Hi Lanrose,

Get a sense this is bad shape for White.
Proverb: Hane at the head of two (enemy) stones:
$$B Hane head of two stones
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . 1 O O . . . .
$$ . . . X X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$B Hane head of two stones
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . 1 O O . . . .
$$ . . . X X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .[/go]
In general -- yes, there are infinite exceptions --
this local shape is good for B, and not good for W.
Thus, the proverb (general guideline): Hane at the head of two stones.
Let's count liberties.
The

string has 4 libs (1 shared);

has 3 (1 shared) --
Black has a total of 6 libs.
White has 3.
The following shape is even better for B, and worse for W:
$$B Hane head & tail of two stones:

tenuki
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . 1 O O 3 . . .
$$ . . . X X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$B Hane head & tail of two stones:
tenuki
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . 1 O O 3 . . .
$$ . . . X X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .[/go]
Liberties -- B: 8. W: 2.
The tiger's mouth is a good shape (barring the infinite exceptions

):
$$B Tiger's mouth
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . . 1 . . . . .
$$ . . X . X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$B Tiger's mouth
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . . 1 . . . . .
$$ . . X . X . . . .
$$ . . . . . . . . .
$$ . . . . . . . . .[/go]
Therefore, locally (ignoring the rest of the board),
the following

-

exchange is good for B, and bad for W:
$$W Bad for W
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . . 2 1 O . . .
$$ . . X . X X . . .
$$ . . . . . . . . .
$$ . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$W Bad for W
$$ . . . . . . . . .
$$ . . . . . . . . .
$$ . . . 2 1 O . . .
$$ . . X . X X . . .
$$ . . . . . . . . .
$$ . . . . . . . . .[/go]
In general, you don't want to do this exchange as White.
(Yes, there are exceptions.)
The situation in your game is not an exception:
$$W Real game: Bad for W
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . 8 7 O . . |
$$ . . . X . X X . . |
$$ . . . . . . . . . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |
- Click Here To Show Diagram Code
[go]$$W Real game: Bad for W
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . 8 7 O . . |
$$ . . . X . X X . . |
$$ . . . . . . . . . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |[/go]
To avoid the above bad shape for W, you first hane the other side;
if B blocks, you connect:
$$W Variation A
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . O 3 . |
$$ . . . X . X X 1 . |
$$ . . . . . . 4 2 . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |
- Click Here To Show Diagram Code
[go]$$W Variation A
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . O 3 . |
$$ . . . X . X X 1 . |
$$ . . . . . . 4 2 . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |[/go]
Next, the following exchange is still bad for White:
(which is the result in your real game)
$$W Variation B: Bad for White
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . 2 1 O O . |
$$ . . . X . X X O . |
$$ . . . . . . X X . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |
- Click Here To Show Diagram Code
[go]$$W Variation B: Bad for White
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . 2 1 O O . |
$$ . . . X . X X O . |
$$ . . . . . . X X . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |[/go]
So, don't do it! Do something else. For example: jump to

:
$$W Variation C
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . 1 . . . . . |
$$ . . . . . . O O . |
$$ . . . X . X X O . |
$$ . . . . . . X X . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |
- Click Here To Show Diagram Code
[go]$$W Variation C
$$ ----------------- |
$$ . . . . . . . . . |
$$ . . . 1 . . . . . |
$$ . . . . . . O O . |
$$ . . . X . X X O . |
$$ . . . . . . X X . |
$$ . . . . . . O . . |
$$ . . . . . . . . . |[/go]