Opposition

Originally posted by Mephisto2
I believe we had this before, but it fits well into the 'opposition' theme, i.e. the generalisation of opposition, where terms are used like 'sister squares', 'heterodox oppposition', 'poles', primary domains' etc... Here is an example, a position from the game Lasker - Reichelm, 1901.

[fen]8/k7/3p4/p2P1p2/P2P1P2/8/8/K7 w - - 0 1[/fen]

White plays a ...[text shortened]... squares are 'b5' and 'g5', the only squares via which white can hope to penetrate.

Its this type of position in which I struggle to relate opposition to the position on the board. Black has the opposition until 3. d3 d7, but white takes it with 4. c4 (where black can't take the opposition with the pawn attacking c6). Is this the point? The moves seems quite natural, even without knowing the concepts behind opposition.

Or have I made a pig's ear of it?

D

Originally posted by Ragnorak
And then?

D

...Black must give up either the d5 or f5 squares, allowing White to penetrate and eventually promote a pawn. I'm too busy to do the full calculation now...

Originally posted by lausey
Here is one line I have found:

1. Kc2 Kb7 2. Kb3 Kb6 3. Kb4 Kc6 4. Ka5 Kb7 5. Kb5 Kc7 6. Ka6 Kb8 7. Kb6 Kc8 8. Ka7 Kc7 9. b4 Kc6 10. Ka6 Kc7 11. b5 Kb8 12. b6 {bad move and draws from here} Ka8 13. b7+ (13. Kb5 Kb7 14. Kc5 Kb8 15. Kc6 Kc8 16. b7+ Kb8 17. Kb6) ..Kb8 14. Kb6 {stalemate}

Well, sure, 12. b6 is a bad move for white. White should play 12. Kb6, which is a textbook win for white. 🙂

Originally posted by Ragnorak
Its this type of position in which I struggle to relate opposition to the position on the board. Black has the opposition until 3. d3 d7, but white takes it with 4. c4 (where black can't take the opposition with the pawn attacking c6). Is this the point? The moves seems quite natural, even without knowing the concepts behind opposition.

Or have I made a pig's ear of it?

D

I don't know. What are your moves 1 & 2?

Originally posted by Mephisto2
I don't know. What are your moves 1 & 2?

1. Kb2 Kb6 2. Kc3 Kc7

D

Originally posted by 93confirmed
...Black must give up either the d5 or f5 squares, allowing White to penetrate and eventually promote a pawn. I'm too busy to do the full calculation now...

Yes, I see it! The idea is similar in either direction.

1.Ke4 Kf6 2.Kf4 Kg6 3. Ke5! Kh6 (or 3. ...Kg7 4. Kf5 Kh6 5. Kf6 Kh7 6. Kg5) 4. Kf5 Kh7 (or Kg7) 5. Kg5, and white gets the h-pawn and wins. Yay! (I'm learning to use my outflanking maneuver!)

Sorry, I forgot to say that I think after white gets the h-pawn, white has to head over to get the b-pawn. The black king can either capture white's h-pawn or try to defend his b-pawn, but he can't do both. 🙂

Originally posted by Ragnorak
1. Kb2 Kb6 2. Kc3 Kc7

D

Yes, you made a pig's ear of it then.

To make the link with opposition, here is some further ideas. If white can reach any of the poles (b5 or g5), he wins. Black has to prevent that. That means he must arrive at g6 on the move after white reaches h4. Vice versa, white must reach h4 while black is still at e8 or e7 (i.e. 2 files ahead of Black). Similarly Black must occupy a6 or b6 on the move after Kc4 by white. But if Black chooses a6, he be two files behind in a race to the other pole and so Black has to chose b6.

There are several routes between the two threats for both sides. One square of White's minimum route has a unique correspondent on Black's minimum route, namely d3 (to c7). Thus, if White moves c4-d3, Black replies ....b6-c7, and will arrive at g6 in time. So, d3 and c7 are sister squares. Similarly, the pairings b6 and c4, and g6 and h4 are also sister squares.

This reasoning can be extended to the rectangles b2--d3 corresponding to a8--c7. The corresponding squares in these 'primary domains' can be obtained by shifting the black domain one file to the right and then folding along the middle of the fifth rank. The sister squares are then obtained by superposition. The sister squares are said to be in heterodox opposition.

Next step is to prove that whoever has reaches heterodox opposition in the primary domain reaches his goal. You should be able to work that out with few variants.

The squares in the larger rectangles a3--d3 outside the primary domain (the left and bottom border for white) is called the secondary domain. Black has no squares available there. Now if white move in the secondary domain in such a way that he can enter the primary position and black cannot reach the sister square, he wins. So, if white moves to b1, he threatens to enter the primary on b2 or c2. Black cannot make a corresponding move without white taking the heterodox opposition.

Hencs, White wins after 1.Kb1. This is just a tip of the iceberg. The hard work is to work out the proof I mentioned above. Playing the game becomes easy then once you know the sister squares.

Originally posted by Wulebgr
white to move and win

[fen]8/8/4k3/1p5p/1P5P/4K3/8/8 w - - 0 1[/fen]

Well, I guess the joke's on me to some degree. I just now realized that this setup looked a little familiar. I checked Purdy's "Guide To Good Chess" again, and sure enough, this principle is in there. It's called the Rule of Limits (attributed to Durand). Had I remembered this, I wouldn't have had to figure it out over the board.

Originally posted by Wulebgr
white to move and win

[fen]8/8/4k3/1p5p/1P5P/4K3/8/8 w - - 0 1[/fen]

[Event "?"]
[Site "?"]
[Date "2007.03.08"]
[Round "?"]
[White "Wulebgr"]
[Black "Fritz 9"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/8/4k3/1p5p/1P5P/4K3/8/8 w - - 0 1"]
[PlyCount "36"]
[SourceDate "2003.01.01"]

1. Ke4 Kd6 2. Kd4 Kc6 3. Ke5 Kd7 4. Kd5 Kc7 5. Kc5 Kc8 6. Kxb5 Kb7 7. Kc5 Kc7
8. Kd5 Kb6 9. Ke5 Kb5 10. Kf5 Kxb4 11. Kg5 Kc5 12. Kxh5 Kd6 13. Kg6 Ke7 14. Kg7
Kd6 15. h5 Kc5 16. h6 Kb4 17. h7 Kc4 18. h8=Q Kd5 1-0