(;AP[HexGui:0.10.GIT]
C[2021/09/05

Black\: Eric
White\: Peter

Black wins.

With lots of questions and discussion, including how to defeat a pivoting template.]
FF[4]GM[11]PL[B]SZ[11];B[k8];W[swap-pieces];B[d8](;W[e4]
C[Peter\: I have a final question\: what do you play here?

Eric\: I play D3.

(Go to next variation).


]
;B[c4];W[c3];B[b4];W[b3];B[d3];W[f2];B[e2];W[c5]
C[Peter\: Here, I was wondering if I could play e5 instead of c5. I seemed to calculate that that would connect to the a-edge, but with weaknesses. 

Since that is more or less what happened in the game, I think the answer is probably yes.

Eric\: I waited on using that weakness because I wanted to keep the possibility of me playing D7 there.
]
;B[b7];W[a6];B[d5];W[e5];B[h4](;W[i2]
C[Peter\: My second question is here, and I think I might have made the wrong choice, except is it not clear if the other choice wasn't also wrong.

What I calculated is that h4 doesn't connect to the 1-edge, but it pivots to f4.

Eric\: yes

Peter\: I considered two moves to make it pivot.

The one I played worked, but gave you i4, which was fatal I think.

The other would have been h3.

I was thinking (after I played i2) that h3 might have not given you i4, so might have been locally better. But I'm not sure.

Eric\: It would not have given me i4, but it would've given me i3 and j3.

Peter\: But I now think it would have given you g4.

Eric\: I don't think it gives me g4.

Peter\: Ah, right. OK.

So i3 and j3 is only marginally better than i4, if at all.

Eric\: My heuristic is that, from Black's perspective here, being closer to the distant edge is more important than ladder escapes or lack thereof.

Eric\: However, the difference is indeed very small.

Peter\: Yes, but functionally, you needed h6 to connect, which it did either way.

Eric\: Yes

Peter\: It might be arguably slightly better for you even.

Eric\: Yes, it now looks like that.

Peter\: In that White now only escapes 2nd row ladders there.

Eric\: yes.
]
;B[i4];W[j2];B[h2];W[h3];B[f4];W[f5];B[g4];W[g6];B[c7];W[d9];B[h6];W[g8]
;B[e8]
C[Eric\:

Someone put a white ghost on E9 and a black ghost on C9, but\:

If White plays E9, then it's more efficient for Black to play B10 instead of C9.]
;W[resign])(;W[h3]))(;W[d3]
C[Peter\: This choice between two corners is always hard.

Do you have a heuristic for d3 vs e4?

Vs h4 vs g5?

Eric\: My heuristic is, get at least 1 corner along each of one's own edges.

Peter\: That used to be my heuristic too.

But then Black gets both obtuse corners, which I usually end up losing against.
]
;B[g5]
C[Eric\: For this, I think White should use H3 and E9.

I would start with H3.
]
;W[h3];B[h5];W[e9];B[c8]
C[Peter\: Something like this?

Eric\: Something like that.

Peter\: I would chicken out at this point.

Eric\: or H2 instead of E9.
]
;W[f4];B[i3];W[j1];B[i2];W[i1];B[h2];W[h1];B[g2];W[g1];B[e2];W[f2];B[e3]
;W[f3];B[d5];W[d6];B[e5];W[e6]
C[Eric\: (Black would likely have gotten J3 earlier).
];B[f5];W[f7]
C[Peter\: Hm, I don't like that.
];B[g7];W[f9]
C[Peter\: Here, it would now be better if Black had j3.

Eric\: I think White would be winning anyway, due to H6.

]
;B[j3];W[k1]C[Peter\: wlog.
];B[g9];W[g8];B[i7];W[g10]
C[Eric\: (This corresponds to a height-4 ladder and A4.)

Peter\: Yes.

There was a lesson here, which I forgot.

Does g10 work with 4th row ladders?

Eric\: It gives H11 both a ladder underneath and a ladder above the original ladder.

Eric\: (In this case, the "above" is just F10.)
]
;B[h9];W[f10];B[h10];W[g11];B[j10];W[j5]
C[Peter\: OK.

I usually avoid playing e9, because c8 is a strong response, and I usually never play h3, because it doesn't occur to me (and it only works in the presence of d3, probably). Maybe I should revise those preferences.

There's also the g3 pivoting response to g5.

Eric\: I believe I told you this some time ago, but as a reminder\: white H3 against the black G5 corner move comes from the bots, and is now my go-to- move against the black G5 corner move.

Peter\: Yes, you did tell.

Eric\: If White doesn't have D3, then H3 lets G5 connect, but White will get compensation for that.

And, against an attempt at pivoting, I try a double-threat, strengthening the effect of pushing through while also threatening to go through the middle.
]
;AE[c8][d3][d5][d6][d8][e2][e3][e5][e6][e9][f2][f3][f4][f5][f7][f9][f10]
[g1][g2][g5][g7][g8][g9][g10][g11][h1][h2][h3][h5][h9][h10][h11][i1][i2]
[i3][i7][j1][j3][j5][j10][k1];B[k8];W[swap-pieces];B[d8];W[d3];B[g5];
W[h3];B[g3](;W[e6]
C[Peter\: So this is against the pivoting?

Eric\: Yes
](;B[h5];W[h2];
B[f4];W[g2];B[e3];W[f1])(;B[f7];W[g4];B[e5];W[f5](;B[j2];W[i4]
C[Eric\: J2 doesn't work for Black, but i3 might.
])(;B[i3];W[h4];B[i4];
W[h5];B[i5];W[h6];B[i6];W[h7];B[i7];W[g10]
C[Eric\: Due to C8, this might come down to how well Black can do in the K11 corner while still making White need an escape in the K1 corner.
]
;B[h8];W[f9];B[g8];W[f8];B[g7]
C[Eric\: After h8, White no longer needs an escape in the K1 corner, so White should play i2, to help against c8.

Peter\: Um. Wait.
]
;W[i2];B[j2];W[e8];B[c8];W[e7];B[d6]
C[Eric\: (The point is, if White needed j2, then Black would get i2 in return, in which case E5 would connect to the 1-edge.)]
;W[f4];B[e3];W[e2];B[f2];W[e4];B[c5];W[d4]
C[Peter\: Ah. OK.

I'll have to remember e6 against pivoting templates.

e6 and not f6, right?

The situation is not quite symmetric.

Eric\: yes]
))(;B[e5]
C[Peter\: What about this?

Eric\: Here, White carries out the other threat.]
;W[f7]
C[Eric\: (White is not connected to the A-edge, but White gets a height-2 ladder towards B10.)

Peter\: Right, because of the d3 foldback.

Eric\: yes

Peter\: I am guessing that something like the e6 response might work for other pivoting templates in similar situations?

Eric\: I don't think I've seen responses like E6 other than the specific \[G5,H3,G3\] situation and the 3 symmetric situations.

(It might be that the analogue of the F7 threat is rarely big-enough.)

Peter\: It seems to me that if you have a pivoting template where the space between A and B is empty, then if White plays outside the template, and Black responds at B, then both A and B are connected to each other and to the edge.

Eric\: That should be the case for most examples that come up, but I expect there's a counterexample.

Peter\: I think what I can prove is that A is connected. (Because any strategy that would occupy B can be modified to connect B to A instead).

Eric\: Yes, that works.]
))(;W[f6]C[Peter\: Not this.](;B[f5]
C[Eric\: or E5 instead of F5.

Peter\: I am guessing this would be pretty good.
]
)(;B[e5]))))
