Early e5 push
This post is incomplete and will be cleaned up like the others.
There are some branch-points to consider. The most important consideration will be the placement of the Black f8 bishop. Is it within the pawn chain or outside of it? A bishop outside the pawn chain is more aggressive and active, but leaves g7 and f6 with one less defender. Let's start with lines where the bishop is outside the pawn chain.
There are many ways the opening can play out to transpose into this kind of position.
OK, let's get started. One fundamental tenet of chess is that you should avoid developing your bishops until you are certain they are going to the most optimal square. In this opening, white playing Bb5 may be slightly inaccurate (Bd3 is often the optimal square). But Black playing Bb4 is more dangerous. Instead, Black could consider other candidate moves to replace Bb4..4. ...d5 or d6 or even a6 should be playable.
With a6, if white does not capture c6 and plays on for the pin, 5. Ba4 b5 6. Bb3 d5. Here Black transposes into a comfortable variation of the St. George defense system (which is playable in bughouse).
So, let's look at the pawn structure.
White took a space advantage in pushing e5. He gains control over f6 (not d6 since that is defended with Pc7, Bb4 and Qd8 indirectly). In exchange, he has maybe over extending his pawn into enemy ranks. This makes e5 a natural target for black, and follows another fundamental tenet of chess: Attack a pawn chain at its base or at its head. Black can play d6 at the right time to challenge e5 and recuperate some dark-square control.
But, there is still one other fundamental difference between the pawn structures: the e-pawns. White's e-pawn exerts control over f6, which can be undermined by focusing on g7. This means his bishop can stay home on c1 but remain, in effect, "developed". The natural threats are P@h6 and N@g5.
That last tidbit makes you appreciate what the black bishop does on f8 for his defenses. Black also worries a bit about the backward e6 pawn which plugs up his c8 bishop. If he could generate a trade on d5 he could open it up. Otherwise he has little to no threat on f3, h3 or g2. For this reason, White's developed bishop leaving g2 weak has far less repercussions than Black's bishop leaving g7 unattended.
Let's re-evaluate the position.
Black is prodded to select a plan. Candidate moves include 5. ...Ng4, Nd5 and Bxc3.
5. ...Ng4
Ng4 plays for e5, and tricks with N@e4 if he can take advantage of the weaknesses on f2 and c3. But, if white can answer it appropriately, I think Black gets punished for leaving his piece out of play.
White surely considered 6. d4 instead of Qe2. If he could castle next, perhaps he could save a tempo. Unfortunately, after d4, Bxc3+ bxc and Nxf2, Kxf2 N@e4+ may start revealing holes and at least some semblance of counterplay if not equality for Black.
7. Bd7 un-pins the knight and allows tactics of Ncxe5 to cycle back with Nxd7. White castles away from Black's pieces, unpinning his knight.
Black has a fun trick line here with 8. ...Nxd4 trading a piece for 2 pawns to open the position, but as you can see, his remaining pieces can be pushed back and he is left with nothing to show for it.
Note that 7. ...dxe5 leaves all of White's pieces with ideal activity, including the c1 bishop. And yet, they retain more potential energy than Black's counterparts. Bg5 allows Rad1 threatening the queen all with free tempi. The f3 knight can open a discovered attack from the queen onto the N on g4. The king has mobility and free reign to castle kingside to safety when threatened. And what does Black have here? There isn't a clear plan of attack to keep going on the natural weakness of e5. Perhaps before d4 is played, N@f4 he can try to create something and at least win g2, but Qe4 Nxg2+ Kf1 leaves black with 3 minor pieces hanging and a double attack on c6. Meanwhile his kingside is empty and easily destroyed.
#2: Nd5
Playing Nd5 changes a few things about the position. Black's pieces are all in the center and none are left on the kingside. This means things can get sharp quick. Some pieces pressure with N@h5 can again push black to crack without perfect defenses (and sometimes even with perfect defenses) if the flow is right.
So is it busted? NO! It is only move 5. If you have not used more than 5 seconds, your opponent is unlikely to have a knight yet and certainly not much more than that. So let's go back to assessing things without that knight.
6. Nxd5 This is the most natural looking move for white. It negates the use of the b4 bishop and trades a queenside piece for a kingside piece. It has drawbacks though too. It moves the e-pawn out of the way of the c8 bishop and gives it life. Castling kingside for white just became more precarious as well.
A common motif in the open variations of the four-knights openings is that Black yearns to be able to play bg4 (or bf5) and get the c8 bishop to break out of the pawn chain. Just like the French defense. If that bishop can come into play without immediate retribution, black can equalize. Recapturing exd5 helps black do just that. So what other options are there?
6. a3 White decides to use a tempo force Black to commit his better bishop to either attack c6 or stay on the a3-f8 diagonal. This line seldom is played but is not without merit.
6. O-O. White momentarily leaves Black in the driver's seat. This keeps the e6 pawn blockading the c8 bishop. It frees the c3 N to come into e4. And later a well-timed d2-d4 push helps reinforce the center and matters will soon shift to the kingside.
Black cannot take c3 without helping further White's plans (Bxc3 dxc3, or Nxc3 bxc3 with d4 coming). Nf4 looks much better than it is and is met by d4. Look at Sorsi's tactics blog to see why Nxg2 is not a meaningful threat. So instead, he should play 6. ...d6.
7. Re1. With this, White looks to improve and punish Black's king for staying in the center. White hopes one day to develop with dxc3 or d4 and keeps nudging black to make things uncomfortable in the meantime. Now, unlike the other lines, c3 would be a real threat after Nxd5 exd, since it will push black's bishop off the a3-f8 diagonal. Black is running out of time to delay things. What are Black's options?
7. ...Bd7 is shown above. This does not respect the tactics around the open e-file.
7. ...O-O risks castling into the attack.
7. ...Bxc3 concedes matters to White who answers with dxc3 and is left positionally superior.
7. ....a6 is possible. White could then capture c6 or take the N on d5 and the bishop on b4. Bf1 looks like it could provide king safety but as you can see it is too slow and loses the battle in the center.
7. ...dxe5 looks to simplify and release the floodgates. Note that there are lots of complicated tactics at play here. There are number of different lines to look into there. Nxc3 looks better than Bxc3 in my estimation.
#3: Bxc3
