The situation around

is kind of weird.
First, if you select to jump out here:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . . . W . . . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Black should be helping his 4-4 stone. The way he played in the game is the wrong direction. He should play like this:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . . . O . . . . . |
$$ | . . . . O . X . . . . . . . . B . . . |
$$ | . . X . O X . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
This way is totally natural, and black is already strong on the left. If he tries to make territory with that wall, he'll just be overconcentrated. Plus, his 4-4 stone becomes weak.
Back to the game, since black left his 4-4 stone weak, I would, as white, consider enclosing the 4-4 stone:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . C W . . . |
$$ | . . X . O X . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
If black tries any funny business in the top right corner, it can't go bad for you. The ladder that could come from the cut at the marked intersection is even good for you.
Compared to the game move, this puts a lot more pressure on the 4-4 stone immediately, and opens up potential for the right side. For example, later, you can approach the bottom right 4-4 stone, and it will work nicely with the potential you have by enclosing his 4-4:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . B . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . . . O . . . . . |
$$ | . . . . O . X . . . . . . . . O . . . |
$$ | . . X . O X . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . W . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
I don't know if black plays 3-3, it's just an example. But it's even better if white gets some sort of influence when black tries to live. For example:
- Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 5 . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . . . O . . 3 . . |
$$ | . . . . O . X . . . . . . . . O 1 . . |
$$ | . . X . O X . . . . . . . . . 4 2 . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . W . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Maybe black doesn't do this and gets sente somehow to play the right side first, but either way, I think the pressure on the 4-4 stone is valuable, because the stone is somewhat weak.
Anyway, the move you played is not terrible, because black is still over-concentrated, but black can get the opportunity to help his 4-4, although it's slightly inconsistent:
- Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . . B . . . |
$$ | . . X . O X . . . . . . . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
But anyway, you played another jump, which is OK, but not doing as much as pressuring the 4-4 like I explained above, in my opinion.
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . . . . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . . . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
That brings us to the 3-3 invasion, which makes me slightly confused. In the immediate local area, ignoring the jumps you made, I feel the 3-3 is too much here, because black can block the other way and damage the group you jumped out with - I feel 3-3 is inconsistent with you jumping out:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . B O . . |
$$ | . . . O X O X . . , . . . C . X . . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . C . . . . . |
$$ | . . X . O X . . . . . X . O . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
If black gets solid, cutting points, like those marked above, could be possible to exploit - anyway, the 3-3 makes your group weaker in this sense.
However...In this case, black has basically tenuki-ed in the 4-4 up until now, so you can't say that his group is totally comfortable by playing in this direction from the 3-3, either. The three stones you jumped out with, while kind of thin and weak against a wall, are somewhat annoying for black, since his group is cramped. For example:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 5 . . |
$$ | . . . O . O X . . . . X . O . 2 1 . . |
$$ | . . . O X O X . . , . . . . . X 3 . . |
$$ | . . O X O X . . . . . X . O . 4 . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . O . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
If black blocks on this side, it's kind of meaningless for him to have blocked with

, above, in the first place:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 5 . . |
$$ | . . . O . O X . . . . X . O . 2 1 . . |
$$ | . . . O X O X . . , . . . . . X 3 . . |
$$ | . . O X O X . . . . . X . O . 4 B . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . O . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
On the other hand, if black plays down, white is somewhat thin, but at least it doesn't feel right to me as black:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . 8 . . . |
$$ | . . . . . . . . . . . . . . 7 6 5 . . |
$$ | . . . O . O X . . . . X . O . 2 1 . . |
$$ | . . . O X O X . . , . . . . . X 3 . . |
$$ | . . O X O X . . . . . X . O . 4 . . . |
$$ | . . . . O . X . . . . . . . . . 9 . . |
$$ | . . X . O X . . . . . X . O . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Maybe there are better moves... Anyway, in conclusion, normally I feel 3-3 here is damaging to your white stones, since black can play this move:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . B O . . |
$$ | . . . O X O X . . , . . . . . X . . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . O . . . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
But the situation is so weird here, since black tenuki-ed twice against the 4-4, so maybe what he did in the game was OK. After he got to this stage, I think black should play something like this:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X . . . . X . O . O O . . |
$$ | . . . O X O X . . , . . . O X X X . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . O . B . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In the actual game, he played several moves in this area, which were unnecessary - just play a single move to strengthen the group.
Either way, getting out seems correct: He is not strong enough to really be fighting you right now, since he tenuki-ed twice in a row in this area. He just needs to get out. Then, later, and only after he's strong, he can consider either the cut like you guys already discussed, or perhaps simply here, depending on what happens in the future:
- Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . B . . . . |
$$ | . . . O . O X . . . . X . O . O O . . |
$$ | . . . O X O X . . , . . . O X X X . . |
$$ | . . O X O X . . . . . X . O . . . . . |
$$ | . . . . O . X . . . . . . . . . . . . |
$$ | . . X . O X . . . . . X . O . X . . . |
$$ | . . X O O X . . . . . . . . . . . . . |
$$ | . O O X X . . . . . . . . . . . . . . |
$$ | . O . O X . . . . , . . . . . , . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . O . . X . . . X . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Either way, black's decision to keep jumping on the left was silly, ignoring the potential of the 4-4 stone in the top right, so he can't expect to get a great result.