Underpromotion

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Ilan Vardi

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May 4, 1989, 1:58:56 AM5/4/89
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Find a position where promotion to a bishop is the only winning move.

David S. Herscovici '87

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May 5, 1989, 12:15:47 PM5/5/89
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In article <89...@polya.Stanford.EDU> il...@Gang-of-Four.Stanford.EDU (Ilan Vardi) writes:
>Find a position where promotion to a bishop is the only winning move.

+---+---+---+---+---+---+---+---+
| | | | | | | b | k |
+---+---+---+---+---+---+---+---+
| | | | N | | P | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | K |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+

Obviously, promotion to a rook or queen stalemates black, and if white
doesn't promote, black can take the pawn. Also, if white promotes to
a knight, black can escape without too much difficulty. However:

1. f8/B any
2. Nf6 any
3. Bg7 mate

Noam Elkies

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May 5, 1989, 3:35:08 PM5/5/89
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>Speaking of minimal positions the Journal of Recreational Mathematics
>around 10 years ago asked for the minimal number of pieces needed to
>set up a double stalemate (both black and white stalemated). The
>Journal correct answer wasn't found there. What is the number and how
>many distinct solutions are there?

I can see several ways to get a mutual stalemate with only six pieces

[W Kh8, Bg8, f6, f7, h7 --- B Kf8 ;
W Kh8, e6, f7, h7 --- B Kf8, e7 ;
W Ka6, a5, b5, b6, b7 --- B Kb8 ]

but cannot obtain one with fewer. It's easy enough to enumerate the
variations of each basic setup, but it looks quite hard to prove that
some list of six-piece mutual stalemates is complete.

In the other direction, has anyone improved on the 30-piece mutual stalemate
in a legal position?

--Noam Elkies (elk...@zariski.harvard.edu / ELK...@ZARISKI.BITNET)
Dept. of Math., Harvard Univ.

Chris Long

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May 5, 1989, 3:44:37 AM5/5/89
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In article <89...@polya.Stanford.EDU>, Ilan Vardi writes:

> Find a position where promotion to a bishop is the only winning move.

Composition by C. Long, 1989:

White to play and win.

+---+---+---+---+---+---+---+---+
| | | | | b | | k | |
+---+---+---+---+---+---+---+---+
| P | | | | | | P | p |
+---+---+---+---+---+---+---+---+
| | b | | | | | | P |
+---+---+---+---+---+---+---+---+
| | | | | N | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | p | | p | | |
+---+---+---+---+---+---+---+---+
| | | | P | p | P | | |
+---+---+---+---+---+---+---+---+
| | | | | K | | | |
+---+---+---+---+---+---+---+---+
--
Chris Long

"If you see a good move, look for a better one."
Emmanuel Lasker

g.l.sicherman

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May 5, 1989, 9:02:51 AM5/5/89
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In article <89...@polya.Stanford.EDU>, il...@Gang-of-Four.Stanford.EDU writes:
> Find a position where promotion to a bishop is the only winning move.

This is too easy! Composers have achieved harder tasks than this.
Here's an obvious solution:

-Q :: :: +S
:: +P :: ::
:: :: :: ::
:: :: :: ::
:: :: :: ::
+K :: :: ::
:: :: :: ::
-K :: :: ::
White wins

You can make the problem harder by barring captures or adding other
restrictions.

-:-
"To a Knight the chessboard presents the aspect of a
densely wooded forest."
--F. K. Young, _The Minor Tactics of Chess_
--
Col. G. L. Sicherman
g...@odyssey.att.COM

Ilan Vardi

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May 5, 1989, 1:16:58 PM5/5/89
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In article <May.5.03.44....@topaz.rutgers.edu> cl...@topaz.rutgers.edu (Chris Long) writes:
>In article <89...@polya.Stanford.EDU>, Ilan Vardi writes:
>
>> Find a position where promotion to a bishop is the only winning move.
>
>Composition by C. Long, 1989:
>
Sorry, I missed that one. But what is the minimum number of pieces
needed to obtain such a position?

Noam Elkies

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May 5, 1989, 10:51:15 AM5/5/89
to
>Find a position where promotion to a bishop is the only winning move.

This, and much more, has been done many times. For instance,
Lommer and Sutherland's _1234_ include the following 1934 endgame
composition by A.O.Herbstmann (#1186):

-------------------
| . _ . _ . r k _ |
| _ . _ q P b _ . |
| . _ . _ . _ . _ |
| _ . _ . _ . _ P |
| . _ . _ . _ . _ |
| _ . _ B _ . _ . |
| . _ . _ . _ . _ |
| _ K _ R _ . _ . |
___________________

(2nd Prize, Ty\"ov\"aen Shakki 1934)

White to play and win.


