Two Knights Defense

The Two Knights Defense is a chess opening that begins with the moves:
First recorded by Giulio Cesare Polerio in, this line of the Italian Game was extensively developed in the 19th century. Black's third move, attacking White's pawn on e4, is a more aggressive continuation than the Giuoco Piano with 3...Bc5. White’s most direct approach is 4.Ng5, immediately attacking Black’s vulnerable f7-pawn. David Bronstein noted that the term defense doesn’t capture the opening’s true character and suggested Chigorin Counterattack as a more accurate name. The Two Knights Defense has been played and analyzed by many aggressive players including Mikhail Chigorin, Paul Keres, and world champions Mikhail Tal and Boris Spassky.

4.Ng5

This move attacks the pawn on f7 in combination with White's bishop on c4. The only good defense for this pawn is 4...d5, blocking White's bishop's line of attack.
This line was very common in the 19th century during the era of Romantic chess, but later attracted criticism from players of the Classical school, who argued that the move is a violation of opening principles, in that it moves a piece twice and attacks before development is complete. The leading German master of the early 20th Century, Siegbert Tarrasch, famously called 4.Ng5 "a duffer's move", more literally rendered as "a typical example of a bungling move" in the English translation of The Game of Chess. 4.Ng5 has continued to be played however, being adopted in the 1990s by Alexander Morozevich and Nigel Short. It remains a popular option for White and has been employed by world champions Wilhelm Steinitz, Bobby Fischer, Anatoly Karpov, Garry Kasparov, and Viswanathan Anand.
After 4...d5 5.exd5, 5...Nxd5?! is considered too risky to play at the board, although it has not been definitively refuted. The standard reply is 5...Na5, the main line being 6.Bb5+ c6 7.dxc6 bxc6. Although 5.exd5 practically wins a pawn by, Black gains with quick and.
Black can ignore the threat to f7 with 4...Bc5!?, the [|Traxler Counterattack], which leads to wild complications.

Main line: 4...d5 5.exd5 Na5 6.Bb5+ c6 7.dxc6 bxc6

This is the usual continuation of the main line. White then most commonly plays 8.Qf3, 8.Be2, or 8.Bd3.
Following 8.Be2, the usual continuation is h6 9.Nf3 e4 10.Ne5. White is behind in but has an extra pawn as well as a better pawn structure. 10...Bd6 is Black's most common next move, and White usually replies with 11.d4, though 11.f4 is an alternative. One possible line is the Knorre Variation, continuing 11...Qc7 12.Bd2, although 11...exd3 and 11...0-0 are more usual for Black.
Alternatives for Black include 10...Bc5, 10...Qc7, the Göring Variation, and 10...Qd4. An alternative for White is 9.Nh3, known as the Steinitz Variation. Although it did not bring Steinitz success in his famous 1891 cable match against Mikhail Chigorin, Bobby Fischer revived it in the 1960s. Nigel Short led a second revival of 9.Nh3 in the 1990s, and today it is thought to be about equal in strength to the more common 9.Nf3.

Kieseritzky Variation: 6.d3

Instead of retreating the bishop, White may instead play to hold the gambit pawn with this move. Paul Morphy preferred this line, named after Lionel Kieseritzky and also known as the Morphy Variation. It is relatively unpopular since Black obtains good chances for the pawn with 6...h6 7.Nf3 e4 8.Qe2 Nxc4 9.dxc4 Bc5 and White effectively concedes the bishop pair. David Bronstein once tried the piece sacrifice 8.dxe4!? with success, but its soundness is doubtful.

Fritz Variation: 5...Nd4

German master Alexander Fritz suggested this move to Carl Schlechter, who wrote about the idea in a 1904 issue of Deutsche Schachzeitung. In 1907 Fritz himself wrote an article about his move in the Swedish journal Tidskrift för Schack.
6.d6?! now is dubious. After 6...Qxd6 7.Nxf7? Qc6! simultaneously attacks the pawn on g2 and the bishop on c4, and if 8.Nxh8? 8...Qxg2 9.Rf1 Qe4+ 10.Be2 Nf3#. White should instead play 7.Bxf7+ Ke7 8.Bb3 Nxb3 9.axb3 h6 10.Nf3 e4 11.Ng1 Kf7 and Black had sufficient compensation for the pawn in Bogolyubov-Rubinstein, Stockholm 1919.
Instead, White's best reply is 6.c3, where the game usually continues 6...b5 7.Bf1! Nxd5, followed by either 8.cxd4, 8.Ne4, or 8.h4.
The Berliner Variation, named after World Correspondence Chess Champion Hans Berliner, continues the Fritz sub-line 8.Ne4 with 8...Qh4, from the famous game Estrin–Berliner, World Correspondence Championship 1965–68, eventually won by Black; this win was pivotal to Berliner's eventual championship victory. That game, which saw Black embark on a very sharp sacrificial path, continued 9.Ng3 Bg4 10.f3 e4 11.cxd4 Bd6 12.Bxb5+ Kd8 13.0-0 exf3. In 1971, IM / GMC Estrin later published a suggestion of the move 14.Qb3!? as an improvement on the game continuation, and this possibility has continued to interest many players.
The main line continues 8.cxd4 Qxg5 9.Bxb5+ Kd8 10 0-0 10...Bb7 11 Qf3 Rb8 12 dxe5 12...Ne3 13.Qh3 Qxg2+ 14.Qxg2 Nxg2 15.d4, where White is a pawn up in a sharp position.

