As someone who enjoys math, I've always liked the endgame, it seems to be the most mathematical part of go. And I haven't had time for a lot of comments lately, So I figured I'd take a little time to examine the position and try to get some idea of what's biggest, and share my thought process.
So here's the board. I've marked the points that seem intuitively like they might be big.
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[go]$$Wcm136 Move #136-8, w+1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . . O O X . . . . |
$$ | . . X . O X . . . O . O . e . X . . . |
$$ | . . X O . O O O O . . . . . . . . . . |
$$ | . . . O . X X X X X O O . . . . X . . |
$$ | . . X O . . O X . X O X O . . O X d . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | . . X . . . . . X . . . . . . O O . . |
$$ | . X . , . . X . X O . O . . . X X d . |
$$ | a O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . . c . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . b . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Ok, first ''a''. I feel like if white plays first, The safe thing is to do something like this:
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[go]$$Wcm136 Choice a
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . . O O X . . . . |
$$ | . . X . O X . . . O . O . . . X . . . |
$$ | . . X O . O O O O . . . . . . . . . . |
$$ | . . . O . X X X X X O O . . . . X . . |
$$ | . . X O . . O X . X O X O . . O X . . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | 4 8 X . . . . . X . . . . . . O O . . |
$$ | 3 X 7 , . . X . X O . O . . . X X . . |
$$ | 1 O O O . O X . X O . . . O . . . . . |
$$ | 5 X X O . . O X X O X X . O X X . . . |
$$ | 6 . X . . O . X O O O . . . O . X . . |
$$ | . 2 . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
This seems to suggest it's about 6 points white sente, or reverse sente for me. I can try to descend right away. If I live, it saves me 2 points, and means this move is only 4 points. But if white can kill or get seki?
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[go]$$Wcm1 Move fight
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . . O O X . . . . |
$$ | . . X . O X . . . O . O . . . X . . . |
$$ | . . X O . O O O O . . . . . . . . . . |
$$ | . . . O . X X X X X O O . . . . X . . |
$$ | . . X O . . O X . X O X O . . O X . . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | . . X . . . . . X . . . . . . O O . . |
$$ | . X . , . . X . X O . O . . . X X . . |
$$ | 1 O O O . O X . X O . . . O . . . . . |
$$ | 2 X X O . . O X X O X X . O X X . . . |
$$ | . . X 6 . O . X O O O . . . O . X . . |
$$ | 7 3 5 X . . . X X X . O . . . . X X . |
$$ | 9 4 . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | 8 X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
It looks to me like W can't make seki, but it's a bit hard to say. It's always a bit frightening to make a play like this against a stronger player, you have to be very confident your reading is correct. But for now will say it's ok, and this move isn't so big.
Ok, let's look at ''b'':
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[go]$$Bcm1
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . 2 1 3 b b X X O O . O |
$$ | . . . . . . . . . . b b b b . . . . . |
$$ ---------------------------------------[/go]
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[go]$$Wcm1
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . 1 2 4 X X O O . O |
$$ | . . . . . . . w w 5 . 3 . . . . . . . |
$$ ---------------------------------------[/go]
It depends how the smaller endgame plays out, but this looks to me around 8 points gote, which is about 4 points miai, which is actually right around par with ''a''. The followup if white gets this move is a bit interesting:
- Click Here To Show Diagram Code
[go]$$Bcm1
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . 1 O O X X X O X X O . . |
$$ | . O O O . . O 2 4 . O X X X X O O . O |
$$ | . . . . . . . . . O . O 3 . . . . . . |
$$ ---------------------------------------[/go]
It's hard for me to know how much to give W in this position, which is why I only counted 2 points in the original diagram.
Moving on to ''c'':
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[go]$$Bcm1 4 points for black
$$ | . O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . 2 1 . X X . |
$$ | . . . . . O . . . O O . 4 3 b X O X . |
$$ | . X X X . . . X X X O O O 5 b X O O . |
$$ | . X O X . O . . O O X X X W X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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[go]$$Wcm1 3 points for W.
$$ | . O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . w O . X . . |
$$ | . . . X . . . X X X . O . w 1 2 X X . |
$$ | . . . . . O . . . O O . w . . X O X . |
$$ | . X X X . . . X X X O O O 3 . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
About 7 points gote, or slightly smaller than ''b''.
