(;AP[HexGui:0.10.GIT]
C[2020/05/24

Black\: Peter
White\: Eric

Handicap\: 1

1-move handicap for Black after swap.

Black wins.

Comments by Eric and Peter]
FF[4]GM[11]SZ[11];B[c10];B[f6];W[e7];B[g6]
C[Eric\: Good. I was thinking of f7, but  5. g6  is better.

Wg7 Bf7 We9  is the only way I see for White to keep that off the 11 edge.
]
;W[h4];B[e5]
C[Eric\: Good.  d5 would also have been good.  (d5 would be a corner move.)
]
;W[d4]
C[Eric\: I now think f3 was White's best try.  After 8. d4, Black has a forced win and kept that win for the rest of the game.

Accordingly, the rest of my comments are just about that win. For them, I use "best" to mean  simplest and fastest and most efficient. Note that playing best moves in this sense is much less important than what that normally means, since the moves you played did keep the win.]
;B[e6]
C[Eric\: 
This looks like the best way for Black to win.  It captures f5 and g5, since if White plays either then Black responds at the other, which kills the White piece on f5 or g5.  Thus, Black connects to the 1 edge\:

https\://www.hexwiki.net/index.php/Edge_templates_everybody_should_know#Fifth_row_edge_templates_with_two_stones

Verifying that Black connects to the 11 edge consists of using that f8 would get a ladder to c10 and using that d8 is fairly-often forcing and checking each of White's tries  .
]
;W[f9];B[g7]
C[Eric\: This looks like the simplest way for Black to win, and looks to be at least as fast and efficient as the other way I see for Black to win.]
;W[e10];B[d8]C[Peter\: Black's group is now connected to the 11-edge.];
W[h1];B[c3]
C[Eric\: g3 was best.  (It connects via f2 or i2.)  f2 would also have won easily, for the same reason as playing it instead of j2 would've won.

To show that Black is still winning after  14. c3,  I use g3 threatening f2 and i2  and  f3 threatening g1 and a ladder to c3 as Black's main threats.    The former beats moves on and to the lower-left of the e1-e4 segment, and the latter beats g3 and moves that trmph displays to the right of that.

f1 and g1 and f3 lose because g3 gets a ladder to c3, and g2 loses because f3 ladders to c3.

f2 loses to f3, since Black defends the bridge and is threatening e3 and i2.

f4 loses to f3, since Wg2 doesn't threaten f3's connection to the edge, so  We4 Bg4 Wg3 Bh3,  after which Black connects with h2 or j2.

]
(;W[e2]
C[Peter\: White d4 is now connected to the A-edge by the ladder escape fork at c2.]
(;B[j2]
C[Peter\: f2 would have been an easy win for Black (see next variations).

Eric\: g3 was best, and f2 also wins easily.

16. j2  does keep the win because Wi3 interferes with neither the g3 win nor the f2 win,
and anything which does interfere with those allows the ladder that actually happened.
]
(;W[g3]
C[Peter\: White's five stones near the 1-edge are now all connected to each other.]
;B[i4];W[h5];B[i5];W[h6];B[i6];W[h7];B[e3]
C[Peter\: Black is just testing the connection...];W[d3];B[i7]
C[Eric\: g8 and h8 lose to i8, making the standard fourth row template. So White plays something else,
after which Black plays h8 forcing Wg8.  After Wg8, White has at most one piece in V2b

https\://www.hexwiki.net/index.php/Edge_templates_with_two_adjacent_pieces#Fifth_row

_and it is Black's turn_.  Thus, Black wins by playing as if White had just played that piece.
]
;W[h9]C[Eric\: After  27. h9,  you won in the best way.];B[i10];W[j8]
;B[h8];W[g8];B[g9]C[White resigns.])(;W[f3](;B[g3];W[i2];B[e3];W[f2])(;
B[f2])))(;B[f2](;W[f3];B[g3];W[g2];B[i2])(;W[e4];B[g3])))(;W[f3];B[g3];
W[h2];B[g2];W[g1];B[f2];W[f1];B[e2];W[e1];B[d2])(;W[f4];B[f3];W[e4];
B[g4];W[g3];B[h3];W[i2];B[h2];W[i1];B[g2])(;W[f2];B[f3];W[f4];B[e4];
W[e3];B[i2];W[h2];B[h3];W[g3];B[g4]))
