I don't get the point of Morphy's Defence in the Ruy Lopez opening:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6
If White's purpose was to exchange Bishop for Knight and take the e5 pawn after it loses its defender (plus create some pawn weaknesses for Black), then the 3...a6 move comes too late to prevent it. Likewise I don't get White's retreat in all the variations that follow except for the exchange variation.
The basic idea of the opening was to snatch e5 pawn, but by playing Qd4 or Qg5 Black returns the pawn with good play.
This forced White to seek other ways of reaching advantage, so he tried with Bxc6 counting on a won pawn endgame. However, things are not so easy since Black has ample of compensation in his bishop pair-remember that bishops are good in open positions-and doubled pawns control a lot of important squares.
Since that try failed, White needed to try something else, and the only option left is bishop retreat. If they play Bc4 Black can transpose into Italian game with the extra temp since a6 has been played. Since a6 is an important move in those lines for Black, he would gain a small plus from the bishop retreat. That leaves Ba4.
With this retreat White keeps pressure on e5 pawn and hopes to force Black into making some concession. Black will do his best to develop and defend without weakening himself but in the end he fails to do so. He must play b5 at some point to release the pressure from the White light-squared bishop. After b5 Black will have compromised pawn structure on the queen side ( backward c pawn and exposed b5 pawn ) and that is the concession White hoped for.
It isn't much-Black is still OK-but it will guarantee White a long initiative-which is better overall result than what other lines offer.
The reason for this being Black's c-pawn is blocked by a knight so he can't participate in the battle for the center. This enables White to seize initiative in the center by forming d4+e4 pawn center supported with the c3 pawn. Black will lose time to reorganize his queen side in order to counterstrike which gives White time to meet comfortably Black's plan. This usually involves Nbd2-Nf1-Ne3/Ng3 maneuver, preparing king side attack, but can be a4 thrust, or simply a favorable change of the pawn center's type-he can block the position with d5 or open it with an exchange like dxe5 or dxc5.
The last option is the most dangerous for Black so he needs to play very passively for a while before he counter-strikes.
In this Wikipedia link you can see the list of variations. Notice that in the main line there is one thing in common for all the Black's responses-they regroup their queen side to meet White's initiative.
To conclude:
By retreating the bishop to a4 White gains small concession from Black in view of compromised pawn structure which results in White's better control of the center, which results in small but lasting initiative.
Hopefully this answer sheds some light for you.
If you have further questions leave a comment.
Best regards.
4.Bxc6 dxc6 5.Nxe5 doesn't win a pawn, as Black has 5...Qd4, attacking the knight and pawn simultaneously and winning the pawn back.
4.Bxc6 is a totally reasonable move, and it's called the Exchange Variation of the Ruy Lopez. White has given up a bishop for a knight, but after White eventually plays d4 and the pawns on d4 and e5 are exchanged, White's 4-pawns-against-3 on the kingside will be more effective at generating a passed pawn than Black's 4-pawns-against-3 on the queenside, because Black's four queenside pawns are occupying only three files.
The main point of 3...a6 is that after 4.Ba4, if at any point in the future Black decides that they want to prevent Bxc6, they can immediately make it impossible by playing ...b5. If Black continued developing without playing ...a6, then they wouldn't be able to prevent Bxc6, because they'd have to start by playing ...a6, and White could immediately respond with Bxc6 before Black was able to play ...b5.
3...a6 isn't the only good move, though. In particular 3...Nf6 (the Berlin Defense) is currently very popular at the highest levels. It turns out that in the main line of that variation Black wants the bishop to stay on b5 for the time being so they can hit it with the knight after ...Nxe4 and ...Nd6.
It is positional to help black achieve equality. The steinitz defense forces black to give up the center or lose a pawn.
It is one alternative to try. The cozio is okay but not quite as good at achieving equality as good. The berlin defense is another solid option slightly better than morphy a6.
Bb4 by black has one of the better scoring statistics.
f5 g6 Bc5 and many other moves give black a chance about as good as a6.
So do you prefer a given line, want to get away from the most played variations, or what? You gotta defend somehow.
