Qxd4 is considered a blunder, but Black can try to hold on till the endgame.

Fritz' book gives
1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 Now White can choose to play 8.d3 or go into the deep dark sea of 8.Bxf7!

Fritz' Book says this is the mainline for the Accepted Double Muzio w/ Qf5

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qf5 10. g4 Qg6 11. Bxf4 Nf6 12. Be5 Be7 13. Nc3 d6 14. Bxf6 Bxg4 15. Qd5+ Be6+ 16. Qg5 Bxf6 17. Rxf6+ Qxf6 18. Rf1 Nd7 Fritz evaluates the position as +3.oo for Black.

I consider this opening a rollercoaster, the main line keeps Black more than alive, but one little mistake and it is all over.

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qxd4+ 10. Be3 Qf6 11. Bxf4 Bc5+ 12. Kh1 Bd4 13. c3 d6 14. cxd4 Ke8 15. Nc3 Kd7 16. Nd5 Qe6 17. Rae1 Qf5 18. Qe3 Qg6 19. Qh3+ Kd8 20. Bg5+ Nf6 21. Qe3 Qe8 22. Bxf6+ Kd7 23. Qh3+ Kc6 24. Rc1+ Kb5 25. Qb3+ Ka6 26. Qa3+ Kb5 27. Qb4+ Ka6 28. Nxc7#

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qxd4+ 10. Be3 Qf6 11. Bxf4 Bc5+ 12. Kh1 Bd4 13. c3 d6 14. cxd4 Ke8 15. Qh5+ Kd7 16. Nc3 Qe6 17. Rae1 Qg6 18. Qh3+ Kd8 19. Bg5+ Nf6 20. Qh4 Rg8 21. Bxf6+ Kd7 22. Re7+ Kd8 23. Rg7+ Ke8 24. Qe1+ Qe4 25. Qxe4+ Be6 26. Rxg8+ Kd7 27. Rd8#

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qxd4+ 10. Be3 Qxb2 11. Qxf4+ Nf6 12. Bd4 Qxd4+ 13. Qxd4 Be7 14. Nc3 Kg7 15. Rae1 Bd8 16. Rxf6 Bxf6 17. Re7+ Kg6 18. Qg4+ Kh6 19. Rf7 Bxc3 20. Rf3 Bd4+ 21. Kh1 Nc6 22. Rh3#

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O Qe7 6. d4 gxf3 7. Qxf3 Bg7 8. e5 Qb4 9. Bxf7+ Kxf7 10. Qxf4+ Ke8 11. c3 Qf8 12. Qg4 Qe7 13. Qh5+ Kd8 14. Bg5 Nf6 15. Qh4 Bh6 16. Bxf6 Be3 17. Kh1 Nc6 18. Bxe7+ Nxe7 19. Qf6 Rg8 20. Qf8+ Rxf8 21. Rxf8#

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qxd4+ 10. Be3 Qxb2 11. Qxf4+ Ke6 12. Qf7+ Ke5 13. Rf5+ Kd6 14. Qd5+ Ke7 15. Qe4+ Qe5 16. Qxe5+ Kd8 17. Rxf8#

1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O gxf3 6. Qxf3 Qf6 7. e5 Qxe5 8. Bxf7+ Kxf7 9. d4 Qxd4+ 10. Be3 Qf6 11. Bxf4 Ke8 12. Nc3 Bc5+ 13. Kh1 Bd6 14. Nd5 Qg7 15. Bxd6 cxd6 16. Rae1+ Ne7 17. Rxe7+ Qxe7 18. Nxe7 Na6 19. Qf7+ Kd8 20. Nd5 Re8 21. Qf6+ Re7 22. Qxe7#

Which leads to another probably apocryphal story involving Emmanuel Lasker. He and a friend stopped at a tavern for lunch and discovered a local champion who gave Knight odds to all comers for small stakes and won every game. No one in the tavern recognized the man who held the World Championship for almost 3 decades.

Lasker and his friend watched a few games. In every game, the local champ played a Muzio Gambit. Lasker whispered to his friend, "This local champion will buy us lunch."

Lasker challenged the champ for a small stake, took the Black pieces--and lost. He got crushed. The locals laughed at him. Then he challenged the champ again, for much higher stakes, but this time, Lasker would have the White pieces and give Knight odds!

The local champ agreed and everyone thought that Lasker would get crushed again--after all, he lost with an extra Knight, right? But Lasker blew the local champ off the board in less than 20 moves and pocketed a handsome cash prize. He then told the locals that giving Knight odds makes the Muzio Gambit a forced win for White.

As he and his friend sat down to their meal, his friend asked, "Was that true, what you said about the Muzio?" Lasker shrugged and replied, "Why do you care? We're eating for free!"

An Englishman: Good Evening: <cuendillar's> comments might have a basis in truth. In many critical variations, White plays Nc3 for no other reason than to develop the QR. The Knight itself is usually superfluous. Therefore, without the Nb1 in an odds game, White saves a critical tempo by developing the Rook immediately.>

There's logic to it. It is however, objectively the opposite. 8.Bxf7+ in a regular position is -2.8 whereas with QN odds it's -9.4 (30-ply SF10).

The problem is the lack of pieces. In the 9....Qf5 variation with odds Black's simply three pieces up. The fact that they're undeveloped doesn't change this fact. After 10.Bxf4 Nf6 they both have just one minor piece developed but White has no more to develop. With major pieces alone you don't win games.

Even if Black plays what are otherwise suboptimal variations in the double Muzio: after 9....Qf5 10.Bxf4 Nf6 11.Rae1 (the point, right?) Nc6?! 12.Qb3+:

click for larger view

Black can defend himself with the otherwise ridiculously looking 12....d5 13.Be5 Nxe5! 14.Rxf5 Bxf5 15.dxe5 Bc5+ 16.Kh1 (Kf1 Nd7 and White's king is confined to the center) Rae8:

click for larger view

Black just surrended Q:R, but is still three pieces up in exchange.