I'm trying to understand why it is somewhat common for White to play move #3 in this opening against the scilian:
1. e4 ... c5
2. Nf3 ... d6
3. d4 ... cxd4
4. Nxd4

There are over 23000 games on chessgames.com with this opening so trading off a center pawn apparently isn't that big a deal for white but I'm trying to understand what the main advantage is for white.

there isn't an advatage for white or black this early in the game. White trades a d pawn for a c pawn not that big of deal. Also with white knight off of f3 white can at some point play f4 and start a king side attack.

Actually, Larsen raised the same question.  He thought it was a positional mistake to trade off a center pawn so early--but then, he really liked center pawns.  Obviously, since so many play this, they think that getting freedom for their pieces and attacking chances is worth it.  However, it is no doubt one reason why so many times Black gets good endgames out of the Sicilian (if he survives to the endgame)--and why, as the proverb goes, short games in the Sicilian are won by White and long ones are won by Black.

Thank you both.

tonydal wrote: Actually, Larsen raised the same question.  He thought it was a positional mistake to trade off a center pawn so early--but then, he really liked center pawns.  Obviously, since so many play this, they think that getting freedom for their pieces and attacking chances is worth it.  However, it is no doubt one reason why so many times Black gets good endgames out of the Sicilian (if he survives to the endgame)--and why, as the proverb goes, short games in the Sicilian are won by White and long ones are won by Black.

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Excellent comment.

Tonydal said it all.   :D

After move 4, the position is unbalanced. This is what many players want. White is ahead in development, but Black is on the move. Each side has a different half open file. White's knight on d4 is well placed in the center and Black will often challenge it. Playing d4 unblocked a white bishop. Pawn moves are made to allow pieces to develop. The game is still balanced.