Smyslov_Fan wrote on 08/23/07 at 00:12:56:


I simply enjoy every mathematical problem. You are right, for practical chess this thread is completely irrelevant. So is the question if we should play 3.Nc3 against the Slav or maybe 3.Nf3 for the subject of exponential functions. You can be sure about the proposition, but for a mathematician that is not enough.
Not seeing the point of a mathematical discussion is about the same as not seeing the point of chess analysis. How does analyzing 1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 Bf5 enrich your enjoyment?
This is a serious answer; Udav's question in fact is about an exponential function. There is a strong trend, stating that the value of mathematics solely depends on its relevance for society and/or other sciences. I clearly am no part of it. Mathematics does not have to have any use imo.
But there is a strong argument to transfer this thread to Chit chat.

thibdb13 wrote on 08/21/07 at 09:00:00:

Where will you find the material (after all consisting of atoms) needed to build these computers? In a neighbouring universe?
Being a teacher in physics I am familiar with the theory described by Udav above. The problem here is, that mankind will not be able to solve chess before the contraction has ended or survive it. Neither is it possible to transfer information to the successing universe. The "new" mankind will have to start over again completely.
So from a practical point of view I maintain that chess is insolvable. It does not matter if we work forward from the initial position or backward with endgame tablebases; the path never will be closed.
I am not sure about MartinC's proposal though. I suppose from at least the 10th or 15th move we should investigate all Black's moves again.

Udav18 wrote on 08/20/07 at 15:07:48:


It appears to me that since the number of chess positions is finite, definitely it is subject to solution.  For the present doing that is certainly impractical, but who knows about the future?

Also, while I disagree with Fischer that chess even now is so "played out" that it isn't worth playing, this will probably come to pass.   

Still, why should it bother me that I am playing a doomed game?  Nothing is eternal, not even this universe, which appears to be gradually expanding and destined to burn out.

Udav18,

Are you familiar with the Nalimov endgame tables? I believe that to "solve" chess, you'd have to work from finishing positions (mate or stalemate) backwards, not from the initial position forward. The endgame tables are now at 6 piece endings, including the two kings. There are only three levels of evaluation. +-, = or -+. Simple really! 

The size of the problem really does mean there is no chance to ever create a 'theoretical answer' without hijacking another universe to perform the calculation in or something!

However if you're prepared to accept that the initial position can't be a black win, and that if it's a white win it will be through some main line theory (say one of e4,d4,Nf3 then popular stuff) then all you need to do is demonstrate one way for black to draw. This kind of solution is of course massively less demanding to produce than generalised perfect play! 
(esp if you choose ultra solid black lines. Say Slav and Petroff and just follow Kramnik's games as much as possible for black.).

Of course it's still a mind bogglingly large calculation and may well still be simply too hard to ever happen. But just maybe....

Quote:


Theoretically yes, practically not yet

Willempie wrote on 08/20/07 at 15:19:43:





Ok there is a limited number of positions,but to get to every position there are again nearly unlimited numers of posiibilities!? So to get to every of this 10^50 position,you have again 10^(10^100000000000000000000000000000000000000000000000000000) posibilities maybe even more.But my logical thinking says also that there must be a limit there,if there is a limit of moves in the games and there must be a limit of the moves,because there are 32 peaces on the board and so the limit of moves must be 30*50 ,or?
Because there is the 50-moves-rule,which says that ,if there was no capture after 50 moves,then the game is drawn(The Kings cant be captured ,so 30).
so a game can only last 1500 moves.So lets say every new move M the number N of possibilities rises in about this way  N=10^(10*1000000000000000000000)*M with  M<=1500 and >=1

This formula is of course wrong,because I invented all the numbers ,without any thinking about them,but its structure is realistic and showes that there must be a limit,because the moves are limited,too. 
Is this logical or rubbish?

Udav18 wrote on 08/20/07 at 15:07:48:

I am very bad with big numbers. But yes the possibilities are limited but huge. If you just look at the tablebases for piece endings and their size, you'll get an idea of how many possible positions there are. Iirc the total possible positions is something like 10^50

In theorie you can solve it by taking all "mate"-positions and work backwards. In practice that is not possible with chess as you would need a rather big (as in impossible for now) computer to use an understatement. So most computer programs work forward (they think about the next move iso the last possible moves) and use an evaluation mechanism to filter out stupid moves. Without that mechanism the newest Fritz and Rybka combined playing on the newest machines would lose to an average club player.