Every game I look deeply at is a chance to improve my own game, so I’m always happy to look.
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. c3
4. c3 is a strange move that looks to immediately lose the e4 pawn. This gambit by white of the e4 pawn does, apparently, exist (de Riviere gambit or Neumann gabit), but it it rare. White’s “compensation” could come via 4…Nxe4 5.Bd5 Nf6 6. Bxc6 dxc6 7. Nxe5 Bd6 8.d4, with material equality. But if white is going to go through all that trouble just to get equal material and yet be that far behind in development, then 4. c3 is just bad. This gambit was played at top-tier level most recently in 2009 in a rapid game between the Teimour Radjabov and former World Champion Vishy Anand. (Anand declined the gambit, playing 4…a6 instead. Any normal player would just take that pawn.)
4…Nxe4 5. d3 Nf6 6. Qe2 Bd6
6…Bd6 cost you the game. You’re not losing here by any sense, but it immediately gets you so tangled up that you never recover and things kinda go downhill. I’d be curious to hear your thoughts on other candidate moves, in particular 6…d6. That looks like the most natural move by far: protects the e5 pawn and gets ready to develop the light-squared bishop (LSB). I wouldn’t have considered any other move seriously at all. In a long game I might look at Be7 for a split second in case there is interesting counterplay against the white queen that ends up a little loose on e5 (e.g., …d5, …O-O, and …Be6 ideas), but I don’t see anything worth pursuing there. (I dropped this into the engine just to see, and apparently there is a line, but it’s craaaazy and not something a human could ever try to find over the board. Besides, 6…d6 is strictly better anyway.)
Anyway, back to 6…Bd6. Issues with this move:
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It blocks your d pawn. …d6 is useful immediately, but …d5 is perhaps a future hope to take more center and to blunt white’s LSB.
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You also must now develop your own LSB to b7. Does that bishop have scope from that square? In the short term it will be blocked by the c6 knight. Often this is a non-issue, but you can’t answer the question “what’s the plan for the g7 bishop?” without a good answer for “what’s the plan for the c6 knight?” That knight can’t move immediately (guarding the e5 pawn) and if ever you get something else helping on e5, b4 from white really freezes the knight.
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Your DSB is now just a “tall pawn”. Rather than helping keep white out of your kingside (g5 is an important square that the bishop can look at from e7), it’s stuck babysitting a pawn.
This one move is at the heart of all future problems.
7. O-O O-O 8. Nbd2
It’s hard to do when playing blindfolded as in this game, but when the opponent makes a knight maneuver, it’s important to consider where that knight is headed and what that implies. In this case, white is surely heading to e4 with the knight, at which point you can already ask what you would do. If you plan to take (which you did), then after Qxe4 in reply, white’s pieces are getting very active on the kingside with Ng5 on deck, as in the game. Anything now that doesn’t deal with that inevitability may prove too slow. 8…h6 could be worth the tempo here (although keep a careful eye on the pin of the f pawn. g6 will be an unguarded square until you get your queen to f6 or the pin is resolved.) The time you take to develop your LSB to g7 won’t pay off for a long time anyway. “Getting developed” is good, but in this case the development is neither meeting white’s initiative-filled development with your own counter-initiative or meeting his with defensive development.
8…b6 9. Ne4 Nxe4 10. Qxe4 Bb7 11. Bd5
Not sure what white’s intention is with 11. Bd5?. You’d love, love, love him to take your knight (your LSB would be the best piece in the game), and it doesn’t do anything active otherwise. Very strange move.
11…Qe7
Why not 11…Qf6 ? Both squares serve to overprotect e5, you leave the e7 square for your bishop or knight when suitable, your queen is much more active, and you may have opportunity to trade queens (squelching the growing attack and heading toward the endgame a pawn up.).
12. Ng5 g6 13. Qh4 h5
All very forcing.
14. g4 Kg7
14…Nd8 is an interesting try, neutralizing white’s LSB one way or another.
15. gxh5 Rh8 16. h6+ Rxh6 17. Ne6+!
Indeed, the move that makes 16. h6+ so strong, as you noted. A good sequence by white.
17…fxe6 18. Qxh6+ Kf7 19. Be4 Rg8 20. Bg5 Qf8 21. Qh7+ Qg7 22. Bxg6+ Kf8 23. Bh6 1-0