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Assuming that the principles of classical chess in the opening are still valid (which thing I very much believe), may we say that "from a theoretical point of view" 1.e4 is the best first move for White? (Occupying the center, freeing two pieces). No other first move can do that.

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    Ironically, it is 1. d4 that seems to be the theoretic preference of top players. – Glorfindel May 16 '16 at 18:22
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    From the ultimate theoretical point of view, probably all 20 moves are equivalent (all draws). – Post-It-Note May 16 '16 at 19:56
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    Perhaps should we first define the terms "from a theoretical point of view"? What do these words mean, concretely? You can see in the answers, it is not clearly perceived. Just one quotation from the next answer : "from the standpoint of first principles". This sentence and others demonstrate things are not clear for everybody, i think. – JohnHawking May 17 '16 at 9:47
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According to some GMs, d4 is the best first move. Alekhine, commenting on a Slav in his greatest games book, claims it gives White more chances of gaining an advantage. After taking the c pawn, Alekhine further comments that White now obtains an appreciable advantage. (Quoted by Hans Berliner.) Hans Berliner, in his book The System--A World Champion's Approach to Chess, claims, and Fischer agrees, that the advantage of the first move is the ability to attack the opponent's pawn center first. Since both agree that the King's Gambit is dubious, that leaves the Queen's Gambit as the only sound opening.

Many GMs have said d4 is better: although they claim it is due to needing a deeper understanding of chess. Anna Zatonskih states it better that you can make some minor inaccuracies and still have a good game. In e4 games, one mistake could cost you the game.

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From the standpoint of first principles, 1. e4 and 1. d4 are equally valid.

First, 1. e4 establishes central control and leads to fast castling. However, 1. d4 has its own unique advantage: it leads to an even stronger position in the center because the pawn on d4 is supported by the queen.

If that seems less significant than castling quickly, consider that the Berlin Defense, perhaps the line that has most frustrated 1. e4 players over the last 16 years, is only viable because of the weakness of the e4 pawn.

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1.e4 and 1.d4, from a "theoretical point of view", are most likely completely equal. When you say "theory", I'm assuming you mean variations. That is, given best play, both will draw.

To clarify what I'm saying: suppose you have the following position:

White: Kf5, f6; Black: Kf7. White to move.

This position is "solved", which means that we can investigate every single possible variation that can result from this position. If we were to consider the moves that white has, we can say that all of them are equal: all of them lead to draws, given black's best responses.

If we somehow solved all of chess, and somehow managed to investigate all the variations, I'm guessing we would see that every single first move leads to a draw with best play. Hence, 1.d4 and 1.e4 are equal in this sense.

However, when you mention "classical principles", this is a little different from theory. General principles are resultant from many observations of positions. For example, "develop pieces" in the opening follows from the fact that development allows you more activity, and hence more ability to restrict the opponent's activity. However, a theoretical opening line (like the poisoned pawn variation of the Sicilian Najdorf) may include good moves that blantantly violate these classical principles, yet still work. There are always exceptions to general principles.

However, both 1.d4 and 1.e4 are great in following the classical view of chess: occupy the center with a pawn, and open lines for quick development. A move that would follow classical chess, but would be still viable, would be 1.g3, which is more of hypermodern chess.

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