original discussion is about which is better). After the play at 4, there is one eye at the bottom, and the top eye is sealed by playing at 2 or 3. Those points are miai - since white can't play at both simultaneously, black takes the other and lives. Note that miai are often a good source of ko threats, and indeed White would get one there. Here's proof that black 1 at 2 (the sagari) makes life:
If white plays 2 anywhere else, black at 2 divides the space into two parts. This is white's first ko threat in this situation. Black 3 still divides the space into two parts, but white isn't done yet because of how the stones are positioned inside the bottom eye. White 4 is the second ko threat, threatening to capture. Black must capture first, and is now safe. Of course, white would only play 2 and 4 as ko threats when an actual ko comes up; otherwise it's just wasting those threats. Back to the original discussion. When black plays 1 in the original diagram, white can play 2 and black's safety is threatened - the player weak enough to play 1 probably doesn't even realize that at the moment, but is simply happy to capture a stone that white seems to be throwing away. Black is still doomed if he doesn't capture, though. For example, if he suddenly realizes the problem and plays at 4 in the original diagram to start making eyes, white plays at 3 and now that eye is destroyed - another miai situation. Once black captures, he would like to play at 4, making the two eyes. But it's white's turn, and white 4 kills the group. Basically, black got too greedy here. Originally either 2 or 4 would let Black live - but only if he played one of them right away. So those points weren't miai. Now, I will work my mid-kyu magic, and remove four stones from the board without changing the situation! :o
Here the same sequence of moves is played with the same result, despite the removed stones. White 4 still kills, because black 3 has reduced the space to BulkyFive and white, having the move, strikes at the VitalPoint. (See life and death if you don't understand this.) Again, black 1 at 2 would have resulted in life, as would 4 or even a, if I'm thinking clearly. The reason I removed the circled stones is so that the play at 2 still works; without sufficient outside liberties, the TwoByThreeBox in the corner would die. (I think I have it right that it will die with only the one outside liberty at 1...) Perhaps that might motivate a move such as black 1, but you have to realize that it doesn't really extend the EyeSpace anyway. The reason black had enough space to live inside the TwoByThreeBox in the original diagram is, somewhat paradoxically, because of the stone at a (making it easier to DivideTheSpace) - though black did need one liberty at 1. (Otherwise he cannot play 3 in the second diagram because of damezumari.) Lessons learned:
This is a copy of the living page "Points Or Ko Threats 1at B" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |