5

In this line of the 3 knights opening

[fen "start"]

1. e4 e5 Nf3 Nc6 Nc3 Bc5 Nxe5 Nxe5 d4 Bd6 dxe5 Bxe5

the best continuation according both to my engines and to databases is 7. Bd3. Why? For instance, can anyone explain why that's better than 7. Be2 or 7. Bc4?

Below some of the reasons I found by myself, but I would love to have confirmation or hear more:

  • If the pawn on e4 moves, the bishop would attack the h7 square which might be helpful for a mating attack in case black castles king-side. 7. Be2 doesn't attack any important square
  • 7. Bc4 would attack f7, but the bishop is undefended on c4 and might become a target
  • 7. Bd3 gives extra protection to the e4 pawn (useful in case white needs to move the knight on c3), neither 7. Bc4 nor 7. Be2 does that
4

A light-squared bishop move here is in order so that white can castle soon. The choices that you mentioned are definitely the only ones that aren't dumb/lose a tempo.

Be2 is probably the worst of the reasonable choices. Its only result is to allow castling, and it kind of clogs up white's middle - potential moves like Ne2 or Qe2, which may show up at some point, are off the plate.

Bc4 and Bd3 are both solid, I think. There likely wasn't much of a difference in the engine evaluation for these moves, and depending on the tools you used to conduct this analysis, the difference may be within the margin of error for the program. Essentially, I'm not sure there is a measurable difference between these moves in terms of evaluation.

Assuming that there is an actual difference, you might also consider that engines are fairly notorious for NOT playing attacking chess. It has been argued that they focus too much on material imbalances and not enough on position/pressure/psychology. The move Bc4 "feels" scary, but the engine sees that with perfect play, it isn't much of a threat. The pressure on the e4 pawn, however, will be real with perfect play, and it moves to defend that pawn.

Essentially, Bc4 might be more practical in a game between imperfect people, but the attack it provides is not real enough to matter in a perfect game - thus Bd3 is technicallybetter.

Play whatever you're more comfortable with.

2

Just to answer directly and concisely to the question:

  1. Bd3. Why?

Well there are 2 reasons for that and one of them you already mentioned:

  • Protecting the e4 pawn

    This is a bit more real than it seems because the most natural moves for black are Nf6 and castles, which immediately threaten the e4 pawn by removing the defender with Bxc3. Bd3 defends it in advance, which is prophylaxis. I personally feel this is the main reason for Bd3 over Bc4.

  • Kingside attack

    In the future, if black castles kingside which is the most natural thing to do, Bd3 aims for h7, becoming an attacking piece, after the pawn moves of course. But the interesting part is that black will have a hard time stopping the advance because at any point white can play f4 to kick any blockading piece.

    Bc4 also targets black in a kingside castled position which is why it is a reasonable move as well, but h7 looks more threatening and harder to defend for black than f7.

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