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Subject: S.Chinchalkar's estimate ...

Author: GuyHaworth

Date: 08:28:31 01/08/03

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The ICGA website 'ICGA_W' at www.icga.org is gradually increasing the
representation of the ICCA/ICGA_Journal's content, obviously working backwards
in time.

Abstracts are being included where they exist.  There is no abstract for SC's
'Note' on the upper bound for chess positions.


SC considers positions different in the same sense as FIDE Rule 9.2, i.e. if
they have a different set of moves, notationally.

He allows in his count positions that would arise from a left-right (a-h) switch
of the initial position and/or from a 'White-or-Black to move first' rule.

However, with these liberalisations, one may focus on the set of positions that
are functionally different.  One may assume that it is wtm and the WKing is on
files a-d.

This immediately divides SC's upper bound by 4.


However, I believe that SC must have missed chess-specific observations that
would have more radically lowered his upper bound, while still counting the
number of 'functionally distinct' positions that are not self-evidently illegal.

The ICCA_Journal Editor added a reference to:
Bonsdorff, Fabel and Riihimaa (1978) Schach und Zahl, 3rd Edition, p10 where
work by N.Petrovic is cited, giving an upper bound of 2*10^43.
Maybe someone can reproduce that argument here.

I.J.Good and Shannon did computations in the very early days, and these are in
the volumes of MTAC somewhere I think.


Given the further data of Nalimov on 3-5-man position-counts (upper bounds), it
is now possible to further reduce the calculated upper bound on the number of
'functionally distinct' chess positions.


VD has perhaps not enjoyed:
http://www.xs4all.nl/~timkr/records/records.htm#Most%20queens
where Tim Krabbe cites one of his own games as a 'spoof' but cites two 5Q games
as genuine.


g



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