Alright, here's an annotation of my game against Art Duval. I'm playing first (black), and he's second (white). This ended up being longer than I planned. Also, I guess I had more to say about my own moves than about Art Duval's moves. This is probably because I know exactly why I played my moves, while I can only guess about Art Duval's.
1. b2.
I've been playing this opening a lot recently, because I think it's underrated. Most top players don't swap this move, but it seems to me like it's difficult to beat. If I was forced to guess, I might guess that it is losing in theory, but in practice I would swap this move even against top players.
2. e6.
This is a standard response to b2. For example, Maciej seems to play this. The idea of this move is that it seems to "perfectly fit" into the remaining space on the left side of the board, forming an efficient pattern. When I say "perfectly fit", I'm visualizing this pattern:
http://www.trmph.com/hex/board#13,b2e6m13d5l13c4k13b3j13d8i13c10h13b12
3. c6.
This move is my invention in response to e6. The idea is that for the purposes of corner patterns, the b2 stone effectively moves the top row two rows down. It "feels" like this:
http://www.trmph.com/hex/board#13,b2e6c6m13c2l13d2k13a2j13e2m12f2m11g2l12
so the idea of c6 is to try to continue this usual corner pattern:
http://www.trmph.com/hex/board#13,e4e4c4
I'm not sure what the correct response to c6 is. It looks like this move has been played only twice before I started playing it (once by Jonathan and once by Jos Dekker), so there's no standard response. Note that simply continuing the corner pattern gives
http://www.trmph.com/hex/board#13,b2e6c6c4d4c7
which I think is strong for the player with the b2 stone (I wonder if other experienced players agree).
4. f7.
I'm not sure I understand this move. I guess it's trying to get close to the right side of the board while maintaining connection to the left. The problem is that this bridge is fragile, and I'm likely to get a free stone at either f6 or e7 later in the game, depending on how things develop.
5. j6.
I've recently started liking moves on the "third diagonal", like l4, k5, and j6. The point of such moves is that the only way to block them from connecting to the top is to start a ladder:
http://www.trmph.com/hex/board#13,b2e6c6f7j6j5i6i5h6h5
Since c6 is a great ladder escape, I feel comfortable with ladders on the top. I played j6 and not k5 to try to exploit the weak bridge. The plan is to continue the ladder by playing something like
http://www.trmph.com/hex/board#13,b2e6c6f7j6j5i6i5h6h5f6g6k5k4l4l3d8
(here d8 is "almost" connected to the top, and is itself on the third diagonal for the bottom.)
6. i10.
The point is to try to block j6 from connecting to the bottom while playing a standard corner pattern, which is efficient.
7. k10.
Standard corner pattern.
8. k12.
Standard corner pattern.
9. j12.
I play j12 and not j10 because I want an escape for my ladders at the bottom, and I'm willing to let my opponent have an escape for ladders on the right. The j6 piece will make such an escape slightly less useful for my opponent than it otherwise would be. Also, j12 is generally better than j10 in the absence of other information.
10. k9.
Standard corner pattern.
11. g9.
This moves is connected to the bottom, and threatens to connect to the top via j6. It also provides an escape for ladders coming from the left. Finally, it forms a relatively efficient pattern with the corner pattern. I also did some searching of reasonable paths to see that I win in most cases.
12. h8.
This is a reasonable way to block g9 from connecting to j6.
13. h9.
This once again threatens to connect to j6, while making the escape on the bottom rock solid. At the time I remember calculating that I might need the extra strength at the bottom (for example, to escape 5th-row ladders).
14. h6.
This move threatens to disconnect j6 from the top (by playing j5) and also threatens to disconnect j6 from h9 (by playing i7). Of course, these two threats overlap. But if I play in the overlap (i6), we get something like
http://www.trmph.com/hex/board#13,b2e6c6f7j6i10k10k12j12k9g9h8h9h6i6i8g7f8g8h5h7j4f6g6d8d9b10
This is complicated, and needs to be calculated carefully. I certainly don't have an easy win if I play i6.
15. d7.
I decided my chances are better if I play d7. The position becomes easier to examine - for example, d8 is one of the only things that can be played at the bottom of the board.
16. d8.
17. e7.
Here I finally exploit the "weak bridge" from the beginning of the game. White has two choices for how to play the bottom of the board. The first is:
http://www.trmph.com/hex/board#13,b2e6c6f7j6i10k10k12j12k9g9h8h9h6d7d8e7f8e8e9c10d9b9c7b6a8c8d6f6
(for this path, I actually use the fact that I have an escape for 5th-row ladders at the bottom - can you see why?)
The second option is:
http://www.trmph.com/hex/board#13,b2e6c6f7j6i10k10k12j12k9g9h8h9h6d7d8e7e8g7g6i6
(there are other variants of this, but they also lose).
18. c4.
White chose to play at the top of the board first. I'm forced to reconnect to the top.
19. d4.
I reconnect to the top. I need to be careful that this:
http://www.trmph.com/hex/board#13,b2e6c6f7j6i10k10k12j12k9g9h8h9h6d7d8e7c4d4f8e8e9c10d9b9c7c8d6f6
still works, which it does.
20. f10.
This is sort of a last attempt by white to gain strength on the left. It's sort of a trap: if I respond with g11, we get
http://www.trmph.com/hex/board#13,b2e6c6f7j6i10k10k12j12k9g9h8h9h6d7d8e7c4d4f10g11e8g7g8f8f9e9d11
(I don't think this quite works for white, but maybe something similar does).
21. f9.
I don't need to worry about what happens if I play g11, because I can play f9 and stay connected to the bottom. The game is basically over at this point.
22. d11.
23. e10.
24. e11.
25. d10.
26. Resign.