FOM: chess contest

Julio GonZaleZ Cabillon jgc at adinet.com.uy
Fri Mar 20 23:42:43 EST 1998

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Venturing further detail, a "chess proof" will be a finite sequence of
moves according to the fixed rules of the game so as to obtain a "winning
position" [= either "White/Black has a forced win" or "neither White nor
Black can lose" (= draw)]. A "chess theorem" [or "true sentence" within
the game] will be a "winning position".

>From a theoretical standpoint chessplayers strive hard:

(A) To discover and formulate significant chess concepts, and to
conjecture significant winning positions relating to them.

(B) To provide, or describe so accurately as possible, demonstrations
of the conjectured winning positions.

No much will I say of golden rules which help us with (A). This activity is
subjective and each chessplayer relies heavily on his/her/its "intuition"
(whatever this term may mean), tempered by experience (or access to libraries
/databases). Since most chess propositions are, from the *practical* point
of view, not always feasibly decidable, blunders are to be expected. The
best GMs today (of course, Deep Blue et al included) may well be unable to
decide (for obvious reasons) whether the proposition under study is a
winning position or not.

* As I already said, some chess propositions are THEOREMS (in the math sense)
within the theory of the game. These theorems are composed positions of the
"White to play and win/draw" type [the so-called "studies"], and positions,
for instance, of four-piece endings. All this is well-known.

====

Theorem:

(H)  White: Ke6, Rf7
Black: Kh3, Nb6

(T) White wins whoever moves first!

Proof: A winning sequence against ANY defense can be found, for instance,
looking it up in Ken Thompson's CD-ROMs.

====

It may be interesting to recall what Dr. John Nunn wrote in the preface
of one of his masterpieces:

"_Secrets of Rook Endings_ provoked some strong responses;
these were mostly positive, but there were a few players
who viewed the production of such a 'Final Encyclopaedia'
with dismay, because it meant that a part of chess was forever
frozen in silicon."

* As I already said, some chess propositions are what I call PLAUSIBLE
CONJECTURES within the theory of the game.

"plausible" = "seeming to be true or reasonable, or valid but often
specious"; "appearing worthy of belief"; "convincing" [from the Latin
*plausibilis*, worthy of applause].

Professional chessplayers (say Shirov, Anand, ..., Deep Blue!) possess
an extraordinary "intuition"; they "know" when these PLAUSIBLE CONJECTURES
are theorems (in the chess sense) although they either are NOT acquainted
beforehand with a forced sequence of moves, or they are unable to prove
the conjecture (exhaustively). In this case, the chess objectivity is
supposedly attained by final appeal to observations and experiments (games
played between the best GMs). This criterion is not available, or is
deemed inappropriate, in the case of mathematics (but certainly NOT inside
chessland!). Reuben, this IS an important difference between mathematics
and chess, taken the present state of affairs of the Royal Game.

I wholeheartedly agree with Joe Shipman when he remarks that:

"...the intuition of a Grandmaster about White's winning
when Black's Queen is removed is strongly justified in a
technical sense -- any GM (indeed any master) could win
this every time within 200 moves against all of the world's
computers and GMs collectively (given a reasonable amount
of time -- a blitz game would not be appropriate but a few
minutes a move would be enough even if White is not allowed
to write anything down or move the pieces).  Further, the
winning technique can be explained in terms of chess strategy.
If you are willing to accept as "axioms" statements that
certain chess advantages suffice to win, then everything from
there on is just like math (when I published a refutation of
a gambit it felt like doing a mathematical proof, leaving
sufficiently easy details to the reader etc., EXCEPT that I'd
break off the analysis when accepted "Chess axioms" like
"a bishop ahead is enough" could be invoked)..."

[cf. FOM list, March 19, 1998 / 23:43:13 -0500]

* Most chess propositions are currently neither PLAUSIBLE CONJECTURES
(theorems in the chess sense) nor THEOREMS (in the math sense).
Fortunately (!) enough (some say), for the health and charm of the game
there still are *many* UNSOLVED PROBLEMS. These are usually labelled:
"unclear positions", "White/Black stands slightly better", "White/Black
has the upper hand", "White/Black with compensation for the material", etc.

On Fri, 20 Mar 1998 04:00:04 +0100, Harvey Friedman wrote:

: Incidentally, "the original chess position is a draw" is not a "plausible
: conjecture".
|
| Not **plausible**? Why not? I do understand why it is not "obvious."

I did not intend

Incidentally, "the original chess position is a draw" is
not a plausible conjecture

but

Incidentally, "the original chess position is a draw" is
not a "plausible conjecture".

I have already explained what I meant by PLAUSIBLE CONJECTURE in the
chess scenery.

Julio GonZaleZ Cabillon

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