--Noam D. Elkies (elk...@zariski.harvard.edu / ELK...@ZARISKI.BITNET)

Mike Coffin

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May 6, 1989, 10:24:17 AM5/6/89
to
Here's one that occured in tournament play. Sokolsky-Ravinsky, USSR,
1938. The move was a8=B "and White won".

+---+---+---+---+---+---+---+---+
| | | | | b | | k | |
+---+---+---+---+---+---+---+---+
| P | | | | | p | P | p |
+---+---+---+---+---+---+---+---+
| | R | | | | P | | P |
+---+---+---+---+---+---+---+---+
| | | r | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+


| | P | | | | | | |
+---+---+---+---+---+---+---+---+
| | K | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+

--
Mike Coffin mi...@arizona.edu
Univ. of Ariz. Dept. of Comp. Sci. {allegra,cmcl2}!arizona!mike
Tucson, AZ 85721 (602)621-2858

Chris Long

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May 6, 1989, 4:46:52 AM5/6/89
to
In article <8...@odyssey.ATT.COM>, g.l.sicherman writes:
> In article <89...@polya.Stanford.EDU>, il...@Gang-of-Four.Stanford.EDU writes:
>> Find a position where promotion to a bishop is the only winning move.
> This is too easy! Composers have achieved harder tasks than this.
> Here's an obvious solution:
> -Q :: :: +R

> :: +P :: ::
> :: :: :: ::
> :: :: :: ::
> :: :: :: ::
> +K :: :: ::
> :: :: :: ::
> -K :: :: ::
> White wins

1. cxb8=N also wins, and an alternate solution that does not involve
minor-promotion is 1. Rh1+ Qb1 2. Rxb1+ Kxb1 3. b8=Q Ka1 4. Qa3, mate.
1. b8={B,N} loses after 1. .. Qb2+ 2. Ka4 Qxh8, but I believe White
also wins with the scenic 1. b8=Q by carefully maneuvering the White
king onto a8 and the White queen onto b7 with the Black queen unable
to take the White rook on the diagonal (then the best that Black
can do is to check on the a-file, to which White responds Qa7!).
Am I correct in this last assertion? Is the position [ White Ka3,
Qc8, Rh8; Black Ka1, Qb8 ], with Black to move, theoretically won
for White?

Mark Webb

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May 6, 1989, 9:32:53 AM5/6/89
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>Find a position where promotion to a bishop is the only winning move.


An easy one this, Ilan.

Try K + (N or B) + P vs. K where promotion of the Pawn leads to Stalemate if
a Queen is selected. The promotion of the pawn to a bishop leads to a win
with K + N + B or K + B + B (different coloured bishops) vs. K.
--
-Mark Webb mw...@maths.tcd.ie

g.l.sicherman

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May 6, 1989, 3:42:57 PM5/6/89
to
In article <May.6.04.46....@topaz.rutgers.edu>, Chris Long writes:
> In article <8...@odyssey.ATT.COM>, g.l.sicherman writes:
) > ... Here's an obvious solution:
) > -Q :: :: +R
) > :: +P :: ::
) > :: :: :: ::
) > :: :: :: ::
) > :: :: :: ::
) > +K :: :: ::
) > :: :: :: ::
) > -K :: :: ::
) > White wins

>
> 1. cxb8=N also wins, and an alternate solution that does not involve
> minor-promotion is 1. Rh1+ Qb1 2. Rxb1+ Kxb1 3. b8=Q Ka1 4. Qa3, mate.

That's because you changed the Knight on h8 to a Rook. Anybody can win
at chess if they substitute pieces when their opponents aren't looking!

-:-
"Well, my opponents are getting weaker, at any rate. This
one didn't even know how to mate me. He just kept queening
pawns for no reason."
--Len Cool, "The Education of a Chess Player"

Chris Long

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May 7, 1989, 2:05:23 AM5/7/89
to
In article <8...@odyssey.ATT.COM>, g.l.sicherman writes:

> That's because you changed the Knight on h8 to a Rook. Anybody can win
> at chess if they substitute pieces when their opponents aren't looking!

I'm sorry; you had an "S" in the original diagram, and for some
reason I thought it was supposed to be an "R".

