In message , jefk
writes
Sanny wrote:
In Chess after every move new 30-40 moves are generated.
well Sanny, that might be correct, but many of these moves are tactical
mistakes, or give away material immediately. and with perfect play
the game in such a case is subsequently lost (excluding some deep
combinations, but these are recognized in 99.99999 % of the
cases by an engine as Rybka imho);
Actually Rybka is fantastically strong at beating other engines, but
deprived of its opening book I would not trust it navigate the
intricacies of some openings without guidance from a human. Shredder and
HIARCS seem to do better in this respect in the opening without a book.
so in reality/practice, there are about 3-12 moves possible
for each side, in sharp play sometimes there's only one
correct move, in positional play/endgames there might
even be sometimes more moves possible than 12;
in any case its much less than the 3-40 you mention
Even if we are very optimistic and allow for a 2x branching factor for
each successive ply the best engines on consumer hardware can still only
reach 24ply in a few days or 30ply in 1 year. Starting from the initial
position that is not even out of the stronger databases for opening
books.
So just in 10 depth we reached 590 Trillion Moves.
well it's less, see above, but it's not a smart way of generating
a database; if you generate a positional database (thats the
way modern opening books are made), because of
the many *transpositions*, the number of positions will
be mcu& *much* less.
In fact, if we exclude tactical mistakes, i believe it would
be possible to generate a database at 25 ply (12.5 moves)
deep with all possible correct/non losing moves.
The trouble is here that you cannot be certain that the perfect winning
line for white doesn't look at some stage like being a pawn down with no
prospect of compensation until the actual mating trap.
Who is to say that the perfect forced winning line for white does start
with something completely absurd like: 1. h3
Only when we have a full depth search result can we be sure.
Say Each Move Generation needs 1000 Calculations.
all this calculations can be done offline, and on other computers,
or by GM's; by loading in slow GM games from history i
already have used lots of knowledge/ human calcuation power..
\
And when using computers/engines, you forget a very important
element in speeding up the calculation, namely the socalled
*alfa/beta* algorithm. from what i vaguely remember
this speeds up the calculation process -to find the right move-
with about 50 times.
Roughly as square root of the number of terminal nodes if the tree was
perfectly ordered and somewhat more effort if not. Then razoring (which
is iffy for formal proof) and killer move heuristics get another order
of magnitude.
Not everybody seems to be aware of such methods, eg.
GM Kasparov in his book 'why chess looks like life',
claims that there are more positions in chess than
atoms in the univers. humbug, but Gary isn't an
astrophysicist, you know; he's a politician.. 
But that is correct. There are.
So to evaluate all moves upto 15 depth even on Fastest Supercomputer
that works at speed of Petaflop will take 5 Months.
i've been busy with computerchess about 15 years, and gradually
have been building up my database; while its'not perfect, i'm
certain that at least until about ply 25 no advantage for white
can be made, wheter you play Italian, 1.d4, or whatever.
In a later stage i thought that a minimal advantage with
the Ruy Lopez could be achieved, but with extensive
analysis with Rybka i've found some novelties and
now am convinced that black also can maintain a draw.
Rybka tends to have a very flat evaluation of the initial opening phase
of the game. Shredder and HIARCS tend to see more of the structure
albeit in a slightly exaggerated way.
To Solve Chess we need to search till atleast 100 depth. That will
take even more than Billions of Billions of Billions of years
we don't have to fully analyze the game i think.
for every winning plan for white, i believe there
exists a proper defence system for black.
(there exist of course some simple games
where all possibilities *can* be calculated , and
it's proven with 100 % certainty they are a draw,
but indeed such a method does'nt seem
possible for chess, at least for some millennia)
The number of positions that needs to be considered is still far beyond
anything that a conventional computer can do now or in the future. If
someone gets a quantum computer to run a chess program all bets are off,
but until that day the best we can say is that it might be a draw.
example, although i'm not an expert in the
game of draughts (or checkers), from what i've
vaguely read/seen in some articles, the scientific/
computer games community seems to be
convinced these games are a draw, even although
they haven't fully calculated all possibilities;
I think you will find they have a formal proof for draughts/checkers
now.
http://chinook.cs.ualberta.ca/users/chinook/index.html
well, i now am convinced the same hold for chess..
It is plausible, but it could equally be a first player win.
but if you disagree, well, than i challenge you just
like Ray Johnston -or others- to show me
a winning line for white; and then i guarantee
that i will find improvement(s) for black
which ensure the draw. Good luck..
Cataloguing the opening tree within 50cp of equality might make an
interesting net distributed computational project.
Regards,
--
Martin Brown
--
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