According to the hierarchy of positional criteria (which looks like a decent algorithm to me) white should try to improve his pawn structure before improving the position of pieces. The question is if white can achieve the ideal pawn center after black has played 1…e5. Let’s look at the two most direct attempts first:
1. King’s Gambit (deflecting the e5-pawn)
The attempt to play the immediate d4 fails due to the check on h4.
Therefore white has to prepare d4 by either Nf3 to prevent Qh4+ or by Bc4 clearing the f1-square for the king. Both can be answered with d5 which eventually leads to the exchange of the e4-pawn.
Black also has the option to strike immediately with d5 (Falkbeer).
If that wasn’t enough, there is also a sequence of moves that also casts doubt on the King’s Gambit for concrete reasons:
The idea to construct the pawn center in a sustained way fails to d5 – even Nf6 is possible – where black can take back with the queen without losing a tempo.
The line that should put the Ponziani out of business as a winning-attempt is this one:
Conclusion: The slow build-up fails to prevent both black counter-operations and should not lead to an advantage for white. Still it has to be mentioned that Nepomniachtchi seems to like this system in blitz. His success with it can be explained with his extreme hustling skills, rather than by it’s objective strength though.
We will now consider the other three white options:
Nc3 (restriction), Bc4 (restriction), Nf3 (attack).
3. Vienna Game
This prevents d5 for now but allows Nf6. After Nf6 black threatens to play d5 and white has a dilemma. If he plays Bc4 to stop it, black has Nxe4. White could live with that if black was forced to enter the Frankenstein-Dracula Gambit (who came up with that name?). Unfortunately black can dodge the fireworks and equalize with Be7.
If white tries to play it with f4, then black can equalize on the spot with d5.
4. Bishop’s Game
This also prevents d5 but allows Nf6. After Nf6 white has the same move-order problem that he has in the Vienna and should go for the passive move d3. Black can counter this with a reversed Ponziani though. The difference is that d5 gains a tempo in the bishop c4.
5. Let’s look at the last option, 2.Nf3
This practically prevents d5, because the Elephant Gambit is bad, and it also allows Nf6, but there are some important details!
a. Counterattack with Nf6 (Petroff)
White does not spend a tempo to protect the pawn-e4, it gets captured, but then a miracle happens and the pawn-e4 rises again like a Phoenix from the ashes. At the same time black got a pawn to d5, so he gets free development.
What happens if black protects the e5-pawn first?
b. Protecting the e-pawn with d6 (Philidor) is passive but also rather solid. White basically gets an improved version of the Scotch.
c. After excluding all the weaker options, the only remaining move is playing the knight out to c6 which protects the pawn and develops a piece at the same time. How shall white continue?
The attempt to construct an idea pawn center fails for the same reasons as above.
bb. Three Knights
At first this line looks like a harmless version of the Vienna Game, because white loses the options to lash out with f4, but in fact it is an improved move-order, since it safely prevents d5 and that is more important.
After Nf6 we reach the Four Knights and the ball is in white’s court on how to continue.
In this line the pawn-e4 gets removed and black has free development, but his pawn structure is slightly worse.
Here the Rubinstein-System seems to be the adequate reply, where black even has two options that both seem to hold tactically:
Since the mainline fails to produce any advantage, white can try Bc4 which loses half a tempo in exchange for luring the knight to d4, but it appears that black has a forced draw in this line also.
cc. 3.Bc4 (improved Bishop’s Game)
In the Two-Knights black threatens once again to remove the e4-pawn, but white has two options here: React with the standard d4 to keep his e-pawn alive in one way or the other and the tactical option with Ng5.
It is not clear if these complications favor white, but in any case black can try to get an improved version of it by playing Bc5 (Italian) first and then follow it up with Nf6.
After Nf6, white can’t ignore the attack on his e-pawn anymore and it seems that all aggressive attempts involving d4 are most likely bound to fail. White can try a slower approach and build up with d3, but that allows black to play d5 at one point. On the other hand the Bc5 gives white the additional option of playing the Evans Gambit and this is actually critical for the assessment of the whole system. The good/bad news is that white has a very tough time trying to maintain equality in the Evans, otherwise it would be a nice freeroll.
dd. 3.Bb5 (Ruy Lopez)
After this move it turns out that white gets everything he wanted. The Ruy Lopez allows white to construct the ideal pawn center, it prevents d5 and white doesn’t make a passive move to defend his e4-pawn against Nf6, at least this was the theoretical conclusion and that’s why the Ruy Lopez was regarded as the queen of e4-openings for almost a century.
The first important discovery was that white didn’t have to defend the e4-pawn (Capablanca-Lasker, New York 1915).
Therefore the e4-pawn will eventually stay alive even in the Open Variation.
Unfortunately things are not that easy as black has shown that the attack with Nf6 is quite effective when played immediately.
White can save his e-pawn in the typical fashion, but the resulting position is pretty much dead.
Even worse, Frank Marshall and modern engines have shown that white cannot even prevent black from playing d5, because it works out tactically.
There is also another very concrete solution for black, an attempt to exploit the position of the bishop on b5: The Schliemann.
Black plays a Vienna Game with colors reversed, where the standard counter in the center runs into tactical problems.
…and that is where the Ruy Lopez stands at the moment.
ee. 3.d4 (Scotch)
Since the Ruy Lopez doesn’t seem to hold promise after all, it is time to look somewhere else for an advantage. How about physically removing the blockade of the e-pawn? This way the e-pawn stays flexible and it is more difficult for black to attack or to exchange it.
While the concept sounds very advanced in theory, it looks like white doesn’t have enough development to support his structure. The jury is still out though, especially since Kasparov himself gave it an outing in his St. Louis Blitz Exhibition.