Chess Opening Theory/1. d4/1...Nf6/2. c4/2...e5/3. dxe5/3...Ng4/4. e4

Variations
This variation is named after Alexander Alekhine probably thanks to his wins in the games Alekhine – Rabinovic (Baden Baden, 1925) and Alekhine – Seitz (Hastings, 1926). Alekhine himself stated: "This is considered with good reason to be White's best system against the Budapest Gambit. White hands the pawn back, but in return gains control of d5. Over the next few moves, however, he has to play with extreme precision, since otherwise his central pawn position may become the object of a successful attack by Black."

White does not try to keep its material advantage (the e5-pawn) and concentrates on building a strong pawn centre, in order to get a space advantage. Notably a controversial point is whether the typical black manoeuvre Bf8–b4–xc3 is advantageous for Black (as it saddles White with doubled pawns) or for White (as it reinforces his centre). Lalic thinks both, considering 6...Bb4+ to be a bad move after 4...Nxe5 5.f4 Nec6 6.Nf3, but a good one after 4...Nxe5 5.f4 Nec6 6.Be3.

After 4.e4 Black has to do something about its Ng4 that is attacked by the Qd1. Apart from the main line, two minor variations have been tried:
 * with 4...h5?! Black does not want to get its gambit pawn back, and prefers to keep the Ng4 on its aggressive position. Thus White has to be careful not to fall in some traps like 5.Nf3? Bc5 or 5.f4?! Bc5 6.Nh3 Nc6 7.Be2? Qh4+. White does best to repel immediately the Ng4 with 5.Be2, after which the move h7–h5 is only a weakness and White has the advantage.
 * with 4...d6?! Black continues in true gambit style, trying to develop rapidly its pieces, but the compensations are not sufficient. Here again, after 5.exd6 Bxd6 White needs to avoid some traps like 6.Nf3? Bc5! 7.Qxd8+ Kxd8 when Black regains the pawn with advantage. White continues with 6.Be2 to gain a tempo on the Ng4 when Black's only option to sustain an initiative is 6...f5 7.exf5 Qe7. Then White has a choice between chasing a slight positional advantage with 8.Nf3, or taking a piece with 8.c5! Bxc5 9.Qa4+ Nc6 10.Qxg4. In the later case, Savielly Tartakower and Max Euwe initially considered Black had enough compensation but more recent analysis proved them wrong.

The main line is 4...Nxe5 5.f4 when Black has an important choice to make about where to move its Ne5:
 * 5...Nec6 is considered to be the best
 * 5...Ng6 is probably playable
 * 5...Nbc6? 6.fxe5 Qh4+, despite being called "highly regarded" by Lalic, is just a bad piece sacrifice with Black hoping for something like 7.g3? Qe4+ that wins a rook. As advocated by John Nunn White can keep the material advantage with the funny 7.Kd2 Qf4+ 8.Kc3 Qxe5+ 9.Kd2 Qf4+ 10.Ke1 Qxe4+ 11.Qe2 when the black queen is pinned.

The 5...Nec6 line
1.d4 Nf6 2.c4 e5 3.dxe5 Ng4 4.e4 Nxe5 5.f4 Nec6

The Knight on c6 is safer than on g6, and can be part of a general strategy on the dark squares. It can go on d4 while the other Knight can go on c5 via a6 or d7.

After 6.Nf3 Bc5 White has difficulties to castle short, because the plan to exchange the dark-squared bishops with Bd3/Qe2/Be3 can be met by Bg4/Nd4 in order to muddy the waters. Therefore, as Lalic points out: "White can no longer castle kingside and will usually have to go the other way. However, this is rather slow and gives Black time to try and undermine the white centre. To this end Bc8–g4 often comes in handy, in order to pin the white knight on f3 against the white queen. Note that Black should wait until his opponent has wasted a tempo with Qe2."

A possible continuation is 6.Nf3 Bc5 7.Nc3 d6 8.f5!? Nd7 9.Bg5 f6 10.Bf4 and here Black has to prepare the exchange of the Bc5 against the Nc3 with 10...Bb4!, because a White knight on the d5-square would be too strong now that it cannot be challenged by Bc8–e6 and it can continue with Nd5–f4–e6 in the long run. A slower course of action is 6.Nf3 Bc5 7.Nc3 d6 8.Bd3 O-O 9.Qe2 Bg4! 10.Be3 Na6 11.O-O-O f6 with a typical game of opposite castles. White cannot, however, afford the luxury of being too slow, e.g. after 6.Nf3 Bc5 7.Nc3 d6 8.Bd3 O-O 9.h3?! Re8 it is already time for White to seek a simplification with 10.Qe2 Nd4 11.Nxd4 Bxd4 12.Be3 Qh4+ 13.Qf2, otherwise Black would soon have strong pressure in the centre thanks to the semi-open e-file.

