(;AP[Hexon:0.0]FF[4]GM[11]SZ[11]C[2022/08/19

Black\: Joyce
White\: Jia

Handicap\: 1.5

White wins.
]PL[B]
;B[f6]
;B[e8]
;W[f5]
;B[g5]
;W[h3]
;B[j2]
;W[i4]
(;B[j4]C[Eric\:

Even locally, this is dominated by J5.

https\://www.hexwiki.net/index.php/Dominated_cell#Star_decomposition_domination

Also, see my comment for the variation.]
 (;W[j3]C[Eric\: Better f4, see next variation.]
  ;B[f4]C[Eric\:


As described in the variation for move 8, E4 and G4 were both winning here.

This _probably_ also wins, but I'm not sure.]
  ;W[g4]
  ;B[d6]C[Eric\:


The full template from D6 to the 1-edge is not one whose size I bother remembering, but based on

https\://www.mathstat.dal.ca/~selinger/templates/

,  if F4 was losing then so was F5.]
  ;W[e5]
  (;B[c5]C[Eric\: Better d5, see next variation.]
   (;W[c3]C[Eric\:


losing

see the variation]
    ;B[d4]C[Eric\: d3 is simpler.]
    ;W[e2]
    (;B[g2]C[Peter\: Losing move. The next variation was also played.]
     ;W[f3]
     ;B[g3]
     ;W[e4]
     ;B[resign])
    (;B[f3]
     ;W[e7]
     ;B[c8]
     ;W[b10]
     ;B[d9]))
   (;W[d5]C[Eric\:


D5 keeps D6 off the 1-edge, giving White at least a height-3 ladder along the A-edge.

In fact, after playing out the following line, I verified that White wins here.

D3 instead of D5 probably also works.]
    (;B[b6]C[Eric\: See next variation for c6.]
     ;W[c8]
     ;B[b7]
     ;W[e7]
     ;B[b10]
     ;W[a9]
     ;B[d8]
     ;W[d7]
     ;B[e6]
     ;W[f7]C[Eric\:

White wins]
     ;B[h6]
     ;W[g8]
     ;B[f8]
     ;W[g7])
    (;B[c6]C[Eric\:

Defending the bridge lets whiteD3 get a height-2 ladder instead of a height-3 ladder.]
     ;W[d3]C[Eric\:

I believe D3 directly, instead of starting with D5, also works.]
     ;B[c3]
     ;W[c4]
     ;B[a5]
     ;W[b5]
     ;B[a6]
     ;W[b6]
     ;B[a7]
     ;W[b7]
     ;B[a8]
     ;W[b9]
     ;B[b8]
     ;W[c8]
     ;B[c7]
     ;W[e7]
     ;B[d8]
     ;W[d7]C[Eric\:

This is locally even better for White than the other line.])))
  (;B[d5]C[Eric\:

This would've connected to the 1-edge, and so been winning.]))
 (;W[f4]C[Eric\:


White still gets a ladder along the K-edge, so I would've stopped Black from pushing through at G4, since as described in the previous variation, that would win for Black.

(This game is high handicap, but F4 is still what I'd do here.)]))
(;B[g4]C[Eric\:


This wins, since Black can pivot at E4 and climb along G4,F6,E8.

https\://www.hexwiki.net/index.php/Climbing

E4 directly also wins and I think would be slightly better in general, but starting with G4 is sufficient here and simpler.]
 ;W[g3]
 ;B[e4]
 ;W[f4]
 ;B[d6]
 ;W[e7]
 ;B[c8]))
