Muzio Gambit with 11...Qd4+

Question

The Muzio Gambit is great fun in blitz games. I realize it's slightly silly to study too much "theory" when it comes to blitz chess, but I figured it couldn't hurt to read up a bit and also see what the engines have to say. In the course of doing so, I discovered that in the variation below, both Stockfish and Leela Chess Zero rather strongly favor 11...Qd4+ whereas the written analyses that I've found discuss only 11...Qc5+ and 11...Qf5. It seems that the rationale is that after White plays 12.Kh1 or 12.Rf2, Black will castle, and his queen can return to the defense with ...Qf6 or ...Qg7, which it can't do after 11...Qc5+.

My question is, is 11...Qd4+ really an improvement over 11...Qc5+ and 11...Qf5? Has anyone analyzed this line carefully before? In something as complicated as the Muzio Gambit, I'm not whether running the engines for a couple of hours on my laptop will give me a reliable assessment.

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[StartPly "22"]
[FEN ""]

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5
8. d3 Bh6 9. Nc3 Ne7 10. Bd2 Nbc6 11. Rae1 

Answer 1

You're right that in this type of position, finding improvements over mainline theory is not as simple as trying to bring the engine evaluation to your side. If the engine is evaluating the position at something like -2.5, it won't matter much if you can make it -2.8 or -2.1.

Instead, we should be looking for moves that make our opponent's play more difficult. I'm not entirely sure if the queen on f6/g7 would be helping the defense or getting in the way. Think of a line like 11...Qd4+ 12.Kh1 0-0 13.Nb5 Qf6 14.Nxc7 Rb8 15.g3