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Why is it important to move the knight first?
I always figured it was because you have a better idea of where your knight belongs.
After 1. e4, for instance, if you're planning to move both the g1 knight and the light-squared bishop next, the question is do you move the knight and then the bishop, or the bishop and then the knight?
You already know your knight almost certainly belongs on f3, since (1) it's a good square; (2) h3 is a bad square; and (3) e2 just blocks in the queen and the bishop which you released with your pawn move.
But the bishop might belong on e2, d3, c4, or b5, depending - amongst other things - on what moves your opponent plays. If you already know the knight belongs on f3, but you're not as sure where your bishop should go, then moving the knight first lets you see an extra move of black's, which gives you more information with which to make the best bishop move (or to make a different move, for that matter).
Also, knights take longer to move across the board than bishops do, so getting them out earlier gives them a headstart, as it were.
Excellent answer. The reasons are exactly right. However, as with everything in life, including chess, there are advantages and disadvantages to every move in chess, the old "double edge sword." The disadvantages to moving the N first to c3 and f3 are: ( On this post I will only detail one of those disadvantages)
1. First and foremost they interfere with the overarching principle:
Winning chess is the strategically/tactically correct advance of the pawn mass.
1.Because they are impeding the advance of the pawns at c2 and f2. For this reason there are exceptions to this development rule of Ns and then Bs. Case in point. In the Ruy Lopez, the moves are 1.e4 e5 2.Nf3 Nf6 3.Bb5. Wait, shouldn't the other N come out first so that White has more Black moves to better determine where the B belongs along the f1 - a6 diagonal. The answer is no, and it is because of the overarching principle. Most players believe, and chess publications confirm that the reason the B is moved to b5 is to threaten Bxc6 after several moves of preparation in order to win the pawn at e5.
The real reason that White played his B to b5 is because the B is actually temporarily restraining Black's Queenside pawns. Especially the pawn at d7. The pawn at d7 is a central pawn, and critical for Black's forces ability to fight for control of the center. The reason the pawn cannot advance is because White would with his next move play Bxc6 and Black's only response would be bxc6; saddling himself with a loose doubled pawn complex. As every strong player knows a loose doubled pawn complex is an exploitable static weakness in Black's position. A compact doubled pawn complex after Bxc6 dxc6, is very difficult to exploit, almost impossible. Emmanuel Lasker had some success in the Ruy lopez with exploiting the compact double pawn complex at first. But as the stronger players realized it is extremely difficult to exploit and white's advantage may be winning but technically/practically not convertible into a won position. In order to effectively exploit the static compact doubled pawn complex, White has to create some pretty sophisticated dynamic advantages in the position. if Black knows how to thwart White's attempts at creating these dynamic advantages, the game ends in a draw. The first step in creating dynamic advantages in order to exploit a static compact doubled pawn complex is the right perspective. White needs to see Black's whole army as one soldier with a limp. As long as a man with a limp is sitting his limp is undetectable. But, as soon as he gets up and begins to walk the limp is evident. So the first step in the methodology/technique to exploit the compact double pawn complex in Black's army is to induce it to advance. That way the the limp/weakness becomes apparent.
The reader problably noticed that I highlighted the word 'restraining' in red. The reason for that is because it is a very important concept and method applied in siege warfare. Chess is siege warfare in the form of a game. Siege warfare was practiced by human armies throughout history in many forms. However, the methodologies common to all forms are: restrain, blockade and execute the enemy.
"My System', by Aaron Nimzowitsch is the best book ever written about how to conduct the 3 methodologies of siege warfare on the chess board. One of the techniques of siege warfare that are detailed in this book is how to step by step exploit a doubled pawn complex. And in addition he details the strenghts of a doubled pawn complex. Can't forget about that old "double edge sword."