(;AP[HexGui:0.10.GIT]
C[2021/04/23

Black\: Sarah
White\: Frank

Handicap\: 0.5

White wins.
]
FF[4]GM[11]PL[B]SZ[11];B[f6];W[d10];B[e10];W[f8];B[e9]
C[Eric\:


E9-for-E8 looks like a very bad exchange for Black.

(though unlike other times I refer to bad exchanges, I certainly can't prove it for this one)]
;W[e8];B[c9];W[d7];B[c7];W[c8];B[a9];W[d6](;B[b11]
C[Eric\:

Black just passed, so White now wins.
(There was no ladder escape fork here, since C10 and D9 will _both_ be ways for C9 to connect after white B10).]
;W[h7];B[i6];W[i7];B[c6];W[b8];B[a8];W[b7];B[a7];W[c4];B[b5];W[d3];B[a4]
;W[b4];B[a5];W[b2];B[resign])(;B[h7]
C[Variation.


Eric\:

Due to E10, H7 has a virtual connection to the 11-edge.  Since there are only 3 rows between H7 and the K-edge, that means the best White can do in this corner is get an escape for all ladders coming in while also _threatening_ to cut H7 off from Black's edge.]
(;W[g9](;B[h9](;W[h8];B[j7];W[i5];B[g6];W[i7];B[k5];W[j5];B[resign])(;
W[j6]
C[Eric\:


The ladder (H8 instead of J6) is probably better for White in general and is a fairly-simple win for White on this board, but J6 yields a local _proof_ that H9 can't be better than I8 for this corner\:

Now _all_ Black has from this corner is the ability to connect through this corner, whereas Black had _at least_ that much from this corner before the H9,J6 exchange, due to I8.]
))(;B[i8]
C[Eric\:

This would reconnect, because it has a ladder-creation template and Black has E10.]
))(;W[h10])(;W[i8]
C[Eric\:


i8 achieves that, and I don't think any other White move in this corner achieves that.

(G9 does not, because it does not guarantee White an escape here\: Black might ignore it to play near the A1 corner.)]
)))