Another try is 6.a3 but it creates a significant weakness in b3 and it is rather slow. For example after the possible 6...a5 7.Be3 Na6 8.Bd3 Bc5 9.Qd2 d6 10.Nf3 O-O 11.Nc3 Bxe3 12.Qxe3 Nc5 13.O-O Re8 14.Bc2 a4 Borik has shown that the possibility to attack the c4-pawn with Be6/Na5 gives sufficient play to Black. Note that Black is not compelled to reply to 6.a3 with 6...a5, and can also treat a2–a3 as a mere loss of tempo by switching to another development like d6/g6/Bg7/O-O with equality. As Lalic puts it: "[I] believe that Black should now opt for the plan of fianchettoing his dark-squared bishop. The black bishop will be excellently posted on g7 and Black's kingside will also be more robust against White's eventual kingside attack. Psychologically, if White has 'all the time in the world' for such moves as 6.a3, it makes sense to divert the bishop to another diagonal instead of 'respecting' White's move with 6...a5."

White has also experimented a plan with a quick queen raid on the kingside, involving moves like Nc3/Qh5/Bd3/Nd5. This plan was first tried in a game of Alekhine against Gilg and after 6.a3 a5 7.Nc3 Bc5 8.Nd5 O-O 9.Bd3 d6 10.Qh5 Nd7? 11.Nf3 h6 12.b4! 12...axb4 13.Bb2 bxa3 14.Bc3 White has a strong initiative. One year later Gilg was playing White and tried to repeat Alekhine's success in a game against Vajda, but the latter improved with 10...Nd4! and won. This plan can also be tried without the advance a2–a3, e.g. 6.Nc3 Bc5 7.Qh5 d6 8.Bd3 Nd7 9.Nf3 Nf6 10.Qh4 and here Lalic recommends 10...O-O.

White takes the diagonal with 6.Be3
1.d4 Nf6 2.c4 e5 3.dxe5 Ng4 4.e4 Nxe5 5.f4 Nec6 6.Be3

The continuation 6.Be3 controls the a7–g1 diagonal, takes the good c5-square from the Bf8, and is considered to be the best reply. If Black wants to contest that he can try 6...Na6 to continue with 7...Nc5, but most of the games continue with 6...Bb4+. Here the best reply for White is controversial. While Borik does not express a preference, Alekhine strongly recommends 7.Nc3 (awarded a "!"): "Much stronger than 7.Nd2, for with the knight threatening to jump to d5, Black will sooner or later be forced to exchange his important dark-squared bishop for it. The doubling of the c-pawns in these circumstances is not something White should fear." Tseitlin agrees, stating that "after 7.Nd2 Black has no difficulty at all". On the other hand, Lalic thinks 7.Nd2 (awarded a "!") is more accurate: "White avoids the doubled c-pawns that are likely to occur after 7.Nc3, and this knight can latter be deployed via the b3-square. The Russian grandmaster Rustem Dautov [...] is the maestro of this variation with many impressive victories under his belt."

Actually Tseitlin's opinion on 7.Nd2 is based on the game Nikolić – Lev (Groningen 1985–86), which continued 7...Qe7 8.a3 ("?" Tseitlin) 8...Qxe4+ ("!" Tseitlin) 9.Qf3 Bxd2+ 10.Kxd2 Qxf3 and White is a pawn up. But what Tseitlin considers a white blunder is called a gambit by Lalic, who gives 7.Nd2 Qe7 8.a3 ("!" Lalic) 8...Qxe4 ("it is probably wise to decline the gambit", Lalic) 9.Kf2 Bxd2 10.Qxd2 O-O 11.Nf3 d6 12.Re1 Qf5 13.Bd3 Qa5 14.b4 Qh5 and White won.

After 7.Nc3 Black has the interesting zwischenzug 7...Qh4+ ("!" Borik) 8.g3 Bxc3+ 9.bxc3 Qe7 so that the diagonal a8–h1 is weakened before Black places his Bc8 on the b7-square. The queen on the e7-square is well placed to pressure the e4-pawn. However, as all Black's pieces are on the queenside, continuing with pawn pushes like f7–f5 is probably too weakening, as Alekhine demonstrated in his game against Seitz in 1925. So Black does best to attack with pieces, possibly with the setup b6/Nc5/Bb7/O-O-O. In that case Tseitlin considers that with a knight on c5 the move d7–d6 should be avoided if Black has to respond to the capture Bxc5 by dxc5, because the white pawns in e4 and f4 would have too much leeway.

