Actually, the hane-and-connect is not technically correct.
We can show that with a difference game.
- Click Here To Show Diagram Code
[go]$$W Difference game
$$ ---------------------------------------
$$ | . . . . O . X O . . . . . . . X . X . |
$$ | . . . . O X O . O O . X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X . X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O W |
$$ | . X X X O . . . . . . . . . . X . X W |
$$ | . O X X X O O . . . . . O X . . X . B |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O B W X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O . X X . X O X . . . . |
$$ | . O . O . . . . . . . X O . X . . . . |
$$ ---------------------------------------[/go]
We set up the difference game by setting up the mirror position and then giving White one play in one position and Black the other play in the mirror position. (The middle becomes no man's land, OC.) Is either player better off after the exchange?)
First question: Can Black to play win?
- Click Here To Show Diagram Code
[go]$$B Black plays first
$$ ---------------------------------------
$$ | . . . . O a X O . 4 5 . . . . X . X . |
$$ | . . . . O X O . O O 1 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X 3 X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O 2 X X . X O X . . . . |
$$ | . O . O . . . . . . . X O . X . . . . |
$$ ---------------------------------------[/go]
is an interesting play. If
mirrors, the board may look like miai, but
is sente. White must play
to prevent having to make a protective play at "a", and
gets the last play to win by 1 pt.
- Click Here To Show Diagram Code
[go]$$B Black plays first
$$ ---------------------------------------
$$ | . . . . O . X O . . . . . . . X . X . |
$$ | . . . . O X O . O O 1 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X 2 X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O 4 X X . X O X . . . . |
$$ | . O . O . . 6 5 3 7 . X O . X . . . . |
$$ ---------------------------------------[/go]
If Black gets the sente, he obviously wins, so let
prevent it. Now Black leaves the two hane-and-connects as miai and plays
on the bottom to get the last play and win.
Second question: Can White to play win? If not, Black's play, capturing the single stone, is technically superior to the hane-and-connect.
- Click Here To Show Diagram Code
[go]$$W White plays first
$$ ---------------------------------------
$$ | . . . . O . X O . . . . . . . X . X . |
$$ | . . . . O X O . O O 1 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X . X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O 2 X X . X O X . . . . |
$$ | . O . O . . . . . . . X O . X . . . . |
$$ ---------------------------------------[/go]
OC, one way to prevent
is to play
. But then
makes both the top and bottom miai and gets jigo.
- Click Here To Show Diagram Code
[go]$$W White plays first
$$ ---------------------------------------
$$ | . . . . O . X O . . . . . . . X . X . |
$$ | . . . . O X O . O O 2 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X 3 X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O a X X . X O X . . . . |
$$ | . O . O . . . . 1 b . X O . X . . . . |
$$ ---------------------------------------[/go]
is a clever play. Now if
, White can play
, which leaves the two hane-and-connects miai, as well as "a" and "b". White wins. Similarly, if Black plays
at 3, White replies at 2, and wins.
- Click Here To Show Diagram Code
[go]$$W White plays first
$$ ---------------------------------------
$$ | . . . . O c X O . 3 2 . . . . X . X . |
$$ | . . . . O X O . O O 4 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X a X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | b O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O . X X . X O X . . . . |
$$ | . O . O . . . . 1 . . X O . X . . . . |
$$ ---------------------------------------[/go]
So Black responds with
. Now if White plays at "a" to make 3 and 4 miai, Black plays the hane-and-connect at "b" to get a mirror position and jigo. So to protect the point at "a" White blocks with
, but then
leaves "a" and "b" miai and gets jigo.
- Click Here To Show Diagram Code
[go]$$W White plays first
$$ ---------------------------------------
$$ | . . . . O a X O . 5 1 3 7 8 . X . X . |
$$ | . . . . O X O . O O 4 X X X X . X O . |
$$ | . . . O . O O O X O O X O O . X O . . |
$$ | . . . O O X X X X X O O O X 2 X . O . |
$$ | . . . O X X . X O O O . X O . X X X . |
$$ | . . . . O O X . X X O O X O O O O X X |
$$ | . . . . . O X . . . X X X O . O . O O |
$$ | . . O . . O X . . . . . X X O O O X . |
$$ | . O . O . . . . . . . . . . X O O O . |
$$ | . X O O O . . . . _ . . . . X X X O O |
$$ | . X X X O . . . . . . . . . . X . X O |
$$ | . O X X X O O . . . . . O X . . X . X |
$$ | X X . X . X O O O . . . O X . . . . . |
$$ | O O X X X X O X X O O . O X X . . . . |
$$ | . O O O . X O . X X X O . O O X . . . |
$$ | . X . O X . X X X O O O O O X X . . . |
$$ | . . X O . X X O X X O X X X . X . . . |
$$ | . X O . O O O O 6 X X . X O X . . . . |
$$ | . O . O . . . . . . . X O . X . . . . |
$$ ---------------------------------------[/go]
is another potential answer to Black's threat on the top. But then
gives Black the last play in the top corridor. After
,
forces
to protect "a". Then Black gets
for jigo.
Capturing the single stone is technically superior to the hane-and-connect.