(;AP[Hexon:0.0]FF[4]GM[11]SZ[11]C[2022/05/06

Black\: Bian
White\: Peter

Black wins.
]PL[B]
;B[k10]
;W[f6]
;B[c4]
;W[c3]
;B[d3]
;W[d8]
;B[e7]
;W[d9]
;B[h6]
(;W[f8]C[Peter\: probably losing. I rejected g7 because it would let Black get g6, but it turns out that g7 was probably the better move. See next variations (that were also played).]
 ;B[i6]
 ;W[h5]
 ;B[j4]
 ;W[j3]
 ;B[i4]
 ;W[i3]
 ;B[h4]
 ;W[h3]
 ;B[g4]
 (;W[g3]C[Peter\: Now Black connects. It turns out that the d3 group does not quite escape a 4th row ladder (in the absence of a foldback threat). The unique defensive move is f2, see next variation.]
  ;B[f4]
  ;W[e3]
  ;B[d5]
  ;W[e1]
  ;B[f2]
  ;W[h7]
  ;B[i7]
  ;W[resign])
 (;W[f2]
  ;B[f3]
  ;W[h1]C[Note\: g2 does not work, as Black then gets g3 and can connect a switchback.]
  ;B[b5]C[Mohex\: this is winning for White.]
  ;W[f4]
  ;B[g3]
  ;W[e3]
  ;B[e4]
  ;W[d4]
  ;B[c6]
  ;W[d5]
  ;B[a10]
  ;W[c7]
  ;B[d6]
  ;W[e5]
  ;B[e6]
  ;W[f5]
  ;B[f7]C[Peter\: it's now too late for j5 to be threatening, as Black no longer needs the j4 group. For this reason, g7 does not work (White gets a 2nd row ladder along the k-edge, which White does not escape. See 2nd variation on the next move.

So what is White's winning move here? ]
  (;W[i7]C[Non-obviously, it is i7.]
   ;B[h7]
   ;W[g9]C[Now White *does* escape the 2nd row ladder.]
   ;B[j8]
   ;W[i8]
   ;B[k6]
   ;W[j6]
   ;B[k5]
   ;W[j5]
   ;B[k4]
   ;W[i5])
  (;W[g7]C[Losing, as it takes away j5 as a 2nd row escape.]
   ;B[g6]
   ;W[i7]
   ;B[h7]
   ;W[g9]
   ;B[j8]
   ;W[h9]
   ;B[k6]
   ;W[j5]
   ;B[j6])))
(;W[g7]
 (;B[g6]
  ;W[h7]
  ;B[e8]
  ;W[e9]
  ;B[f8]
  ;W[f9]
  ;B[g8]
  ;W[g9]
  ;B[j7]
  ;W[i8]
  ;B[j8]
  ;W[i7]
  ;B[j6]
  ;W[i6]
  ;B[j5]
  ;W[i4]
  ;B[i5]
  ;W[g5]
  ;B[f7]
  ;W[e6]
  ;B[d7]
  ;W[d6]
  ;B[b7]
  ;W[c5])
 (;B[i6]
  ;W[i7]
  ;B[h7]
  ;W[g9]
  ;B[j8]
  ;W[h9]
  ;B[k6]
  ;W[j6]
  ;B[k5]
  ;W[j5]
  ;B[k4]
  ;W[j3]
  ;B[j4]
  ;W[i4]
  ;B[e9]
  ;W[f8]
  ;B[e8]
  ;W[e6]
  ;B[d7]
  ;W[d6]
  ;B[b7]
  ;W[c5])))
