Breaking down the Berlin Wall- Spanish opening

Breaking down the Berlin Wall- Spanish opening

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A well known opening at top level is the Berlin Defense.

If you play the normal move 4.0-0, the famous endgame ends up being something like this 

While white has chances, this is a dry type of position and Black has shown the position is quite resilient. This all started with Kramnik against Kasparov in World Championship 2000, but since most top GMS have used this as Black, including Magnus Carlsen, Grischuk, Karjakin and many others.

Therefore White has tried 4 d3 to have a more interesting game. Black tends to reply 4..Bc5, actively developing the piece. We reached a key position in the opening, a Tabiya where both sides have plenty of options. 

1e4 e5 2Nf3 Nc6 3 Bb5 Nf6 4 d3 Bc5


Now I have some experience with the White pieces, and it is not easy to gain an advantage with White here.

I played 5.0-0 once and I lost. Here's the game

of course one can try  5.c3!? with later d3-d4.
I also lost a game with this , here's the game


By no means do I imply that my 5th moves are incorrect. I am facing strong opponents and maybe the middlegame is where I erred, but at any rate, 4 d3 side-steps the endgame tabiya but Black has many ideas in this line as well.
So at some point, it is interesting to see how GMs handle this line 
1e4 e5 2Nf3 Nc6 3 Bb5 Nf6 4 d3 Bc5
and one better attempt to fight for the advantage is 5 Bc6 dc6 6 Nbd2

Giving up the bishop pair is not obvious to me, but White can really continue aggressively and play for the advantage.
lets see top game #1 featuring @Hikaru with White and Firouzja @Firouzja2003 with Black
___

and game 2 features Streamers @EricHansen with Black and @Hikaru with White
note the early g2-g4 by White.