Please ignore that man behind the curtain. :-)

Chris Long

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May 7, 1989, 12:05:22 AM5/7/89
to
In article <May.5.03.44....@topaz.rutgers.edu>, I wrote:

> Composition by C. Long, 1989:

> White to play and win.

a b c d e f g h
+---+---+---+---+---+---+---+---+
8 | | | | | b | | k | | 8
+---+---+---+---+---+---+---+---+
7 | P | | | | | | P | p | 7
+---+---+---+---+---+---+---+---+
6 | | b | | | | | | P | 6
+---+---+---+---+---+---+---+---+
5 | | | | | N | | | | 5
+---+---+---+---+---+---+---+---+
4 | | | | | | | | | 4
+---+---+---+---+---+---+---+---+
3 | | | | p | | p | | | 3
+---+---+---+---+---+---+---+---+
2 | | | | P | p | P | | | 2
+---+---+---+---+---+---+---+---+
1 | | | | | K | | | | 1
+---+---+---+---+---+---+---+---+
a b c d e f g h


Solution:

If 1. Nc6 then 1. .. Bxc6 and 2. .. Bxa8 stalemate; any other knight
move and 1. .. Bxa7 wins for Black.

If 1. a8={R,Q} then 1. .. Bxf2+! 2. Kxf2 e1=Q+ 3. Kxe1 f2+; if 4. Kxf2
or 4. Kf1 stalemate; if 4. Kd1?? then 4. .. f1=Q, mate; if 3. Kxf3??
then Black wins with 3. .. Qh1+.

If 1. a8=N then 1. .. Bd8! wins a piece and the game for Black.

If 1. a8=B! White threatens 2. Bd5+ Bf7 3. Bxf7, mate. Black's
best try is 1. .. Bc6; if 2. Bxc6?? then Black can stalemate with
2. .. Bxf2!; White has a standard win after 2. Nxc6. If 1. .. Bf7,
2. Nxf7 Kxf7 3. Bd5 wins for White. White has little trouble
handling any other moves by Black, as Bxf2 is ineffective.

David Furtney

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May 7, 1989, 2:30:32 PM5/7/89
to
In article <10...@megaron.arizona.edu> mi...@arizona.edu (Mike Coffin) writes:
>Here's one that occured in tournament play. Sokolsky-Ravinsky, USSR,
>1938. The move was a8=B "and White won".
>
> +---+---+---+---+---+---+---+---+
> | | | | | b | | k | |
> +---+---+---+---+---+---+---+---+
> | P | | | | | p | P | p |
> +---+---+---+---+---+---+---+---+
> | | R | | | | P | | P |
> +---+---+---+---+---+---+---+---+
> | | | r | | | | | |
> +---+---+---+---+---+---+---+---+
> | | | | | | | | |
> +---+---+---+---+---+---+---+---+
> | | P | | | | | | |
> +---+---+---+---+---+---+---+---+
> | | K | | | | | | |
> +---+---+---+---+---+---+---+---+
> | | | | | | | | |
> +---+---+---+---+---+---+---+---+
>

Chris Long posted this position just before Ilan asked about
underpromoting to a bishop. Does anybody have the continuation
of this game, it would be fun to see it.

Chris asked me in an e-mail message if the position was really a
win for white. I thought it was obvious since Blacks king is
immobilized, but that is what makes the position interesting.

Here are some sample variations:

Note that Black can draw by

1. Unloading his bishop followed by perpetual check with the rook.
2. Unloading his rook (perpetual check) if his Be8 is pinned.

1 a8B! Rc8 (plan 1) 2 Bd5 (working on f7) Rd8 3 Bc4 Rd2+ 4 Kc3 Rd8
5 Rb7 (Blacks Be8 is now immobilized) Rc8 6 Re7 (Blacks rook now
pinned to first rank) Rb8 (... Bb5 7 Rxf7! Bxc4 8 Rf8+ Rxf8
9 gxf8Q+ Kxf8 10 Kxc4 wins) 7 Kd4 Rd8+ 8 Ke5 Rb8 9 Kd6 Ra8
10 Bd5! Rc8 11 b4 (waiting) Rd8+ 12 Kc7 Rd7+ 13 Kc8 (13 Rxd7 Bxd7
14 Bxf7+ also wins) Rxe7 14 fxe7 Bb5 15 Kd8 Be8 16 Bc4 (waiting) Bc6
17 e8Q+ Bxe8 18 Ke7 Bd7 19 Bxf7#.

Another try is 2 ... Bd7 3 Rb7 Re8 4 Kc3 Rd8 5 Kc4 Rc8+ 6 Kd4 Rd8
7 Ke5 Re8+ 8 Kd6 Rd8 9 Bxf7+ Kxf7 10 Rxd7+ Rxd7 11 Kxd7 wins --
11 ... Kg8 12 b4 Kf7 13 g8Q+ Kxg8 14 Ke7 Kh8 15 Ke8 Kg8 16 f7+ Kh8
17 f8Q#.

