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Traxler Counterattack, And A Problem with Stockfish 8.

Traxler Counterattack is: 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 Bc5.
All the engines evaluate the position as about +1.5 for white.
But after 5. Nxf7 Bxf2+ 6. Kf1 Qe7 7. Nxh8 d5 8. exd5 Nd4. Stockfish 8 says 9. c3 is +2 until depth 15, equal after that, and only on depth 21, it says 9. c3 is -2.5. I drew and won some games against SF8 in this site playing the Traxler.
Please tell your thoughts. How can this happen ?
Stockfish is weak in openings when it has no access to its opening book. In the TCEC computer match Stockfish 8 - Houdini 5 both engines evaluated -0.50 after 1 e4 e5 2 f4 exf4 3 Bc4, but both engines won against each other with white. In this match they used top hardware and deep search. So in gambits and counter gambits the compensation lies often behind the horizon of the engine even at high search depth.
You may want to look up some correspondence chess games with this line. Modern correspondence chess in ICCF is engine assisted anyway: the humans typically use two or three engines and evaluate their analysis before deciding on the move.
Most humans over the board prefer 5 Bxf7+, for example Anand-Beliavski, Linnares 1991.
Horizon-effect for sure. it is (theoretically) known that 9. c3 is a bad move; people tend to think 9. d6 is a better try for white. And as @tpr says, 5. Bxf7 might be better, especially practically.

To be honest, I play the Traxler sometimes with black and in blitz it's a nice try. Pretty cool games can come from this.
Stockfish is not a perfect player. It can surely miscalculate some messy positions with hidden possibilities like that after 9. c3. On a higher depth it says 9. d6 is the only winning move, which is probably correct. The reason is most likely some pruned line that Stockfish thought is bad to go for the side to move but under closer inspection on the higher depth it discovered that it is actually good. Just like human can blunder some rook sacrifice because it seems like you're losing the rook, but if you calculate further, you can see that the opponent loses a queen or get mated, for example.

In long time controls you woudn't have a single chance against Stockfish 8 in Traxler.
9. d6 is the only winning move, and 9. Be2 & 9. h3 are dead even ( d=28. )
Thanks for your help everyone !
Is 9 c3 Bg4 10 d6 not just the same?
No.
Black can choose from two winning options ( one of them is better )

-3.83 10...Qd7 11.cxd4 Bxd1 12.Kxf2 Qxd6 13.d3 Qxd4+ 14.Ke1 Bh5 15.Nc3 Ke7 16.Rf1 Rxh8 17.Rf2 e4 18.Nb5 Qb6 19.Nc3 Rd8 20.Kf1 exd3 21.Bf4 Qb4 22.Bxc7 Qxc4 23.Re1+ Kd7

-1.87 10...cxd6 11.Qa4+ Kf8 12.cxd4 Bh4 13.g3 exd4 14.Kf2 Bh3 15.Qd1 Ng4+ 16.Qxg4 Bxg4 17.Re1 Qf6+ 18.Kg1 Bh3 19.Bd5 Re8 20.Rxe8+ Kxe8 21.Bg2 Bxg2 22.Kxg2 Qe5 23.gxh4 Qe2+ 24.Kg3 Qe1+ 25.Kg2 Qxc1 26.b3 Qe1 27.h3 Qxh4

Stockfish 8.
#7 well Qd7 is pretty easy to spot, just wins material.

9. d6 is much more interesting, as black can go either Qxd6 or cxd6; but have potential.

Also, I do want to point out that even if SF8 says the positions after 9. Be2/9.h3 "are dead equal", this has says nothing about the practicality of the lines. It's definetly useable for a lot of people.

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