[BrianWall-ChessList] Any books on mathematical analysis of chess?

[Brian Wall]

----- Forwarded message from ptrschilling <schillip at optonline.net> -----
    Date: 26 Mar 2007 22:59:52 -0700
    From: ptrschilling <schillip at optonline.net>
Reply-To: Chess_Library at yahoogroups.com
 Subject: [Chess_Library] Re: Any books on mathematical analysis of chess?
      To: Chess_Library at yahoogroups.com


In reply to John in China: The last point is the only place I have a
right to an opinion. I am a very mediocre chess player, but very strong
in computer knowledge. I have been in the computer field for about 25
years.  Computer chess and AI (Artificial Intelligence, not American
Idol) are hobbies of mine.



How computers play chess (greatly simplified and condensed, books have
been written on this ) is as follows:

1.      In the openings, computers use a book constructed by humans,
without which they would have no idea what to play, even less than a
mediocre human (an explanation of why later).

2.     In the fundamental endings, computers use a database, commonly
called a tablebase, previously constructed by brute force calculation of
every possible move in every legal position. Tablebases are a case where
chess (up to 6 men currently) has been "solved". They are 100%
correct, no "thinking" involved. Prior to tablebases, computers
were notorious for poor play in that phase. Ken Thompson, one of the
creators of the Unix operating system crated the first tablebases and
called it "playing chess with God" on his website

3.     The middle game is the only area where they "play".  What
they do here is to build a tree starting with all possible moves, which
is why they never miss a tactic.  They then evaluate the leaf nodes of
the tree and choose the one with the highest score, assuming the best
reply by the opponent. If a move leads to mate in one, they build the
tree branch of one move and evaluate it. Much of the progress has been
as a result of learning to "prune" a tree of obviously bad moves
(null move etc.). Progress here has been massive, and of great use to
computer science in general.  Other areas of dramatic improvement have
been due to increases in cpu speed, parallel processing (bigger trees,
faster), and more memory (hash tables, not rebuilding the same tree
segment over and over). Whenever they can build the tree deep enough,
they query a tablebase for the evaluation, which is infallible.  At the
end of this process the position is reduced to a number expressed in
hundredth's of a pawn, and the computer plays whatever moves scores
the highest. A computer doesn't think "I am a computer, I am
better at tactics than my human opponent, therefore I will open up the
position with this piece sacrifice, even though the sac scores 0.03 less
than the quiet move".



What a computer does not do is "The computer, likewise looks at the
position and fills in the blanks with what is needed". Write some
code that does that and you have made a major break thru in "strong
AI" and you will most likely win a Nobel Prize. Please show it to me
first though, I would love to steal it and take the credit J



If you look in the literature of chess and computer chess, the one
advantage that humans have is that they can think abstractly about a
problem. In the case of chess this is often called schematic thinking.
Even a weak player (that would be me) can look at the "square of the
pawn" and determine whether it would queen safely without
calculating the moves, even if the potential endgame is many moves away.

A computer has no clue that the Exchange variation of the Ruy Lopez
(Spanish Game) is played with the idea of trading off all the pieces
into a winning endgame. If you point that out to weak club player, he
would understand the concept immediately. He would not have the
technique to realize this advantage against strong opposition, and would
probably lose.

A computer playing from it's opening book is analogous to human playing
a memorized line. However, if you take away a computers book, it will be
at a huge disadvantage and play some pretty bad moves. A human being can
fall back on "general opening principles" such as "control the center",
"develop the pieces", "don't loose time" ... A computer just starts
calculating all the moves in the position.



Computers used to miss tactics due to "horizon effect". They
would build a tree to a fixed depth, and evaluate. If they were in the
middle of a combination at ply 12, and were a Queen up, they would stop,
not "seeing" the next move was "obviously" a recapture
of their Queen. One move is the same as any other to a computer and code
had to be inserted to tell it to calculate capture sequences to
quiescence, regardless of the depth.  Computers still mis-evaluate
(mis-over-estimate our President might say) defensive fortresses and
will play on forever thinking they are up +5.08 (a Rook), where again, a
patzer like myself will eventually see there is no sequence of moves
that will lead to a breakthrough.



  In the 1960's M. Botvinnik, World Champion, PhD. in EE, computer
chess pioneer, tried to create a chess program based on Schematic
thinking, and positional knowledge. Even by the very low standards of
that period, it was not competitive. All other chess programs followed
the rough outline above, and no one has successfully revived the
Botvinnik approach, hence my Nobel Prize joke.



Online chess "freestyle" competitions tend to be won by
Man-Machine combinations because they think differently, and therefore
see different things. A strong player will guide the computer's
calculations into "interesting" lines.



If you have a chance read "Modern Chess Analysis" by Robin Smith
ISBN: 1904600085 it will enlighten you considerably on this subject. He
is a correspondence chess Grandmaster and obviously knows a lot about
computer programs.



I guess one reason for this long rant is that I have had this discussion
several times with a chess acquaintance who is a stronger chess player
than I am, but doesn't have a clue as to how computers compute (not
think).  People watched Star Trek 25-30 (?) years ago and thought
computers were unbeatable (then) when they played at a club level. A lot
of people don't understand computers (no shame in that unless you
work with them for a living as I do).



  Trust me on this- my analogy about birds and airplanes was carefully
considered and is accurate. The way people think about Chess and the way
computers calculate variations and evaluate positions are very
different.  Think of birds flying and airplanes flying. They accomplish
the same end by very different means.


--- In Chess_Library at yahoogroups.com, John Woodbury <johnchinawood at ...>
wrote:

 I agree with you upto the last point. The way a advanced program
thinks and evaluates moves and positions are somewhat the same as a
grandmaster. A grandmaster does not remember all possible moves just
looks at a position, makes his moves based on what the position needs.
The computer, likewise looks at the position and fills in the blanks
with what is needed. They arrive at the same moves in a like manner, and
it just so happens the book will tell us less gifted humans to make that
move. John in China

 ptrschilling schillip at ... --- In Chess_Library at yahoogroups.com,
"cbbs70b" cbbs70b@ wrote:

 Hello;
 I am somewhat new to the game and I am looking for any books,
 articles, etc that do a mathematical analysis of chess. The only
 books
 I see are books that use chess to discuss mathematical puzzles like
 "how many rooks can you put on an NxN chessboard such that one rook
 cannot capture another in only 1 move". I am looking for something
 useful that I can use to improve my game.
 Thanks
 Frank

 I am not sure that a mathematical analysis of Chess would be useful
 in improving your game. Chess is essentially a language, in the same
 sense as a computer language (e.g. Java). Mr. Jersawitz is right on
 the money when he talks about how to improve (not an endorsement, I
 have never seen his web site).

 On Dan Heisman's truly excellent website (go to the articles page)
 http://mywebpages.comcast.net/danheisman/Main_Chess/chess.htm, there
 are 2 articles by IM Larry Kaufman that deal with mathematical
 evaluations of the pieces (Evaluation of Material Imbalances and All
 About Doubled Pawns).

 If you are interested in a mathematical analysis of Chess for its own
 sake, get the source code to publicly available chess programs such
 as CRAFTY (there should be others) and look at the evaluation
 functions. This is where a person who understands Chess, Programming,
 and basic Mathematics is attempting to analyze a position. Some
 insight might be gained, but the amount of work involved would be
 vastly disproportionate to the amount of improvement in your game.

 The way people think about Chess and the way computers calculate
 variations and evaluate positions are very different. Think of birds
 flying and airplanes flying.


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