After 7.Nd2 the pressure on the e4-pawn with 7...Qe7 does not live long after 8.a3 Bc5 9.Bxc5 Qxc5 10.Qf3 and now 10...Nd4 would be premature so that Lalic recommends 10...a5. The introduction of the intermediate 7...Qh4+ 8.g3 Qe7 does not change the picture for Lalic, as after 9.Bg2 Na6 10.a3 Bc5 11.Bxc5 Nxc5 12.b4 Ne6 the bishop was well placed in g2 and Black experienced difficulties to develop his own Bc8. But Lalic does not mention the game Pomar – Heidenfeld cited by Borik, in which Black played the advance a7–a5 to avoid the white advance b2–b4, hence reaching equality after 9.Bg2 a5 10.Ne2 Na6 11.O-O d6 12.Nb3 Bg4 13.h3 Bxe2 14.Qxe2 a4. Instead, he recommends 7...d6 8.Nf3 O-O 9.Bd3 and now the same development as in Pomar's game: "9...a5 and 10...Na6 deserves attention, when White's movements on the queenside are more restricted and the black knight will be able to settle on the c5-square without being kicked by the thematic b2–b4. It may appear that we have reached the same position elaborated in previous games a tempo down for Black, since he has committed hi bishop to b4 and will later drop back to the c5-square instead of heading there at once. However, the white knight is less actively placed on d2 and in fact this fully compensates Black for the slight loss of time."

The 5...Ng6 line
1.d4 Nf6 2.c4 e5 3.dxe5 Ng4 4.e4 Nxe5 5.f4 Ng6

The Knight on g6 puts the f4-pawn under pressure, but may be embarrassed and lose a tempo if White pushes f4–f5. Now 6.a3, an attempt to take all squares from the Bb8 by continuing with b2–b4 or Bc1–e3, does not work that fine after 6...Bc5! 7.b4?! Bxg1! 8.Rxg1 O-O! 9.Qf3 d6 10.g4 a5 11.b5 Nd7 12.Ra2 Nc5 when Black's superior pawn structure and well-positioned Nc5 gives him the advantage. That leaves White with the choice between 6.Nf3 and 6.Be3.

The move 6.Nf3 controls the e5-square in order to prepare the push f4–f5. Unlike after 5...Nec6, White does not have to fear 6...Bc5?!, which runs into difficulties after 7.f5! Nh4 8.Ng5!, when the Black knight is already in danger of being lost to Qd1–g4 or Qd1–h5. Thus Black must react quickly with 6...Bb4+ 7.Nc3 when he can adopt a normal setup with d6/O-O/Nc6/b6 or act boldly with 7...Qf6 threatening both the Nc3 and the f4-pawn. One point in favour of 7...Qf6 is that after 8.e5 Qb6 the black queen prevents White to castle short and is well placed if White castles long.

The move 6.Be3 takes the a7–g1 diagonal from Black's Bf8 and may in some lines prepare the long castle. After the mandatory 6...Bb4+, during several moves Black will have the choice between aggressive and quiet continuations:
 * White can opt for 7.Nd2 to avoid having doubled pawns, but he must be prepared to sacrifice a pawn after 7...Qe7 8.Kf2!? Bxd2 9.Qxd2 Qxe4 10.Bd3 with piece activity for the pawn deficit, because the normal defense 8.Bd3? runs into 8...Qd6! and both the Bd3 and the f4-pawn are attacked.
 * White does not need, however, to bother about the doubled pawns and after 7.Nc3 Bxc3+ 8.bxc3 Black can choose the quiet 8...b6!? followed with a normal development like d6/O-O/Bb7/Nd7/Re8/Nc5.
 * An ultra-aggressive continuation for Black is 7.Nc3 Bxc3+ 8.bxc3 Qe7 9.Bd3 f5!? 10.Qc2 fxe4 11.Bxe4 when Black can free his play with the pseudo-sacrifice 11...Nxf4 12.Bxf4 d5 13.cxd5 Bf5 regaining the piece. Lalic continues this line by 14.Qa4+ b5! 15.Qxb5+ c6 "with great complications".
 * Lalic proposes Black with a middle way, after 7.Nc3 Bxc3+ 8.bxc3 Qe7 9.Bd3 O-O 10.Qd2 and only now that Black has his king safe shall he unleash 10...f5!?, when "it is not so easy for White to meet [10...f5] as the two main responses, 11.e5 and 11.exf5, allow Black promising chances with 11...d6 and 11...Nxf4 respectively".

Theory table
1.d4 Nf6 2.c4 e5 3.dxe5 Ng4 4.e4