When I was a young, ambitious and aggressive player = long before computer era, I played a similar line called Steintz Gambit in several games that ran 1 e4 e5 2 Nc3 Nc6 3 f4 exf4 4 d4 Qh4+ 5 Ke2 and main line was here d5 leeding to a total mess. I remember a blitz game at local club in this line where I defeated a 2000 player when my king somehow somewhow ended up at a8. I think I meet d6 in one standardtime game and b6 Nb5 Ba6 a4 in a couple of blitz games. However there was some reason why I gave up this line, fails to remember why. Perhaps I gave up Nc3 becouse of some line after Nf6 or most likely I wanted to play safer lines with white.

]1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bxf4 Bb4 10.Bd3 d6 11.Qd2 Kg7 12.0-0-0 Nxd4 13.e5 Nh5 14.Rhf1 Be6 15.exd6 Bxd6 16.Be3 Nc6 17.Be4 Be5!? 18.Qe1 Qe8 19.Bxc6 bxc6 and that extra piece on h5 is quite silent after 20.Bxh6+ Kxh6 21.Qxe5 Qg6 22.Qxc7.
Please note that I don't strive to find anything decisive for White but long term compensation. It's not my task to find a forced win.

1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bc4+ d5 10.Nxd5 f3 11.gxf3 Kg7 12.Be3 Na5 13.Nxf6 Nxc4 14.Nh5+ Kg6 15.Nf4+ and White still has chances. It doesn't matter so much thatpieces are exchanged. What matters is which pieces are exchanged. In this case it's all Black's active ones.

brabo wrote on 10/16/10 at 11:27:17:

I still have to see any crushing attack against White's King in the Hamppe-Allgaier. This factor is one of White's minor worries.
Of course there is also JediKnight's 11.Qd2 to deal with.
Don't worry, I don't intend to play this in neither corr. or OTB chess. My interest is only and purely academical. As such I am happy with equality, unclear play, sufficient long term compensation and even a perpetual.

SWJediknight wrote on 10/16/10 at 13:23:57:

Rybka, after fed with the recommended moves for Black, quickly gives equality, eg 14.Bc4 Qe7 (Qxh4 15.Bg3 or Rf8 15.Bxh6+) 15.Qd2 Nd8 (to protect f7 and prepare ...Be6) 16.e5 Be6 17.d5.
At the other hand Rybka prefers 12...Ba5 at once to 12...Nh5.

[quote author=5D4D5E5D503F0 link=1208413606/11#11 date=1286993300][quote author=6F6B765958555752555B54483C0 link=1208413606/10#10 date=1286971544]There was an analysis of the Hampe-Allgaier at this thread:
http://www.chesspub.com/cgi-bin/yabb2/YaBB.pl?num=1217111507/19#19   10.Bd3 is a better option for White in your first line, and that the H-A-G is currently looking unclear/equal.
[/quote]
I can't see why this is a better option for white after 10...d6.
I give one sample line (starting from move 1 just to read easier and avoid confusion) :
1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bxf4 Bb4 10.Bd3 d6 (Don't see this mentioned in the old thread although it is Rybkas and Fritz first choice. So like to know what you recommend against it.) 11.Qd2 Kg7 12.h5 Nxd4 13.Bxh6+ Rxh6 14.Qg5+ and black still has a slight advantage.[/quote]

I think white should build up his attack first, if possible so I'd suggest the natural 11.0-0, something like this:

1. e4 e5 2. f4 exf4 3. Nc3 Nc6 4. Nf3 g5 5. h4 g4 6. Ng5 h6 7. Nxf7 Kxf7 8. d4 Nf6 9. Bxf4 Bb4 10. Bd3 d6 [i][b]11. O-O[/b] Kg7 12. Ne2 Qe8 13. c3 Ba5 14. Ng3[/i] with compensation according the engine, though only at 23ply. Maybe black should prefer 12...Bxc3 13.bxc3 Qe8 though a later Bf4-d2-c3 could make the king a bit uncomfortable.

Just my 2 cents, unless it's already been mentioned somewhere...

Ooops, [quote]I think that objectively speaking White's hopes rest on my earlier suggestion, 9.Bxf4 Bb4 10.Bd3 d6 11.0-0. [/quote] just noticed this now. Anyway, I agree :)

MNb wrote on 10/15/10 at 00:37:14:

I see black being a full piece up while white has no clear attacking scheme so I bet on blacks chances. Besides
1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bxf4 Bb4 10.Bd3 d6 11.Qd2 Kg7 12.0-0-0 Nxd4 13.e5 Nh5 14.Rhf1 Be6 15.exd6 Bxd6 16.Be3 Nc6 17.Be4 Be5!? (This looks easier than your 17...Ne5 to keep the advantage) 18.Qe1 Qe8 19.Bxc6 bxc6 and can't find anything decisive for white while blacks extra piece starts to talk more and more.
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1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bc4+ d5 10.Nxd5 f3 11.gxf3 Kg7 12.Be3 Na5! looks again easier than your 12...Bd6 after which white has to permit some exchanges and his attack mostly runs out of steam. I am pretty sure you get a huge score with white on the board but in a high level correspondence game I estimate whites drawing chances rather slim. Besides in the Cochrane gambit whites king is safe while in this variation this is certainly less the case.

