(;AP[HexGui:0.10.GIT]
C[2021/07/02

Black\: Peter
White\: Frank

Black wins.
]FF[4]GM[11]PL[B]
SZ[11];B[a11];W[swap-pieces];B[g4];W[f6];B[h7];W[h5];B[g6];W[g5];B[e6];
W[e7];B[d7];W[d8];B[c8];W[c9];B[a10](;W[c10]
C[Peter\: White may as well tidy up, since a10 was going to connect to the 11-edge anyway. See next variation.]
;B[a11];W[b9]
C[This doesn't look good for White, since it is unclear how White can connect to the A-edge, and there isn't any switchback potential (there is not enough room for the 2-to-6 switchback).

Nevertheless, according to Mohex, this position is winning for White. The trick seems to be to turn the ladder at the precise moment that is inconvenient for Black.


Eric\:

I likely would've tried C4, as described at https\://www.hexwiki.net/index.php/Cornering#C4_corner_move .

Since you didn't mention it, I'm guessing that would lose.


Peter\: Yes, I've added information on that to move 26 in one of the variations.]
;B[a9];W[b8];B[a8];W[b7];B[a7](;W[c4]
C[This works. Alternatively, White can keep pushing, see next variation.]
;B[b5](;W[d3]
C[Mohex\: losing move. b6 was winning, see next variation.

Eric\:

k2,j3,i4 are white-captured and C6 is empty, so White can't need to immediately play B6\:

Due to the captures, whiteB6 will always be absolutely forcing, and if Black pre-empts by playing A6 or B6, then White responds at C6, making Black's piece completely useless (since A6+B6 would be black-captured anyway).

In particular, whatever White plays just after Black responds at A6, that instead of B6 also wins for White.

Mohex\: Yes indeed, c5 is also winning. But not d3.]
;B[c5];W[e4];B[e5];W[h2];B[g3];W[g2];B[e3];W[resign])(;W[b6];B[a6];W[c5]
;B[b4];W[c2];B[c3];W[d2];B[d3];W[e2];B[e3];W[f2];B[f3];W[g2];B[j2](;
W[g3];B[f4];W[h3];B[i3]
C[Eric\:

An important part of _why_ they were White-captured, is that White's center group is still connected to the K-edge.]
;B[j1];W[h4];B[i5];W[i4];B[k3];W[j4];B[k4];W[j5];B[k5];W[j6];B[k6];W[j8]
;B[j7];W[i8];B[i7];W[g9];B[h9];W[h8])(;W[i3]
C[Eric\:

This is the local response to enforce that k2,j3,i4 are white-captured.]
)))(;W[b6];B[a6](;W[b5];B[a5];W[b3];B[b4];W[e2];B[c3];W[d1];B[d4];W[f3];
B[f4];W[h2])(;W[d3]
C[Mohex\: this is losing. 

However, if Black responds as suggested at https\://www.hexwiki.net/index.php/Cornering#C4_corner_move, White wins.]
(;B[b5]C[Winning.];W[d2](;B[b3];W[b4];B[c4];W[c3];B[d4];W[e3];B[f4])(;
B[c4]C[Eric\:

Black does not need to first exchange B3 for B4.]))(;
B[c4]C[Losing. b5 was winning.];W[b3];B[b4];W[e2]))))(;W[a11];B[b10];
W[b11];B[c10];W[c11](;B[d10];W[d11];B[e10];W[e11];B[g10];W[f10];B[g8])(;
B[e9]C[Eric\:

Black can alternatively do this in less space.];W[e10];
B[g9])))
