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In order to find the answer to this hypertheoretical question, it is necessary to first eliminate all of Black's inferior defences, until we are eventually left with just the one good defence for Black, which draws the game.
(For more ideas about the "hyper-theory" of chess, I strongly recommend Rowson's "Chess for Zebras". Note that in the hyper-theoretical sense, terms such as 'potential' and 'capacity to increase one's advantage' are more important than 'initiative' and 'counterplay').
First of all, most of Black's first moves other than 1...Nf6 and 1...d5 (excluding transpositional possibilities, e.g. 1...e6 2.c4 d5) give White a small but lasting edge. Black's other main options are 1...c5, 1...d6 and 1...g6 (for simplicity I will not mention the other possibilities, since they either transpose or give White very good hyper-theoretical winning chances), but each of them have their disadvantages, especially if Black refuses to transpose to the King's Indian.
1...g6 may be a "draw" if White plays c4, but after 2.e4, Black cannot equalise, and White's advantage is of a gradually increasing nature in the main lines, which means that with best play from both sides, White's more active pieces would vastly increase White's winning chances.
1...d6 has a similar "problem" if White plays 2.e4!, again transposing to a Pirc/Modern - see above.
1...c5 looks too positionally uncompromising to be a hyper-theoretical draw, since after 2.d5, White can play Nc3 and e4, which ensures White of a positional edge which will probably increase if White plays flawlessly.
Oops, I almost forgot the Dutch. Personally I think that Black's control over e4 is only temporary, while the resultant weaknesses cannot be fully covered in the long term. For the record, the main main lines put White in an excellent position to exploit Black's positional concessions.
Many would think that the clearest way for Black to draw is with 1...d5. However, the disadvantage is that after 2.c4 Black has to make a concession of some sort, which increases White's potential for increasing his advantage in the middlegame. Lines such as the Albin Counter-Gambit and Chigorin are unsound with best play, and White has more than one way to obtain a large capacity for turning his positional advantages into a win.
I don't trust 2...dc4 either, since after 3.e4 White is considered better in all lines, and usually Black relies on active piece play to counter White's greater control of the centre. I personally don't think that this counterplay makes up for Black's positional concessions, and with best play White will obtain a lasting positional edge.
The QGD is a tough nut to crack, and in my opinion the only way for White to play for a win hyper-theoretically is the Exchange Variation with Nge2. There Black has no way to entirely prevent White's plan of f3 and eventually e4, and since White has more space and more active pieces, he will create good winning chances regardless of what Black plays.
The Slav is without doubt Black's most solid defence to 1.d4, following 1...d5 2.c4. It is quite clear that White's early initiative is easily neutralised in the Exchange, Classical or Slow Slav variations, so the best winning chances are provided by either the Anti-Meran (6.Bd3 looks more and more like a hyper-theoretical draw nowadays), or the 5.Bg5 variation. Black can avoid the latter variation with 4...dc4, but then 5.a4 Bf5 6.Ne5 makes things very difficult for Black, and in spite of Black's lack of weaknesses, White's much easier development gives him very good winning chances. The theory of the 5.Bg5 is changing so quickly and rapidly that one cannot really judge whether White can obtain a "hyper-theoretical" win, although my personal opinion is that Black is walking a very fine line here indeed. The Anti-Meran with 5.e3 Nbd7 6.Qc2 Bd6 7.g4 h6 is currently very unclear, and currently Black's long-term potential gives him excellent chances of securing a half-point.
I will comment on White's "hypertheoretical" winning chances against Black's defences with 1...Nf6 in a later post. For now, it seems that White's winning chances after Black's alternatives to 1...d5 and 1...Nf6 are very good, and the QGA and QGD are facing a serious threat at the moment, but the Slav is very flexible, and with best play Black could hold the half-point in view of his lack of weaknesses and good development.
Of course, some people will entirely disagree with some of my opinions here, especially since most of this post would sound ridiculous if considered in a "practical" viewpoint. However, the point of this post is to evaluate White's winning chances on the basis of potential and positional advantages, while downplaying Black's counterplay in many variations.
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What is the best defence against 1.d4 (Read 49842 times)
