conjugated squares

Mephisto2
Posers and Puzzles 05 Apr '05 14:06
1. 05 Apr '05 14:06
A few weeks ago, someone asked about the theory of conjugated squares. I replied with a relevant article around a position from a Lasker game. Here a study (by Euwe) where the concepts opposition and conjugated squares can be helpful to find the solution. White to play and win.

Invalid FEN inserted - 8/5k2/p7/P3p1p1/3p2P1/3P1PP1/7K/8/ w
2. XanthosNZ
Cancerous Bus Crash
05 Apr '05 15:05
1. Kg1 Kg7 2. Kf1 Kf7 3. Ke1 Ke6 4. Kf2 Ke6 5. Ke2 Ke6 6. f4 exf4 7. gxf4 gxf4 8. Kf3 Ke5 9. g5 Kf5 10. g6 Kxg6 11. Kxf4 and mate will follow.

Did I miss a better move by black?
3. Alcra
Lazy Sod
05 Apr '05 15:07
Originally posted by Mephisto2
A few weeks ago, someone asked about the theory of conjugated squares. I replied with a relevant article around a position from a Lasker game. Here a study (by Euwe) where the concepts opposition and conjugated squares can be helpful to find the solution. White to play and win.

[fen]8/5k2/p7/P3p1p1/3p2P1/3P1PP1/7K/8/ w[/fen]
Ok, I will put my head out on a limb (nice mixed metaphor!).

What are "conjugated squares"?

4. 05 Apr '05 15:203 edits
Originally posted by Alcra

What are "conjugated squares"?

Geriatric lovers who on marrying are more commonly referred to as 'related squares'.

5. 05 Apr '05 15:23
Originally posted by XanthosNZ
1. Kg1 Kg7 2. Kf1 Kf7 3. Ke1 Ke6 4. Kf2 Ke6 5. Ke2 Ke6 6. f4 exf4 7. gxf4 gxf4 8. Kf3 Ke5 9. g5 Kf5 10. g6 Kxg6 11. Kxf4 and mate will follow.

Did I miss a better move by black?
You've got it. A few remarks

- There must be a typo in at least one of the three consecutive Ke6 moves. 3.Ke6 - 4.ke7 - 5.Ke6 will do, so would 3.Ke7 - 4.Kf6 - 5.Ke6 to the same white moves.

- for completeness, the continuation after 5. ... Kg6 (instead of 5.Ke6) could be given.
6. XanthosNZ
Cancerous Bus Crash
05 Apr '05 15:28
Originally posted by Mephisto2
You've got it. A few remarks

- There must be a typo in at least one of the three consecutive Ke6 moves. 3.Ke6 - 4.ke7 - 5.Ke6 will do, so would 3.Ke7 - 4.Kf6 - 5.Ke6 to the same white moves.

- for completeness, the continuation after 5. ... Kg6 (instead of 5.Ke6) could be given.
1. Kg1 Kg7 2. Kf1 Kf7 3. Ke1 Ke6 4. Kf2 Kf6 5. Ke2 Ke6 (5... Kg6 6. Kd1 Kf7 7. Kc2 Ke7 8. Kb3 Kd7 9. Kc4 Kd6 10. f4 exf4 11. gxf4 gxf4 12. Kxd4 f3 13. Ke3 Kc5 14. Kxf3) 6. f4 exf4 7. gxf4 gxf4 8. Kf3 Ke5 9. g5 Kf5 10. g6 Kxg6 11. Kxf4

Corrected and with bonus variation.
7. 05 Apr '05 15:411 edit
Originally posted by THUDandBLUNDER
Geriatric lovers who on marrying are more commonly referred to as 'related squares'.

lol, my bad. I 'translated' the term from my Dutch reference. In Dutch the term 'conjugated' is more accurate than 'related'.

edit. I found in other references the terms 'related' squares, 'conjugated' squares, as well as 'corresponding' squares.
8. 05 Apr '05 15:521 edit
Originally posted by Mephisto2
lol, my bad. I 'translated' the term from my Dutch reference. In Dutch the term 'conjugated' is more accurate than 'related'.

