[Retros] Dead position with eternally moving Queen YefimT 08/26/2004

[TregerYefim at aol.com]

             Hello, Michael and everybody! Yefim.
I received, Michael, your last letter with suggestions about math model of 
chess. I am categorically and ironically (:  :) against them. Part 1 of my 
letter is dedicated to general question what is math model in science or in some 
activity; Part 2 specifically criticizes your suggestions. And do not worry, I 
will be short. 
     Part 1. 
 Definition of Math model (encyclopedia): It is any set of formulae, 
equations, axioms, etc, that describe (even approximately, but essentially) the 
behavior of any system in purely math terms. 
     My system satisfies to this definition. Your system (or system and 
suggestions of somebody) satisfies too, if it deals with pure math terms…
    Part 2.
        You wrote:
I think a node of your tree should contain all the information in FEN 
without the move number, but also the following:
1) all positions since the last pawn advance or capture
2) the state of the game: 0 for "no draw offer, not finished", 1 for 
   "White offered draw", 2 for "Black offered draw", 3 for "Black 
    resigned", 4 for "White resigned", 5 for "draw agreed", 6 for 
    "stalemate", 7 for "mate", 8 for "draw claimed", 9 for "Black 
    lost on time", 10 for "White lost on time"
   (I hope that's all...)
           My critical notes:
a)  The first implies 50-moves rule?  The last one does not concern position 
itself, it concerns a game as a sequence of them and corresponds to the 
definite path in a graph when the distance between some different type positions is 
at least 100 edges (even for a game it does not mean Draw look below).  
b) Your list in principle cannot be complete because it implies mostly human 
behavior (which is very complicated) and is expressed not in pure math terms.
 b1). About  0 for no draw offer. 1 for White offer 2. Black offer Draw.
What next? 1a- White offered Draw and Black refused 1b- White offered Draw 
the second time and Black refused by complaining  to the director (there is a 
rule about it for annoying:); 1c-White offered Draw the third time and got the 
warning due to the unsporting behavior …1z White offered Draw (or claim draw in 
your  example K against K+N+B) several times) and got sanctions including 
loosing a game :(.
Or: 2a1 Black offered Draw incorrectly, not in his move (Fide rule), White 
told him to make a move -> 2a2 offering a draw after a move (this affects at 
least two positions). 2z:  Black after White's reply is saying "If I make a move 
I will not agree to a draw" and White, not knowing what to do, agreed for a 
draw (yes, you know  a special rule about that saying that the offer is still in 
effect, but, as I said it affects all next positions which are upon your 
model will be different in comparison with simple draw offer for them…) Or 5z: 
draw agreed due to misunderstanding (remember history about Keres and soviet 
chess grossmasters: they agreed because of KGB had ordered to do so; so now 
5corruption: will mean  "A game of 195n year agreed to a draw after 3 moves…due to 
official order :)" 
B2). Lost on time? What about in mate position? Mate is superior but player 
did not understand that (I saw this situation myself!) and admitted his lost :( 
Or how about 9z10 "math" term: Both flags are down after White exclaimed it 
first allegedly noticed of opposite flag falling. Then came director (judge, 
referee, arbiter  - I am speaking for all your countries,  knowing  that 
director in USA is called arbiter in Russia …) and decided:
9z10a1 draw; 9z10a2- White won; 9z10az White won and Black appealed to some 
officials and again Draw…;) 
c) Mate and stalemate positions are given in your list correctly, but they as 
usual position are present in my tree. They mathematically  reflect the 
following fact: they are nodes in a graph that is: no more positions from them (set 
of all direct moves is empty). In this aspects there some facts in my theory 
but about it next time, let me finish with your letter.
d) your "possible action" (resigning, accepting and/or claiming a draw) 
cannot be understood as characteristics of position, they are characteristics of a 
game. 50-moves rule 3-repetition are also elements of a game (by the way, in 
Fide rules those rules do not mean automatically draw, if both players want to 
play they will and with time delay clock their play may be infinite :(: (  or 

:) ) 

   Here is my 7 example for you to criticize me. I have constructed dead 
position with eternally moving Queen and Rook. 
FEN:
   7k/b1p3pP/1pP3P1/1p6/BP6/QP1p4/1P1P4/RKB5 w 0 - - 1
White: Kb1, Qa3, Ra1, Ba4, Bc1 pp:b2,b3,b4,b5,c6,d2,g6,h7
Black: Kh8. Ba7 pp:b6,c7,d3,g7 White to move but this position will never end 
by mate or stalemate by any moves.
    I was trying to construct a position with at least one eternally moving 
Knight possessing this property (no both draw rules) and I…Interested?
  Yefim 08/26/2004
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