The idea behind Nf6 is that it immediately attacks the queen. The queen is forced to move, generally capturing the pawn, allowing Black to develop a second piece, again attacking the queen. The queen is forced to move again and so Black has developed 2 pieces and White's queen is still exposed, allowing Black to gain more tempos after securing the position. White's development is even slower than the Nc6 mainline.
The problem is that you have to be prepared for several continuances and if Black doesn't play accurately (like many gambits) White can trick Black into going gung-ho against the queen and get into a forced material loss. But after 4. ...O-O Black should be able to avoid anything forcing and Black is just better, having better activity, king safety, a semi-open center file to attack the still centralized king, and White's queen is still exposed. The pawn advantage is worthless unless White can find a way to hold for the entire middle game.
So which is better? 2. ...Nc6 or 2. ...Nf6 Well, it just depends on how aggressively you want to play. They're both going to give you an advantage under proper play.
awesomer: I think you are right. Upon closer inspection of 7.Qe3?? f6! 8.d4 fxe5 9.dxe5 Bg4!! and white is toast! However, I still think that my suggested move 7.Qa4!? gives white an equal position.
Thank you, Shakespeare for your extended analysis. Indeed 9...Bg4 in the 7.Qe3 line makes whites position look very unattractive. in the 7.Qa4 line i would suggest 7..c5 and i still like black. Another possibility for white is 4.Qg3 but i also see nice compensation for black here (4...0-0 5.e5 Ne4).
All four moves, 2...Nf6, 2...Nc6, 2...d6 and 2...Qe7 are probably good for equality or more. The reason why i like 4...Nf6 best is that white has to make a lot of non-intuitive moves to keep the balance, and even then it is not trivial to do so. While black attacks whites center with normal looking developing moves.
On the other hand a pawn is a pawn and black may prefer one of the other three second moves for black. There are attractive ideas for black here too, eg in the main line Nc6-a5 with the idea to grab the bishoppair. Black has a few possibilities to get a comfortable game against 2.Qh5.
Talking about this opening, I've just won a nice attacking game with the Kiddie:
http://en.lichess.org/BsozbCylSurely most of it was unsound but it was still fun.
Nice game with nice finish. 4.Qg3 is one critical variation. You played 4...Nc6 instead of 4...0-0, then 5.e5 has to be answered with 5..Nh5 which protects g7. On 4...0-0 both Knight moves are possible.
For the benefit of those readers who do not yet fully grasp the significance of the bishop to g4 move in the line 1.e4 e5 2.Qh5 Nf6 3.Qxe5+ Be7 4.Qf4 O-O 5.Nf3 d5 6.e5 Nh5 7.Qe3?? f6! 8.d4 fxe5 9.dxe5 Bg4!! I will continue my analysis.
If white plays a seemingly normal developing move like 10.Be2? then black replies with 10...Nf4! 11.O-O Nxe2+ 12.Qxe2+ Bxf3 13.gxf3 and white's King side has been ripped wide open! White now has more weaknesses in his position than he knows what to do with! Black has a very big advantage in the resulting position.
On the other hand, if white plays a more conservative move like 10.Nbd2 then black replies 10...Nd7! There are several possible moves here for white to play--none of them are very appealing. White can try moves like 11.Qd4, 11.Qc3, and 11.h3.
If white tries 11.Qd4 then there follows 11...Nf4 12.h3 Be6 and black has a significant positional advantage.
If white tries 11.Qc3 then there follows 11...Bc5 12.Nb3 Bb6 and black's pressure on f2 and e5 will eventually cause one or more of white's weak pawns to drop. For example, 13.Be3 Bxe3 14.Qxe3 Bxf3 15.gxf3 and now the pawn on e5 drops because the king and queen are in the line of fire on the e-file! For example 15...Rf5 16.O-O-O Rxf5 and black has a significant advantage.
If white tries 11.h3? then there follows 11...Bc5 12.Nd4 Re8 13.hxg4 Rxe5 14.Rxh5 Rxe3+ 15.fxe3 Nxf6 16.Rf5 Qe7 and black has a significant positional advantage.
Thus, after 1.e4 e5 2.Qh5 Nf6 3.Qxe5+ Be7 4.Qf4 O-O 5.Nf3 d5 6.e5 Nh5 7.Qe3?? f6! 8.d4 fxe5 9.dxe5 Bg4!! black has a significant advantage no matter what white plays.
Looking now at the line 1.e4 e5 2.Qh5 Nf6 3.Qxe5+ Be7 4.Qf4 O-O 5.Nf3 d5 6.e5 Nh5 with my suggested move 7.Qa4 and awesomer's suggested move 7...c5 it seems that white has about equal chances here. One possible continuation might be 8.d4 Nc6 9.Be2 f6 10.exf6 Nxf6. White now has several choices which I think will maintain equality:
11.O-O, 11.dxc5, and 11.c3.
I hope that my analysis of the Wayward Queen Attack will prove to be useful to anyone who plays this opening regularly.
You are right, Shakespeare. 7.Qa4 is the best move. Black has compensation but not more. This seems to be the critical line of the Kiddie Gambit. A game could eg develop like this:
http://de.lichess.org/vqjidaj9#13Meanwhile i like this more positional setup most:
http://de.lichess.org/4NTlRJtf#16