In fact, Google does turn up 3 hits for 'conjugated squares" and 40 for "'related squares' AND chess".
9. Bowmann
Non-Subscriber
05 Apr '05 15:59
Originally posted by THUDandBLUNDER
In fact, Google turns us 3 hits for 'conjugated squares" and 40 for "'related squares' AND chess".
"geriatric lovers" gets 30.
10. 05 Apr '05 16:04
Originally posted by Bowmann
"geriatric lovers" gets 30.
why don't you explain the theory of 'related squares' in perfect English? Because we probably dind't satisfy the question yet.
11. Alcra
Lazy Sod
05 Apr '05 16:10
Originally posted by Mephisto2
why don't you explain the theory of 'related squares' in perfect English? Because we probably dind't satisfy the question yet.
Thanks guys, I now know what it means, but haven;t the foggiest "what it means!"

Can someone talk to me like a little child and explain it ðŸ™‚

12. 05 Apr '05 16:16
Originally posted by Alcra

Can someone talk to me like a little child and explain it ðŸ™‚
First, do you know what 'opposition' means?
13. 05 Apr '05 17:582 edits
Originally posted by Alcra
Thanks guys, I now know what it means, but haven;t the foggiest "what it means!"

Can someone talk to me like a little child and explain it ðŸ™‚

Let me try to explain a few terms. Others will gladly correct both my mistakes and/or bad english.

idea 1: opposition

Invalid FEN inserted - 4k3/8/3PK3/8/8/8/8/8/ w

The two kings cannot approach each other. If white is to play, he doesn't want to play d7+ because after Kd8 Kd6 we have stalemate. It is said that black has the 'opposition' and can draw the game. If black is to play, he has to get 'out of the way' of white's king because of 'opposition' and will lose (e.g. Kd8 d7 Kc7 Ke7 wins).

14. 05 Apr '05 18:001 edit
Originally posted by Alcra
Thanks guys, I now know what it means, but haven;t the foggiest "what it means!"

Can someone talk to me like a little child and explain it ðŸ™‚

idea 2: distant opposition

Invalid FEN inserted - 8/8/4k3/8/8/8/3KP3/8/ b

If white is to move, he cannot prevent black from taking opposition as soon as white moves to the third rank. However, if black is to move, he can play Kd6! taking distant opposition. White cannot 'mirror' his move because his own pawn stands in the way on e2, therefor he has to allow black to take opposition and draw.

15. 05 Apr '05 18:001 edit
Originally posted by Alcra
Thanks guys, I now know what it means, but haven;t the foggiest "what it means!"

Can someone talk to me like a little child and explain it ðŸ™‚

idea 3: related (conjugated) squares

Invalid FEN inserted - 8/k7/3p4/p2P1p2/P2P1P2/8/8/K7/ w

White would win if he could get the king to b5 or g5. To get him on g5 is a matter of gaining enough tempi to be at h4 faster than black can get to f6.
Similarly, white could reach b5 only from c4 if black cannot go to a5 or b5 in time. But a5 is not good enough when white has the move because then white has the necessary tempi to reach h4 ahead of black to f6. Therefor, c4 and b5 are 'related' squares, and have the equivalent effect as opposition.
Going a step further, the squares couples b3-a7, c3-b7 and d3 - c7 are 'related square' couples. Whoever enters one of these first has to give up 'opposition' if the other one can reach the 'related' square.
Going one more step further, b2-a8, c2-b8, and d2 c8 are 'related' squares. More generally spoken (and assuming that the tempo battle towards h4/f6 is still in balance) the rectangles' b2-d3' and 'a8-c7' are 'related. They are called the 'primary domain'. Whoever enters that domain first is bound to give up opposition.

White can win here with the following sequence: 1.Kb1 (stays out of the primary domain) Kb7 (follows and keeps the squares on 8th rank free to be able to occupy them if white moves to the second rank) 2.Kc1 Kc7 (he has to follow towards f6) 3.Kd1 Kd7 4.Kc2! Kc8 (black cannot reach b8) 5.Kd2! (occupies the related square) Kd7 6.Kc3 Kc7 (he has to follow) 7.Kd3! and wins because blackhas to leave the related square, and cannot prevent that white will access either b5 or be fast enough to h4.

EDIT: it is probably too abstract (and hopefully without too many mistakes) but I hope it at least illustrates the ideas.