Sorry for taking so long to respond.
dhu163 wrote:Bill: Yes it is interesting.
You say B gains 3 points, I normally say it is worth 6 points. I suppose we mean the same thing.
Right.
I can agree that in general your 3rd diagram is marginally better for white than the 4th, but by 1/6.
I’ll explain in more detail below.
$$Bc Original position
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . O . . . X . |
$$ | . X X O . . . . . . . . . O X O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc Original position
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . O . . . X . |
$$ | . X X O . . . . . . . . . O X O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
Here is the original position. Let’s evaluate it using a couple of sente sequences.
$$Bc Sente sequences
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C 6 3 7 C C |
$$ | . . X O O . . . . . . . . O 4 2 1 X C |
$$ | . X X O . . . . . . . . . O B O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc Sente sequences
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C 6 3 7 C C |
$$ | . . X O O . . . . . . . . O 4 2 1 X C |
$$ | . X X O . . . . . . . . . O B O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]

-

is a sente sequence, and later so is

-

. We can count 3 points for White, the marked point plus the captured stone and eye, and 6 points for Black, all marked. The net count is 3 pts. for Black.
Next let’s look at the game result after Black’s gote.
$$Bc Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . O 2 1 3 X . |
$$ | . X X O . . . . . . . . . O B W W X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . X O O . . . . . . . . O 2 1 3 X . |
$$ | . X X O . . . . . . . . . O B W W X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
To evaluate this we can do sagari-sagari on the edge and let Black take the

stones and White take back.
$$Bc Evaluation
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C O X C C C |
$$ | . . X O O . . . . . . . . O O X X X C |
$$ | . X X O . . . . . . . . . O . O . X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc Evaluation
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C O X C C C |
$$ | . . X O O . . . . . . . . O O X X X C |
$$ | . X X O . . . . . . . . . O . O . X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
White gets 3 pts., 1 for the marked point and 2 for the captured stones. Black gets 9 pts., 7 for the marked points and 2 for the captured stones. The net count is 6 pts. for Black. Black has gained 3 pts.
$$Wc White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C 5 1 4 C |
$$ | . . X O O . . . . . . . . O C 3 2 X C |
$$ | . X X O . . . . . . . . . O B O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Wc White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C 5 1 4 C |
$$ | . . X O O . . . . . . . . O C 3 2 X C |
$$ | . X X O . . . . . . . . . O B O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
White can play this gote sequence. White gets 5 pts. and Black gets 5 pts., for a net count of 0. White has gained 3 pts.
$$Wc White gote (II)
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . a . . |
$$ | . . X O O . . . . . . . . O . 1 . X . |
$$ | . X X O . . . . . . . . . O X O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Wc White gote (II)
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . a . . |
$$ | . . X O O . . . . . . . . O . 1 . X . |
$$ | . X X O . . . . . . . . . O X O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
After

either side can gain 1 pt. in gote, starting with a play at “a”. We can evaluate this position with sagari-sagari to get a net count of 0, the same as the previous position. Which gote is better depends upon the rest of the board.
$$Wc White gote (III)
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . 2 . . |
$$ | . . X O O . . . . . . . . O 3 . 1 X . |
$$ | . X X O . . . . . . . . . O B O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Wc White gote (III)
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . . 2 . . |
$$ | . . X O O . . . . . . . . O 3 . 1 X . |
$$ | . X X O . . . . . . . . . O B O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
I evaluate the count after

as 1/3 for Black. Let’s look at the follow-up plays.
$$Bc White gote, Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . 4 3 1 X . C |
$$ | . . X O O . . . . . . . . O O . O X C |
$$ | . X X O . . . . . . . . . O C O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc White gote, Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . 4 3 1 X . C |
$$ | . . X O O . . . . . . . . O O . O X C |
$$ | . X X O . . . . . . . . . O C O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
Black has a gote follow-up with

. To evaluate the resulting position, let Black play the sente sequence,

-

. White gets 2 points and Black gets 5, for a net result of 3 pts. for Black.

gains 2 2/3 pts.
$$Wc White gote, White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . 1 X . . |
$$ | . . X O O . . . . . . . . O O . O X . |
$$ | . X X O . . . . . . . . . O . O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Wc White gote, White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . . . 1 X . . |
$$ | . . X O O . . . . . . . . O O . O X . |
$$ | . X X O . . . . . . . . . O . O O X . |
$$ | X O O O . O O . . O . . . . O X X . . |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
I evaluate the count after

as 2 1/3 pt. for White (-2 1/3 for Black).

gains 2 2/3 pts. Let’s look at the follow-ups.
$$Bc White gote, White gote, Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C O X 1 C |
$$ | . . X O O . . . . . . . . O O C O X C |
$$ | . X X O . . . . . . . . . O C O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Bc White gote, White gote, Black gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C O X 1 C |
$$ | . . X O O . . . . . . . . O O C O X C |
$$ | . X X O . . . . . . . . . O C O O X C |
$$ | X O O O . O O . . O . . . . O X X C C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
After

each player gets 5 pts., for a net count of 0.

gains 2 1/3 pts.
$$Wc White gote, White gote, White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C O B 1 . |
$$ | . . X O O . . . . . . . . O O C O X 3 |
$$ | . X X O . . . . . . . . . O C O O X 8 |
$$ | X O O O . O O . . O . . . . O X X 4 C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |
- Click Here To Show Diagram Code
[go]$$Wc White gote, White gote, White gote
$$ ---------------------------------------
$$ | . . X X O . . . . . . . . C C O B 1 . |
$$ | . . X O O . . . . . . . . O O C O X 3 |
$$ | . X X O . . . . . . . . . O C O O X 8 |
$$ | X O O O . O O . . O . . . . O X X 4 C |
$$ | . X O . . O X . X O . . . O . . . . . |
$$ | . X X X . O X X O O . . . . O X . . . |
$$ | . . . . X . X O X . . . . O X X . . . |[/go]
To evaluate the position after

, let White play

-

with sente. Later

and the White connection at

are miai. White gets 6 pts. for the 4 marked points plus 2 captured stones. Black gets 1 marked point plus 1/3 pt. for the

stone in ko. The net count is -4 2/3 (for Black).

gains 2 1/3 pts.