# [Retros] Full-point non-Zugzwang :-)

Noam Elkies elkies at math.harvard.edu
Thu Jun 23 13:13:27 EDT 2005

Valery Liskovets writes:

> A nice retro-problem, but what a challenge? I found a list of

> endgame papers by Haworth but none joint with Bourzutschky only.

Thanks. As for the "challenge", it is from recent correspondence.
The history is roughly as follows.

Marc Bourzutschky wondered whether lists of mutual Zugzwangs
extracted from endgame databases might be missing some positions
whose outcome depende on e.p. status. He found a few examples such as:

Ka1, pawns a2,b3,c4 / Ka3, pawn b4:
Draw unless White just played c2-c4, in which case BTM loses;

Kc4, pawns c3,b5 / Kb6, pawns b7,c5:
Whoever moves loses unless Black just played c7-c5, in which case WTM draws.

["Full-point Zugzwang" is equivalent to "whoever moves loses".
It seems that I was the first to use the phrase "full-point Zugzwang":
"full point" as in 1 point for a win, 1/2 for draw, 0 for loss,
so a f.p.Z. is one where the side on move is a full point worse
than if (s)he could pass -- in most mutual Zugzwangs only
a half point is at stake.]

Guy Haworth then observed that there was a third possibility
not contained in the present 6-man tables, and I constructed
this 11-man pawn ending:

.k......
pP.p....
Kp..p...
.Pp.P...
..P.....
........
........
........

White Ka6, pawns b5,b7,c4,e5 / Kb8, pawns a7,b6,c5,d7,e6:
Whoever moves loses unless Black just played a move *other* than c7-c5,
in which case WTM draws (because White is stalemated).

Guy Haworth noted that diagram labels such as "White didn't just play c7-c5"
are not recognized in orthodox studies, so I produced the following
pair of positions X,Y:

(X)
Ka5, pawn a3,b4,c5,c6,d4,e6,g5 = 8
Ka7, Ra8, Bb8, pawns a4,a6,b5,c7,d5,e7,g6,h7 = 11

r b . . . . . .
k . p . p . . p
p . P . P . p .
K p P p . . P .
p P . P . . . .
P . . . . . . .
. . . . . . . .
. . . . . . . .

rb6/k1p1p2p/p1P1P1p1/KpPp2P1/pP1P4/P7/8/8

(Y) = (X) without White pawns a3,d4,g5 (5+11)

X is certainly a mutual Zugzwang: White wins BTM but not WTM.
But is it a full-point Zugzwang? WTM: 0...b7-b5 forced -- note
that bPd5 plays a double role in the retroanalysis, preventing
both 0 d5xc6+ Ka7 and 0...f7xg6 -- so 1 cxb6+ cxb6+ 0-1;
BTM 1...h6(h5) 2 gxh6 and mate in 4, since the ep capture 1...a4xb3
(noted by G.Haworth) certainly cannot be established retroanalytically.
So it looks like a -/+ Zugzwang, but if it's BTM and Black plays
a null move, can (must) White play cxb6+, or is it stalemate?...
In (Y) WTM loses as before and BTM draws.

Then Guy mentioned castling and I eventually composed the position
I sent to the retros list four days ago.

NDE