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Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!snorkelwacker!ai-lab!cracraft
From: cracraft@wheaties.ai.mit.edu (Stuart Cracraft)
Newsgroups: rec.games.chess,gnu.chess,comp.ai
Subject: A Study by Reti
Message-ID: <5785@rice-chex.ai.mit.edu>
Date: 8 Jan 90 00:47:29 GMT
Reply-To: cracraft@wheaties.ai.mit.edu ()
Organization: Project GNU
Lines: 120


A famous Reti endgame study is listed here with some machine analysis
and a question for the reader.

The Reti problem consists of the White king on h8, White pawn
on c6, Black king on a6, and the Black pawn on h5. It is White's
move.

                         Endgame Study
                    composed by Richard Reti
                    ------------------------
                    -- ** -- ** -- ** -- WK
		    ** -- ** -- ** -- ** --
		    BK ** WP ** -- ** -- **
		    ** -- ** -- ** -- ** BP
		    -- ** -- ** -- ** -- **
		    ** -- ** -- ** -- ** --
		    -- ** -- ** -- ** -- **
		    ** -- ** -- ** -- ** --
		    	White to draw


***** SPOILER HERE ! IF YOU WISH TO SOLVE YOURSELF, READ NO FURTHER ***
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The winning strategy involves straddling the a1-h8 diagnoal with
White's king, permitting escort of the c-pawn to queening in those
variations in which black is also allowed to queen, and secondly to
allow entering the "square of the pawn" of the black h-pawn
threatening to queen thus preventing it.

>>> Machine analysis <<<

The Reti position was submitted to GNU Chess 1.55 on a one-user
Sparc-1, Fidelity Mach 3 (16mhz 68000), and AI Chess 1.46
(unreleased; 16mhz 80386).

Solution was taken to be the point at which the program saw an
approximate draw value in the material (e.g. neither side having
significant material advantage.) Since during most of the search for
all three programs, the material evaluation was heavily in Black's
favor by 3-7 pawns, this appeared reasonable.  Also, examination of
the principal variation (AI and GNU show full variations while
Fidelity shows only four ply of the solution) was done in those
cases where it was available.

A summary:

		Solution	At what ply   Seconds  Speed	   Evaluation
AI Chess	  yes		during 10th	168   1351 pos/sec    0.00
Fidelity	  yes		after 11th	 13   1500 pos/sec    -.25
GNU Sparc	  yes		after 11th      503   5100 pos/sec     .06
	
Note that AI is the only program that saw the true flat draw.
AI also finds the solution at least one ply earlier due to its
search strategies.

The solution is Kg7 with either K-f6-e6-d7 or K-f6-e5-f4-g3-h2-etc.

Fidelity's speed on this problem is incredible. All three programs
use tranposition tables in the search -- so Fidelity must be using
some other trick.

Here is GNU's printout for statistics hounds...

Your move is? white

Move# 0    Target= 12000    Clock: 36000
 1.      8    0      13    c6c7  a6b7 
 2.    -76    0      51    h8g7  h5h4 
 3&    -60    0      83    h8g7  h5h4  c6c7  a6b7 
 3.    -60    0     118    h8g7  h5h4  c6c7  a6b7 
 4-   -232    0     180    h8g7  h5h4  g7f6  h4h3 
 4&   -226    0     397    h8g7  h5h4  g7f6  h4h3 
 4.   -226    1     503    h8g7  h5h4  g7f6  h4h3 
 5&   -210    1     902    h8g7  h5h4  g7f6  h4h3  c6c7  a6b7 
 5.   -210    1    1089    h8g7  h5h4  g7f6  h4h3  c6c7  a6b7 
 6-   -465    1    1549    h8g7  h5h4  g7f6  h4h3  f6e5  h3h2 
 6&   -437    1    3085    h8g7  h5h4  g7f6  h4h3  f6e5  h3h2  c6c7  a6b7 
 6.   -437    1    3352    h8g7  h5h4  g7f6  h4h3  f6e5  h3h2  c6c7  a6b7 
 7+   -226    2    5173    h8g7  h5h4  g7f6  h4h3  f6e6  a6b5  c6c7 
 7&   -448    3   11858    h8g7  h5h4  g7f6  h4h3  f6e6  h3h2  c6c7  a6b7 
                           e6d7 
 7.   -448    6   27063    h8g7  h5h4  g7f6  h4h3  f6e6  h3h2  c6c7  a6b7 
                           e6d7 
 8+   -242    7   30565    h8g7  h5h4  g7f6  h4h3  f6e6  a6b6  e6d7  b6c5 
 8&   -251   13   57468    h8g7  h5h4  g7f6  a6b6  f6e5  h4h3  e5d6  b6b5 
 8.   -251   47  246906    h8g7  h5h4  g7f6  a6b6  f6e5  h4h3  e5d6  b6b5 
 9-   -474   50  259215    h8g7  h5h4  g7f6  a6b6  f6e5  h4h3  e5d6  h3h2 
                           c6c7  b6b7  d6d7 
 9&   -447   54  274343    h8g7  h5h4  g7f6  a6b6  f6e5  h4h3  e5d6  h3h2 
                           c6c7  b6b7  d6d7 
 9.   -447   54  275069    h8g7  h5h4  g7f6  a6b6  f6e5  h4h3  e5d6  h3h2 
                           c6c7  b6b7  d6d7 
10+   -192   59  295192    h8g7  a6b6  g7f6  h5h4  f6e5 
10&   -207   66  321423    h8g7  a6b6  g7f6  h5h4  f6e5  h4h3  e5d6  b6a6 
                           c6c7  a6b7  d6d7 
10.   -207   96  481186    h8g7  a6b6  g7f6  h5h4  f6e5  h4h3  e5d6  b6a6 
                           c6c7  a6b7  d6d7 
11+    -39  104  510968    h8g7  a6b6  g7f6  b6c6  f6e5  c6b5  e5e4  b5c4 
                           e4e5 
11&      6  117  559208    h8g7  a6b6  g7f6  b6c6  f6e5  c6b5  e5f4  h5h4 
                           f4g4  h4h3  g4h3 
11.      6  503 2557132    h8g7  a6b6  g7f6  b6c6  f6e5  c6b5  e5f4  h5h4 
                           f4g4  h4h3  g4h3 
Nodes= 2557132  Eval= 23625  Hash= 23934  Rate= 5140  CPU= 08:17.45

My move is: h8g7

If anyone would care to speculate on Fidelity's programming tricks
for solving this problem, please do.

	Stuart