White needs one more move at the marked point.
hexkid: -- I counted myself (White) some 20+ points behind, so I had to try something more active.
unkx80: At first, I thought Black is going to win this game...
Gronk: a is the vital point for Black.
Gronk: Keep reading. Consider Bd after Wc. I believe B can get an eye at the edge if White tries to take the one at b away with Wc. It takes some reading and it is always possible I missed something. Nevertheless, B should have lived in the center and had many chances to do so. It makes for an easy victory.
hexkid: No, I don't mind it at all. Thank you.
Gronk: For example, Ba works now. at c is trickier to read and results in miai for an eye at the edge or at b, if I am reading correctly. Details omitted.
unkx80: But Black gets his liberties all filled up. As a result, Black loses the capturing race instead.
And hey, displays atari-blindness!
Gronk: Now it should be clear that takes the vital point.
hexkid: And at a now would make the group alive, I think.
Gronk: No need to guess. My advice: Prove it to yourself that B needs too. If B is unconditionally alive then W can never remove it from the board. If needed, put stones to board to see for yourself. Then try to visualize it in your head.
Gronk: Good for you! The best way to progress is to do the analysis yourself on a board. Based on what you've shown here, some review of life and death would be beneficial. There are good problems on SL to help. See BeginnerExercises.
Walin: at on the other hand lives, as white can't play at a next due to shortage of liberties. So as Gronk pointed out is the vital point.
hexkid: Thank you for a very clearly written material. When I was playing I remember thinking about the safety of these key stones but figured they were safe. My opponent didn't see it either and if it weren't for you, I'd be one important point poorer. Thank you.
Black 65 was at a. If Black plays at instead, then the stones get captured. I will attempt to show you why later, but be aware that a lot of detail has been omitted. Note that these stones are key stones, so when they are captured, then the middle Black group gets connected to the upper left Black stones all the discussion about the life and death of the middle Black stones becomes moot.
If , then captures in a net. Similarly, if at a, then Black plays as well.
If here, then simply blocks. The capturing race is three liberties for Black to two liberties for White, so Black wins this capturing race by one move.
The connection at here would be a mistake. Then blocks. Note that cannot play at . So if atari, then connects. Black loses this capturing race (why?).
hexkid: The black group has two liberties, the white group has three liberties. If Black plays one point below his group has three liberties, but White goes first and wins the capturing race. Playing two points below also doesn't help.
The solution is actually to atari at and , forcing and , and then blocking at . Note that if is at instead, then White connects at instead and White wins the capturing race (why?).
hexkid: Why? Hmmmm ... I'll need to get home and fire up CGoban2 ...
Blacks gets three liberties, White also has three liberties (and a Black stone in atari) but Black gets to play first. Maybe he can play at a and ignore the stone in atari ...