Chess Gambits- Harking back to the 19th century!
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The Göring Gambit

The Göring Gambit is a 19th-century style gambit beginning with 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.c3!? (or 2.d4 exd4 3.Nf3 Nc6 4.c3).

Contents

1.  Introduction (below)
2.  Accepted with 4...dxc3, White settles for sacrificing one pawn with 5.Nxc3
3.  Accepted with 4...dxc3, White offers a second pawn with 5.Bc4
4.  Black declines the gambit with 4...d5
5.  Black declines with 4...Nf6
6.  Black declines with 4...Nge7 or 4...d3
7.  Other ways of declining

Introduction

Instead of capturing on d4 with the f3-knight, White offers the d-pawn as a gambit by challenging Black's d4-pawn with c2-c3.  The idea is to open up lines for the white pieces, gain a lead in development and use these advantages to help launch a direct attack on the black king, often particularly aimed at Black's weak point on f7.  White often plays Bc4, Qb3 and/or Ng5 at some stage to pile up on f7.  Another common motif is to strive for Nc3-d5, which often disrupts Black's development.

The gambit was first played at high levels by Howard Staunton in the 1840s, but the gambit is named after Carl Theodor Göring, who was the first player to introduce it into master play.  It is essentially a Danish Gambit (1.e4 e5 2.d4 exd4 3.c3) with Nf3 and ...Nc6.  The inclusion of the knight moves perhaps doesn't make much of a difference to its objective soundness, but my feeling is that it narrows down Black's options more than White's, especially in the double pawn sacrifice line with 4...dxc3 5.Bc4, whereupon it is harder for Black to engineer the freeing ...d7-d5 break because e4xd5 will hit Black's knight on c6.  As with the Danish, the one pawn sacrifice with 4...dxc3 5.Nxc3 is almost certainly sound as well as quite dangerous, while sacrificing the second pawn with 5.Bc4 is more dangerous but less definitely sound.

Although the Göring Gambit has never gained much popularity at the highest levels of play, some players rated in the 2300-2600 Elo bracket have used it frequently at some point, e.g. Jonathan Penrose, Ljubomir Ljubojević, Douglas Bryson, Igor Dolgov and Dimitrios Mastrovasilis.  There was a rare GM outing in the gambit in 2011, when Yu Yangyi used it successfully against Rimat Jumabayev.   Alexander Alekhine often played 1.e4 e5 2.d4 exd4 3.c3 dxc3 4.Nxc3 in casual games, which often transposed after a subsequent ...Nc6 and Nf3.

The most common objection to playing this gambit is that Black can equalise by striking out in the centre with 4...d5 and steer the game into rather sterile endgames, via a line with ...Bb4, ...Bg4xf3 and ...Qd5-c4 introduced in the game Marshall-Capablanca, Lake Hopatcong 1926 (for more information on this see the analysis of the declined variations).  I don't doubt that 4...d5 equalises, but I think there are at least a couple of ways for White to avoid those endings and achieve interesting and equal play. 

4...Nf6, also counterattacking against e4, and 4...Nge7 intending 5...d5 are also playable but less likely to fully equalise.  "Pushing past" with 4...d3 is also playable but tends to lead to rather passive positions for Black, with White enjoying a persistent space advantage.  Other methods of declining allow White to establish a strong "classical pawn centre" for free by playing 5.cxd4.

Common ideas

When putting pressure on Black's f7-pawn with Bc4 and Qb3, White must beware of the ...Nc6-a5 "fork", which can force the exchange of White's light-squared bishop (an important attacking piece in the Göring Gambit) for the black knight on c6.  The position on the left can arise from the common sequence 4.c3 dxc3 5.Bc4 d6 6.Nxc3 (or 5.Nxc3 d6 6.Bc4) Nf6 7.Qb3 Qd7.  The queen move looks awkward, blocking in the bishop on c8, but as well as defending f7, it blocks possible checks on the a4-e8 diagonal and so prepares ...Nc6-a5. 

In that line White should increase the pressure on the f7-pawn with 8.Ng5, which typically leads to board-wide chaos, but instead White has rather naively castled, 8.0-0?, allowing 8...Na5.
Another common motif is that White must often complicate matters to maintain the initiative.  The position on the left arises from 4.c3 dxc3 5.Nxc3 Bb4 6.Bc4 d6 7.Ng5 Ne5 8.Bb3 h6.  Black is hoping for 9.Nf3, which allows Black a relatively comfortable game, but here White can complicate matters with 9.f4, attacking the knight on e5.  It can lead to an exchange of knights, but it also opens up more lines and makes the position more crazy.  Situations like this are quite common in the accepted lines of the Göring.
Black has to be wary of playing ...Nf6 without preparing it with ...d6 first, because White's initiative often accelerates after hitting the knight on f6 with the e4-e5 pawn push.  This position is a particularly bad version for Black, arising from 4.c3 dxc3 5.Nxc3 Be7?! 6.Bc4 Nf6?!.  After 7.e5, Black can lash out with ...d7-d5 in some situations, counterattacking against the bishop on c4, but then lines open up and the position becomes messy.  Often White accepts a queen exchange but catches the black king in the centre in the process, leaving it vulnerable to attack from the white pieces.

Repertoire/transposition issues

If White uses the move-order 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.c3, then White has to be ready for the Petroff Defence (2...Nf6) and the Philidor Defence (2...d6) and the dubious but tricky Elephant (2...d5) and Latvian (2...f5) gambits.  After 2...Nc6 3.d4, however, Black has no good way to maintain the strong-point on e5.  3...d6 is well met by either 4.dxe5, simplifying to a better queenless middlegame, or 4.Bb5, transposing into the Steinitz variation of the Ruy Lopez, which is quite passive for Black, or 4.Bc4 which tends to lead into the Hungarian Defence.

If White tries 1.e4 e5 2.d4 exd4 3.Nf3 Nc6 4.c3, then Black has no particularly strong alternative to 2...exd4, although 2...Nc6 (transposing to a line of the Nimzowitsch Defence, 1.e4 Nc6 2.d4 e5) is playable.  2...d6 can lead into a Philidor Defence after 3.Nf3 although White can also consider 3.dxe5 intending 3...dxe5 4.Qxd8+.  
At move 3, 3...Nf6 transposes into the Old Petroff (here White can consider heading into the Urusov Gambit with 4.Bc4, which is actually how I have most commonly reached it in practice).  3...Bb4+ is a problem for players who use the double pawn sacrifice line 4.c3 dxc3 5.Bc4 as a way of avoiding 5.Nxc3 Bb4, since after 3...Bb4+, there is nothing better (for either side) than 4.c3 dxc3 5.Nxc3 Nc6, transposing to the position following 3...Nc6 4.c3 dxc3 5.Nxc3 Bb4.  However, if White is happy to head into that line, then he or she should be happy to see 3...Bb4+.
Sources and further reading
Internet articles

John Watson's book review #62, Danish Dynamite
Mark Morss, Hard Chess, The Importance of the Open Games, the Goering Gambit
Gary Good, The Goring Gambit- A Return to the Romantic
(ChessCafe.com links have been removed because the site went behind a paywall).
A special thanks also goes to Mark Nieuweboer for contributing a large number of ideas.

Books
Karsten Müller & Martin Voigt, Danish Dynamite, Russel Enterprises 2003.
John Emms, Play the Open Games as Black, Gambit 2000.
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