Bki wrote:More importantly, then, is what would have been a better way to play the endgame to maximize the points I got from this corner.
Well, what is outside the corner matters for the endgame.
$$Bc Black to play
$$ ------------------
$$ | . . . . b . . . .
$$ | . . . X X O . . .
$$ | . X X X O O . . .
$$ | a X O O O . . . .
$$ | c O O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ------------------
$$ | . . . . b . . . .
$$ | . . . X X O . . .
$$ | . X X X O O . . .
$$ | a X O O O . . . .
$$ | c O O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
For instance,
a, b, or c is sente for White, but then, after securing the corner Black has a sente hane-connect.
$$Bc Black to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . X X O . . .
$$ | . X X X O . O . .
$$ | . X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . X X O . . .
$$ | . X X X O . O . .
$$ | . X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
For reference, here is a simpler position where Black has no sente. What is Black's play?
$$Bc Black to play
$$ ------------------
$$ | . a . . . . . . .
$$ | . 1 . X X O . . .
$$ | . X X X O . O . .
$$ | . X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ------------------
$$ | . a . . . . . . .
$$ | . 1 . X X O . . .
$$ | . X X X O . O . .
$$ | . X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
After

or
Ba, the rest is miai.
$$Bc Miai
$$ ------------------
$$ | C C C 3 2 4 C . .
$$ | C B C X X O . . .
$$ | C X X X O . O . .
$$ | 7 X O O O . . . .
$$ | 5 O , . . . . . .
$$ | 6 . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Miai
$$ ------------------
$$ | C C C 3 2 4 C . .
$$ | C B C X X O . . .
$$ | C X X X O . O . .
$$ | 7 X O O O . . . .
$$ | 5 O , . . . . . .
$$ | 6 . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
In the marked region, Black gets 6 pts. in the corner and WHite gets 1 pt. outside, for a net result to Black of 5 pts.
What is the result if Black plays a descent instead?
$$Bc Black to play
$$ ------------------
$$ | . 4 2 . 1 . . . .
$$ | 6 3 . X X O . . .
$$ | . X X X O . O . .
$$ | 5 X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ------------------
$$ | . 4 2 . 1 . . . .
$$ | 6 3 . X X O . . .
$$ | . X X X O . O . .
$$ | 5 X O O O . . . .
$$ | . O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
If

,

causes difficulties for Black.

leads to seki, possibly ko later.

at 4 lets White make ko. This descent is not good.
$$Bc Black to play
$$ ------------------
$$ | . 4 5 . 6 . C . .
$$ | 3 2 . X X O . . .
$$ | C X X X O . O . .
$$ | 1 X O O O . . . .
$$ | 7 O , . . . . . .
$$ | 8 . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ------------------
$$ | . 4 5 . 6 . C . .
$$ | 3 2 . X X O . . .
$$ | C X X X O . O . .
$$ | 1 X O O O . . . .
$$ | 7 O , . . . . . .
$$ | 8 . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
If

,

threatens the corner. Black keeps sente, but the net result is 4 pts. for Black, 5 pts. for Black in the corner minus 1 pt. outside for White. This descent may be correct, depending on the rest of the board.
$$Wc White to play
$$ ------------------
$$ | C C C 4 3 5 C . .
$$ | C 2 C X X O . . .
$$ | 6 X X X O . O . .
$$ | 1 X O O O . . . .
$$ | 7 O , . . . . . .
$$ | C . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Wc White to play
$$ ------------------
$$ | C C C 4 3 5 C . .
$$ | C 2 C X X O . . .
$$ | 6 X X X O . O . .
$$ | 1 X O O O . . . .
$$ | 7 O , . . . . . .
$$ | C . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
White to play can hold the net result for Black to 3 pts., 5 pts. for Black in the corner minus 2 pts. for White outside. The Black descent at 1 prevents that with sente. This position is ambiguous, as Black can choose to play sente or gote.
$$Wc White to play, II
$$ ------------------
$$ | . 2 . 6 1 7 . . .
$$ | . . . X X O . . .
$$ | 4 X X X O . O . .
$$ | 3 X O O O . . . .
$$ | 5 O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Wc White to play, II
$$ ------------------
$$ | . 2 . 6 1 7 . . .
$$ | . . . X X O . . .
$$ | 4 X X X O . O . .
$$ | 3 X O O O . . . .
$$ | 5 O , . . . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

here is an alternative, leading to the same net result.
