In my game as white, I forwent connecting up my groups (move 66) thinking that my center group was alive as is. Looking back, I'm not sure if that was necessarily the case.

Even if it could live, was it better to connect up?

@ M16 maybe.

Well, it's important to count. Is white ahead or behind at move 66? I think that affects strategy. Can you connect in sente?

At 82, count again. Can you afford to live in gote?

I remember a lecture Andy Liu 1p gave. His advice to kyu players: assume your groups are alive. Your opponent will probably be incompetent at killing them. (He often gives offbeat advice.)

Thanks. I decided that my question is moot though. If I just took at p8, I would have connected in sente... I don't know why I didn't see that.

P8 is not sente. Those black stones near there are light if white just captures, and it's not biggest for black to defend them. You may, however, experience that you can play moves like P8 in sente against some opponents. That's why improving at this game is so hard.

At move 66, I would have connected with P8. Initially it looks like gote. Even then, it is a good gote because it connects one maybe alive group and one probably alive group.
Doing so removes many ko threats and kakaris against you. It allows you many more options in the future.

However, it would be good if you could avoid having to make decisions like that. Your group got heavy very fast. I think that you would do better to play more lightly in such situations. Let's look at a lighter alternative a few moves back.

My understanding of a move like P18 is that it is a probe. It asks the opponent which he values more: the side or the corner. If he plays R17 or Q17 or Q18, he is answering that he likes the corner more. If he replies as he did, he is telling you that he likes the side more.

Given that information, you nonetheless chose to invade the side, and a rather deep invasion at that. It is not surprising that you got into a difficult game.

I would have reduced rather than invaded. If he really wants the upper side, concede it, but keep him low. Save the aji of the P18 stone for a future corner invasion starting with 'a'.

Click Here To Show Diagram Code

[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 1 a . . . |
$$ | . . O O X . . . . . . . . . 2 . . . . |
$$ | . . O X . . . . . X . . . . . X . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . 3 . . . . . . X . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . b . . |
$$ | . . . . . . . . . . . . . . . . c . . |
$$ | . . . O . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . X . , . . . . . X . O . |
$$ | . . O . . X . . . . . . . X . . X . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In the above diagram, is safe because it has plenty of room to run southward if needed. Your is light, and eventually he has to play one more move near it - in gote! - to ensure that it doesn't cause trouble.

Another effect of the aji of is that 'b' is now sente for you, but if he plays there first, 'c' is gote for him.

Someone will probably tell you that LZ says play 'a' immediately. That strikes me as rather vulgar. LZ really likes corner invasions - maybe too much.
Given the black wall at E17/D14, a lighter, more flexible, and more influential move seems best.

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Play lightly, make threats.

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Everything with love. Stay safe.