Tuesday, April 5, 2011

Chess960-SP139: Questions of positional symmetry - part 1

Chess960 makes you think about symmetry in the opening quite a lot. The reason is that sometimes there seems to be a single standout best opening move and so black thinks "well if white plays it, why don't I?"

The answer regarding symmetry is simple but deep. Since white plays first, if both players play identical moves one of two situations will eventually arise:
  1. White will exploit a material gain situation and so black must break symmetry
  2. White will exploit a positional gain situation and so black must break symmetry
Note: There is a  third rule of symmetrical and that is that white must not steer the symmetry in a direction where it is he that looses the initiative. This can only occur when white breaks symmetry temporarily by handing black a complementary Zwischenzug type move like this example:

In SP139, there seems to be an interesting case where if both players play a very natural and safe first move and proceed by symmetry, white does not get a tactical exploit but instead get's a positional exploit. However I'm not good enough a player to prove categorically how good white's position becomes. Take a look at the final position. It is amazing how white's single tempo advantage at move one translates to a more developed position in the end. Here is the game scenario:

SP139: 1. c4 (a natural first move for both sides)

This line has been double checked by Rybka4-960 although human eyes tend to find c4 before the machine does. There are other good choices. My first reaction was 1.d4 to release the e1 bishop, but it has it's own set of problems. 1. c4 is not an aggressive move and does not release a bishop quickly, but for the sake of this discussion, it does achieve a number of "naturally" good things:
  1. develops Nc3
  2. contests control of the centre
  3. leaves open a contest of black's control of the long dark diagonal
  4. allows the dark bishop to control the c1-h6 diagonal which will open after g6
  5. blocks white's diagonal attack line Be8-Bb5+
  6. does not impede any of the other pieces
  7. allows solid pawn structures down the track
  8. gives the corner knight a developing square c2 that does not block the b-pawn
Ok now that we agree it is a natural first move, the example above shows what happens when black simply says "hey if they do it, why not I?"

The important point is the final position in the example. If you fast forward to the end and pause the replay, you can see what white has obtained for the opening symmetrical line. As far as I can see (which is not very far), white has a number of nice features positionally speaking:

White's advantages in the final position:
  1. more control of space
  2. a path for his king to centralise g2-f3-e4
  3. the minor pieces do not impede pawn advance
Black's advantages:
  1. the bishop is better developed than white's
So if there is anybody out there that understands chess, tell me what you think. Has black's decision to follow symmetry in SP139 doomed them to a miserable game? Another great contemplation is to look at the original starting position at move zero, and try to see how white causes the positional gain from symmetry. I think the answer is because white's rook is on b1 and this gives white the initiative once the breaking move b4 is played.

At some other time, I'll try to find examples of where white get's a tactical situation that forces black to break symmetry. I think those examples are more common than this positional example.

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