Ok, this is a lot of text, but I want to keep going. ''d'' is a tricky position, and the very fact that it's hard to see how best to play makes me think it may be urgent. I think It's best to play this way:
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[go]$$Wcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . . O O X . . . . |
$$ | . . X . O X . . . O . O . . . X . 8 . |
$$ | . . X O . O O O O . . . . . . . . . 6 |
$$ | . . . O . X X X X X O O . . . . X 2 5 |
$$ | . . X O . . O X . X O X O . . O X 1 7 |
$$ | . . X O . . O O X X X X O . O . O 3 . |
$$ | . . X . . . . . X . . . . . . O O . . |
$$ | . X . , . . X . X O . O . . . X X 4 . |
$$ | . O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
- Click Here To Show Diagram Code
[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . . O O X . . . . |
$$ | . . X . O X . . . O . O . . . X . b . |
$$ | . . X O . O O O O . . . . . . . . . b |
$$ | . . . O . X X X X X O O . . . . X b b |
$$ | . . X O . . O X . X O X O . . O X 1 . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | . . X . . . . . X . . . . . . O O 4 . |
$$ | . X . , . . X . X O . O . . . X X 2 . |
$$ | . O O O . O X . X O . . . O . . . 3 5 |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Hmm, since B loses two points on the other side even when going first, It seems like only about 2 points W sente, which is a lot smaller than I thought it would be. One concern I have is about this:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X 6 5 . . . |
$$ | . . . X O . X . . . . . O O X . 7 . . |
$$ | . . X . O X . . . O . O . . . X . . . |
$$ | . . X O . O O O O . . . . . . . . . . |
$$ | . . . O . X X X X X O O . . . . X 2 . |
$$ | . . X O . . O X . X O X O . . O X 1 . |
$$ | . . X O . . O O X X X X O . O . O 3 . |
$$ | . . X . . . . . X . . . . . . O O . . |
$$ | . X . , . . X . X O . O . . . X X 4 . |
$$ | . O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
It's amazing how often endgame problems are actually life and death problems in disguise. In this case I think B is ahead in the capturing race.
- Click Here To Show Diagram Code
[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . 4 7 . |
$$ | . . . X O . O . . . . O X X X O . 5 6 |
$$ | . . . X O . X . . . . . O O X . O 2 . |
$$ | . . X . O X . . . O . O . . . X 1 3 . |
$$ | . . X O . O O O O . . . . . . . . . . |
$$ | . . . O . X X X X X O O . . . . X X . |
$$ | . . X O . . O X . X O X O . . O X O . |
$$ | . . X O . . O O X X X X O . O . O O . |
$$ | . . X . . . . . X . . . . . . O O . . |
$$ | . X . , . . X . X O . O . . . X X X . |
$$ | . O O O . O X . X O . . . O . . . . . |
$$ | . X X O . . O X X O X X . O X X . . . |
$$ | . . X . . O . X O O O . . . O . X . . |
$$ | . . . X . . . X X X . O . . . . X X . |
$$ | . . . . . O . . . O O . . . . X O X . |
$$ | . X X X . . . X X X O O O . . X O O . |
$$ | . X O X . O . . O O X X X O X X O . . |
$$ | . O O O . . O . . . . . . X X O O . O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Ok, last one:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . 7 6 8 . . . . . . |
$$ | . . . X O . O . . . 9 O X X . 2 . . . |
$$ | . . . X O . X . . . . w O O X . . . . |
$$ | . . X . O X . . . O . O w w 1 X . . . |
$$ | . . X O . O O O O . . . w w 5 4 . . . |
$$ | . . . O . X X X X X O O w w . 3 X . . |
$$ | . . X O . . O X . X O X O . . O X . . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | . . X . . . . . X . . . . . . O O . . |[/go]
- Click Here To Show Diagram Code
[go]$$Bcm1
$$ ---------------------------------------
$$ | . . . X X O . . . . . . . . . . . . . |
$$ | . . . X O . O . . . . O X X . . . . . |
$$ | . . . X O . X . . . . 6 O O X . . . . |
$$ | . . X . O X . . . O . O 5 1 . X . . . |
$$ | . . X O . O O O O . . . . . . 3 . . . |
$$ | . . . O . X X X X X O O . . . 2 X . . |
$$ | . . X O . . O X . X O X O . . O X . . |
$$ | . . X O . . O O X X X X O . O . O . . |
$$ | . . X . . . . . X . . . . . . O O . . |[/go]
This one also seems about 7 points in gote, very similar in size, but still slightly smaller than ''b''. Also if W plays this way it removes my aji underneath and frees the followup marked above, so it may be more like 4 or 5 points gote.
Well, after all that, it seems to me like ''b'' is biggest, so that's what I'm going with. There's certainly some sticky aji in my positions, but if I don't learn to trust my reading I can never improve.