MNb wrote on 10/12/10 at 22:06:02:

Not exactly like this. White must move his pawn a bit further 11.d4, because the text enables 12...Qxh1 option, after which 13.Bxf4 Nf3+ 14.Ke2 Nf6 gives Black better chances (e.g. immediate 15.Nc7 fails 15...g5 16.Bg3 Nh5).

Re. "the opening", I meant the Hampe-Allgaier branch rather than the Mason Gambit as a whole- I hope I've made that clear!  Note that 1.e4 e5 2.f4 exf4 3.Nc3 Nc6 transposes directly to the Vienna Gambit (1.e4 e5 2.Nc3 Nc6 3.f4 exf4) so if 3.Nc3 is insufficient due to 3...Nc6 so is the Vienna Gambit against 2...Nc6.

As it happens, checking MNb's lines:

(1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6)

A: 9.Bxf4 Bb4 10.Bd3 d6 11.Qd2 (I prefer 11.0-0 for the reasons I gave before) 11...Kg7 12.0-0-0 Nxd4 13.e5 Nh5! indeed looks much better for Black.  

B: 9.Bc4+ d5 10.Nxd5 f3 11.gxf3 Kg7 12.Nxf6 (12.c3!?) 12...Qxf6 13.e5 (13.Be3!?) 13...Qf5 14.Be3 looks unclear/equal to me.  White now has two pawns for the piece as well as attacking chances and a strong centre.

I see Micawber also suggested 3...Qh4+ 4.Ke2 Qe7, and I found a source on it here:
http://www.kjcchess.com/gambitopeningg0.html
The conclusion of that article was quoted in Chess Monthly at a column where the late Mike Fox (a devotee of 3.Nc3) and Richard James used to comment on random stuff.  Hansen,LB: 'This game could be a serious blow to the 3.Nc3 line in the Kings Gambit.'

After 3...Qh4+ 4.Ke2 Qe7 5.d3 Nf6 6.Bxf4 d5 7.Kd2 (this is indeed probably best), Fritz 10 suggests 7...d4, e.g. 8.Nd5 Nxd5 9.exd5 g5 10.Qh5 Qb4+ 11.Kd1 Qxb2 12.Rc1, which might give an edge for Black- though admittedly it's exactly the sort of chaotic position that a 3.Nc3 aficionado would feel at home in!  Maybe you are right that 5.d3 is the best reply.

5.Kf2!? (mentioned by Micawber) might be worth a look, since the draw offer 5...Qh4+ can be met by 6.g3 fxg3+ 7.Kg2 gxh2 8.Rxh2.  I don't believe White has enough compensation here, but I imagine that fans of the line could have a lot of fun with this in rapid games.

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I agree with that assessment, both for the Hampe-Allgaier branch that arises from 3.Nc3 Nc6 and the Mason Gambit as a whole.

MNb wrote on 10/13/10 at 23:29:21:

I think black can improve in this line with 13.. Nh5 instead of 13.. Nd5 see:
1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bxf4 Bb4 10.Bd3 d6 11.Qd2 Kg7 12.0-0-0 Nxd4 13.e5 Nh5 14.Rhf1 Be6 15.exd6 Bxd6 16.Be3 Nc6 and I believe blacks chances are still better.
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Also here I've some other analysis in my database.
1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.Nf3 g5 5.h4 g4 6.Ng5 h6 7.Nxf7 Kxf7 8.d4 Nf6 9.Bc4+ d5 10.Nxd5 f3 11.gxf3 Kg7 (I believe this is stronger than your Be6) 12.Nxf6 Qxf6 13.e5 and now Qf5 as Nxe5 look very good for black.

My personal opinion is
that a safe way for black and an annoying one for white is
3.Nc3, Qh4+ 4.Ke2,Qe7!? (4...c6 as safe and sound as well)
In Bauer-Bracot 1999 things went wrong for white as early as move 5:
5.d4,Nf6 6.e5,d6 -/+.
(of course 5.d3 and 5.Kf2 are probably somewhat better, but Black is OK anyway).

As for "Wellings variation"  iso 
6....Nc6 Black can also consider 6...Bd6 7.d4,Bxf3 (7...Nc6 is now possible as well) 8.gxf (8.Kxf3?!,Qh5+ 9.Kf2,Qxd1 10.Bb5+,c6 is dubious) 8....,c6 (unclear; Grafl-Wisnewski, 2000)