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2. Bc4 !? against the sicilian

Sure Bc4. Läufer („runner“), the Dutch say Loper as far as I know.

Small lies, big lies and statistics.
White scores badly with it, but the white players who play it are considerably weaker than the black players.
Many stong players play 1...c5, but very few play 2 Bc4.
This explains why black usually has the higher rating and that explains why black scores so well.
You could argue that no good players play it because it is bad, but it is the other way around.
I am quite sure that if you had takes statistical results of the London System some years ago, before the strong players picked it up, that the statistics would be comparable to what you find on the Bowdler Attack.
If you look at the statistics of the few games with a strong white player, or at the games of players with commensurate strength, then the score goes the other way.

That is all correct..However, If we dive in more deeply, the reason I don't find 2.Bc4 natural is because we are encouraging Black to go for d5 which he wants to play anyway. 2.Bc4 "provokes" e6 which isn't bad move for Black anyways. Black could gain a tempo on that Bishop later with d5 or b5. I have to mention I like your disagreement since it proves you have an open mind.
You guys are trying too hard to make this move look good, but it just isn't. I think we can conclude this by saying this move is not recommended.
Correspondence chess, top classical chess, and top engine games like TCEC all come close to the truth.

However, if say a 2200 rated correspondence player loses against a 2500 rated correspondence player, that does not necessarily say something about the merits of the opening. If the 2200 player had chosen say a mainline Najdorf variation, then we would not blame the loss on the opening.

The argument about black playing ...b5 can easily be dismissed. 1 e4 e5 2 Nf3 Nc6 3 Bb5 a6 4 Ba4 also allows black ...b5. Also Fischer's favourite 1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 a3 6 Bc4 e6 allows ...b5 and creates a vis-a-vis of Bc4/Bb3 and e6-f7, which Fischer used to attack with f2-f4-f5.

The argument about ...d5 is more fundamental. For sake of the argument I accept 1 e4 e6 2 Bc4 would be a poor idea.
However 1 e4 c5 2 Bc4 e6 is different for several reasons. White can fight against ...d5.
1 e4 c5 2 Bc4 e6 3 Nc3 (stops ...d5) Nc6 (if 3...Nf6 or 3...Nge7 then 4 e5) 4 d3 Nf6 5 Bf4 d5 6 Nb5 (surprise).
White can also play 1 e4 c5 2 Bc4 e6 3 Nc3 Nc6 4 d3 Nf6 5 Nf3 d5 6 Bb5 with a reverse Nimzovich Indian Defence.
White can also play 5 f4 in the style of the Grand Prix Attack.
If black plays 5...a6 to stop 6 Nb5 or 6 Bb5, then 6 e5 allows to answer 5...d5 with 6 exd6 e.p.
A position can only be drawn or won. Everything else is estimatrics - it doesn’t come to the point.

At least I gave you some facts, e.g. how often it has been won actually.

Yes, exactly: the positions after 1 e4 c5 2 Nf3 and 1 e4 c5 2 Bc4 most probably are both drawn with best play from both sides, so objectively one move is not better or worse than the other.

Yes, it is a fact that white scores badly with it in the database. That does not necessarily mean the move is bad, it can also mean that the move is played by weaker white players say 200 rating lower than the black players. The black players score better because they are stronger, not because of the weaker player's opening choice.

Here is an example of a strong white player playing it and winning.

2.Bc4 is a bad way to get out of the theory..I recommend the best move for White played by Nakamura himself 1.e4 c5 2.Qh5!! developing with tempo. Isn't this what GMs say? Always try to develop with tempo? After 2...e6 3.f4!! Nf6 4.Qf3 d5 5.d3 Nc6..I know it looks like something has gone wrong for White..but we already developed the Queen and connected Rooks while Black has 4 more moves to be completely mobilized. I don't think I'm missing anything.. Although it looks bad and it smells bad, it's a great move, just like 2.Bc4. Well, my discussion ends here. Good luck with refutation. Sarcastic? A little bit

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