Ulvestad Variation: 5...b5

This line is related to the Fritz Variation as they share a common subvariation. American master Olav Ulvestad introduced 5...b5 in a 1941 article in Chess Review. White has only one good reply, the counterintuitive 6.Bf1!, protecting the undefended pawn on g2, so White can answer 6...Qxd5 with 7.Nc3. Both replies 6.Bxb5 Qxd5 7.Bxc6+ Qxc6 and 6.dxc6 bxc4 7.Nc3 are weak for White. After 6.Bf1, Ulvestad's first idea 6...h6 is refuted by 7.Nxf7. The move 6...Nxd5, Ulvestad's second idea, is considered Black's best response. Black can also transpose to the Fritz Variation with 6...Nd4, making another advantage of 6.Bf1 apparent; the bishop is not attacked as it would be if White had played 6.Be2.

5...Nxd5?!

This recapture is extremely risky. Albert Pinkus tried to bolster this move with analysis in 1943 and 1944 issues of Chess Review, but White gets a strong attack with either the Lolli Attack, which Bobby Fischer thought to be very strong, or the sacrificial Fried Liver Attack, which leaves Black's king in the middle of the board after 6...Kxf7 7.Qf3+ Ke6 8.Nc3. These variations are usually considered too difficult for Black to defend.

Traxler Variation: 4...Bc5

This bold move ignores White's attack on f7 and leads to wild play. Czech problemist Karel Traxler played it against Reinisch in Prague in 1890. Later, Frank Marshall named it after Wilkes-Barre, a town in Pennsylvania, claiming to be the first to analyze and publish it, so 4...Bc5 is known both as the Traxler Variation and, in the United States and the United Kingdom, the Wilkes-Barre Variation.
White can play 5.d4, 5.Nxf7, or 5.Bxf7+:

After 5.d4 d5!, White's best move is 6.Bxd5, reapplying the pressure on f7.
5.Nxf7 is very complicated after 5...Bxf2+. The current main lines all are thought to lead to drawn or equal positions, e.g. after 6.Kxf2 Nxe4+ 7.Kg1, or even 7.Ke3.
White's best try for an advantage is probably 5.Bxf7+ Ke7 6.Bb3, although some writers such as Lawrence Trent recommend 6.Bd5. No grandmasters have regularly adopted the Wilkes-Barre as Black, but Alexander Beliavsky and Alexei Shirov have played it occasionally even in top competition. Beliavsky even ventured it twice, holding then-World Champion Karpov to a draw and defeating Anand. No clear refutation is known. A tricky variation is 5.Bxf7+ Kf8!?, where Black plays for one last trick with 6.Bb3 d6 7.Nf7 Qe7. If White plays the seemingly standard 8.Nxh8, Black is now winning after 8...Bg4 9.f3 Nxe4, making use of the pinned f3-pawn. This pawn cannot capture the bishop as 10.fxg4?? Qh4+ 11.g3 Bf2+ wins by force for Black.
Ponziani–Steinitz Gambit: 4...Nxe4

4...Nxe4?! is considered unsound but must be handled carefully. 5.Nxe4 d5 poses no problems for Black. If 5.Nxf7? Qh4! 6.g3 6...Qh3 7.Nxh8 Qg2 8.Rf1 Nd4 9.Qh5+ g6 10.Nxg6 hxg6 11.Qxg6+ Kd8 and Black has dangerous threats.
Correct is 5.Bxf7+! Ke7 6.d4! and now:

6...d5 7.Nc3! 7...Nxc3 8.bxc3 Qd6 9.a4! Kd8 10.Bg8! Ke8 11.Bxh7±.
6...h6 7.Nxe4 Kxf7 and now 8.dxe5 Qe8 9.f4 d6 10.0-0 Kg8 11.Nbc3 dxe5 12. f5 Qf7 13.Nd5 Bd7 14.f6 g6 15.Ne7+! and White has excellent chances.
Closed Variation: 4.d3

The quiet 4.d3 is White's most common fourth move. It is sometimes called the Modern Bishop's Opening. By playing d3, White tries to avoid the tactical battles that are common in other lines of the Two Knights and to enter a more positional game. The resulting positions take on some characteristics of the Ruy Lopez if White plays c3 and retreats the bishop to c2 via Bc4–b3–c2. This move became popular in the 1980s and has been used by John Nunn and others.
Black can and often does transpose into the Giuoco Pianissimo by playing 4...Bc5, but there are also independent variations. The other most common responses by Black are 4...Be7 and 4...h6, which often lead to closed, positional games. Another option is for Black to open the game with 4...d5, a dynamic but risky line.

Open Variation: 4.d4

White can choose to rapidly with 4.d4 exd4 5.0-0. Now Black can simply by eliminating White's last center pawn with 5...Nxe4, after which White regains the with 6.Re1 d5 7.Bxd5 Qxd5 8.Nc3, but Black has a comfortable position after 8...Qa5 or 8...Qh5.
The wild Nakhmanson Gambit 6.Nc3 gives White compensation if Black accepts the piece with 6...dxc3 7.Bxf7+ Kxf7 8.Qd5+ and then makes the intuitive move 8...Ke8?! Instead, 8...Kf6! has been analyzed to offer Black a substantial edge with best play. Victor Bologan suggests declining the gambit with 6...Nxc3 7.bxc3 d5 8.Bb5 Be7 leading to a better position for Black.
Alternatively, Black can enter the extensively analyzed Max Lange Attack after 5...Bc5 6.e5 d5, which can also arise by transposition from the Giuoco Piano or Scotch Gambit. White can choose to avoid these lines by playing 5.e5, a line often adopted by Sveshnikov. After 5.e5, either 5...Ne4 or 5...Ng4 is a reply, but most common and natural is 5...d5 6.Bb5 Ne4 7.Nxd4 Bc5, with play. The tricky 5.Ng5?! is best met by 5...d5! 6.exd5 Qe7+!