The simplest mutual full-point Zugzwangs

Tim came to the club buzzing with these a few weeks ago.

[Skip intro]

A Zugzwang (German: forced move) is a chess position where, if it's your turn to move, you lose, and if your opponent has the move, you might be OK.

Here's an example from one of my own games: anything White does loses. We say, White is in Zugzwang.

--------
p----p--
-p-bp---
r----k--
---P-P--
--P---K-
P----R--
B-------

Black can doodle happily with pawn moves, but any move of a white Pawn or piece loses at least a Pawn. White in fact threw himself on the sword with
43. c4 Ra3+ 44. Kh4 Be7+ 45. Kh5 Rh3#

The simplest Zugzwang position of all is known from the theory of Pawn endgames, with two Kings and one pawn trying to promote.

--k-----
--------
--KP----
--------
--------
--------
--------
--------

Black to move loses, but with White to move, it's a draw.

A mutual or reciprocal Zugzwang is where neither side wants to move, and this position is indeed a mutual Zugzwang.

A mutual full-point Zugzwang (m-f-p-Z) is where both sides are in Zugzwang. In the Pawn endgame, White to move concedes a half-point to Black, but in a m-f-p-Z White loses a whole point. Here's an example, known as the trebuchet:

--------
--------
--------
---pK---
--kP----
--------
--------
--------

All OK? So, these ideas have been around for dickey's years, but what Tim was enthusiastic about was learning of positions with King each, a Pawn each and a single white piece (Bishop, Knight or Rook), which met the conditions of a m-f-p-Z. In fact, Tim was more mischievous than just to show us: he set us the task of finding the positions! I'll give you an hour or so now to have a go yourselves...

(...)

Finished? How many did you get?

Solutions for 5-men positions:

Bishop:

-bk-----
--p-----
K-P-----
--------
--------
--------
--------
--------

A couple with a Knight:

------nk
---p----
---P--K-
--------
--------
--------
--------
--------

--------
-pPKn---
-k------
--------
--------
--------
--------
--------

Rook:

--------
--------
--------
--------
--------
--p-----
-kP-----
--RK----

Nothing so simple exists for a Queen, but if you are prepared to add extra pawns, or an enemy Queen:

k-------
q-PK----
P-------
--------
--------
--P-----
--------
--------

--------
--------
--------
-Pq-----
--------
-K-Q----
-----p--
--k-----

Here are solutions for 6-men positions with B N or R:

--------
--------
--------
--------
---K-k-p
---P--p-
------B-
--------

--------
--------
--------
--------
----kp-p
---N----
--KP----
--------

--------
--------
------R-
k-P-----
--K-----
-------p
------p-
--------

And if you have a Rook each, we have examples like:

--------
--------
--------
--------
--------
rPK-----
-RP-----
--k-----

More?

Full set:
http://www.k4it.de/egtb/zugzwang.php/
Article about 6-man tablebases:
http://ticc.uvt.nl/icga/acg12/proceedings/Contribution104.pdf

John Nunn got a bit interested in all these, and I refer you to his excellent books based on comprehensive computer endgame databases, recently updated since the emergence of the 6-man tablebases:
http://www.amazon.co.uk/Secrets-Rook-Endings-John-Nunn/dp/1901983188/
http://www.amazon.co.uk/Secrets-Pawnless-Endings-John-Nunn/dp/190198365X/

P.S.

Candidates for the Immortal zugzwang game include this classic from Nimzowitsch:

Samisch - Nimzovitch [E06] Carlsbad, 1923

And two he would rather forget:

Nimzovitch,A - Capablanca,J [B12] New York, 1927
Alekhin - Nimzowitsch [C17] San Remo, 1930

All are to be found in the Canon:
http://www.exeterchessclub.org.uk/content/canon

Chess Quotes

From: Dan Scoones

Moments when you should sense DANGER in chess:

  1. There has been a change in the pawn structure. Your opponent has 8 and you don't have any.
  2. Your opponent begins to throw pawns at your eyes.
  3. You have a postion won but your opponent has a gun.
  4. The Director tells you not to bother turning in your scoresheet after the game.
  5. Before game begins you notice your opponents 1st initials are 'GM'.
  6. After completing your development you sense your opponent playing the endgame.
— -- I don't know the composer of this - anyone? By the way, I.M. George is distinguished local player! Ian isn't actually an IM but he won the West of England Championship last year