Sidenote: My chess computer was almost completely useless for this kind
of analysis! It was not willing to sac Blacks bishop for the
resulting perpetual. It would find the short range stalemates, however.
Conversely, from Whites viewpoint, it would not seriously consider
sacrifices by Black.

David Furtney

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May 7, 1989, 1:52:42 PM5/7/89
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In article <May.7.02.05....@topaz.rutgers.edu> cl...@topaz.rutgers.edu (Chris Long) writes:
<In article <8...@odyssey.ATT.COM>, g.l.sicherman writes:
<
<> That's because you changed the Knight on h8 to a Rook. Anybody can win
<> at chess if they substitute pieces when their opponents aren't looking!
<
<I'm sorry; you had an "S" in the original diagram, and for some
<reason I thought it was supposed to be an "R".
<
<Please ignore that man behind the curtain. :-)

This is not that well known by those of us who are not problemists.
Would anybody who is knowledgable about these matters be willing to
explain some of the terms and ideas used by chess problem composers?
Why is S used instead of N for knight? Is N used for anything else?
Can you give an example of a helpmate and selfmate?

I am becoming more interested in these lately. Do people find that
the skill developed while solving these problems transfers to playing
chess?

Eugene Wallingford

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May 8, 1989, 10:26:22 AM5/8/89
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In article <86...@boulder.Colorado.EDU>, David Furtney writes:

>
>This is not that well known by those of us who are not problemists.
>Would anybody who is knowledgable about these matters be willing to
>explain some of the terms and ideas used by chess problem composers?
>Why is S used instead of N for knight? Is N used for anything else?
>Can you give an example of a helpmate and selfmate?
>

I am no problem composer, but the "S" used to represent a knight
in international chess -- and especially in composition -- stands
for "Springer" (which, in German, is the name for the knight).
I managed to pick up all kinds of esoteric knowledge chess knowledge
as I studied German in school; as I have learned a little about
composition, it is nice to see that some of it is useful!

Incidentally, the _Chess Life_ column by David Brown concerning
chess problems and composition had a discussion of notation not
too long ago (i.e., in the last year or so). His column is quite
a nice way to learn about composition and related matters.

g.l.sicherman

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May 8, 1989, 7:40:46 PM5/8/89
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In article <86...@boulder.Colorado.EDU>, fur...@boulder.Colorado.EDU writes:
>
> Can you give an example of a helpmate and selfmate? ...

Here's a helpmate from 1860:

Sam Loyd.

:: :: :: +R ::
:: :: :: :: -Q
:: :: :: ::
:: :: :: -K ::
:: +K +B ::
:: :: :: ::
:: :: :: -B
:: :: :: ::

Black to play and help White mate in three moves.

If anybody has an older helpmate, I'd like to see it...!

-:-
"Oh--is it my move?"

Chris Long

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May 8, 1989, 8:44:31 PM5/8/89
to

Unfortunately, it turns out that my compostion does not satisfy
Ilan Vardi's criteria, as there is another winning move for White!
Consider 1. Ne7!!. Black *must* take the pawn! If not, White has
an easy win with 2. a8=Q. After 1. Ne7!! Bxa7, 2. Nf6+! Kf7
3. g8=Q+ wins it all for White.

I still can't believe I missed this.
--
Chris Long

"If you see a good move, look for a better one."

Emanuel Lasker

LTH network news server

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May 10, 1989, 1:59:55 PM5/10/89
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In article <86...@boulder.Colorado.EDU>, David Furtney writes:

>Why is S used instead of N for knight? Is N used for anything else?

It so happens that the abbreviations of the chess pieces in German,
Swedish, Danish, and (I believe) some other languages are:

Eng. Ger. Swe. German and Swedish meaning
--------------------------------------------------------
Pawn B Bauer Bonde (Peasant)
Knight S Springer Springare (Jumper)
Bishop L Laufer Loepare (Runner)
Rook T Turm Torn (Tower)
Queen D Dame? Dam/Drottning (Lady/Queen)
King K Koening Kung (King)

The German/Swedish/... notation has become a kind of standard, even
used by, say, Russians. By the way, I have heard that it is only
the western civilization that has a female piece as "queen".

--
Jan Eric Larsson Jan...@Control.LTH.Se +46 46 108795
Department of Automatic Control
Lund Institute of Technology "We watched the thermocouples dance to the
Box 118, S-221 00 LUND, Sweden spirited tunes of a high frequency band."

Col. G. L. Sicherman

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May 12, 1989, 2:48:02 PM5/12/89
to
In response to overwhelming demand (from David Furtney), here's the
solution to that Helpmate.

1. Kf6 Ra8; 2. Kg7 Bb8; 3. Kh8 Be5.

Now, wasn't that refreshing?

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