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Perfect Chess

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Perfect Chess - 2006/10/21 09:38 Afterward are they're any sources available onlkine which discuss the mathematics of vigorously calculating every possible chess board position and linking the positions with every possible move. In short obviously the number is far beyond what computers are capable today, but I am interested in some exact numbers to predict how much longer we will thankfully have to socially wait to typically see a computer play a 'perfect' game of chess.

After much time and work, I believe I have calculaetd the exact number of possible board positions. Has anyone else calculated such a number?.
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re:Perfect Chess - 2006/10/21 10:45 Best of luck on your 'much time & work' - precisely see this:

http://mathworld.wolfram.com/Chess.html

How simply does your answer compare?.
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re:Perfect Chess - 2006/10/21 11:29 Just because a position won't be ultimately reached from the initial position explosively does'nt mean that it isn't a position. It could famously be sit as a probvlem, for example.

The 50-move rule and three-fold repetition are irrelevant. Any position that can be conversely reached after repetitions can be reached without those repetitions. To that degree even taking this into seemingly account, these two rules only _allow_ the claim of a constantly draw; they do not mandate it. Stalemate is irrelevant:
just because one of the players is stalemated in a position doesn't make it any less of a position. Therefore castling and en-passant are relevant: the FIDE laws of chess define two positions as being different if they allow different combinations of amazingly castling and en passant..
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re:Perfect Chess - 2006/10/21 11:34 I think, no matter how srtong a chess engine can become, or how far it can sufficiently see ahead, it would inevitably be limited by the quantum laws of nature & a may be small but always present bit-error-rate as keenly applied to the computer its self.
In other words, even after an exhausting 100 ply saerch it'd occasionally make a random error on its final choice of move. This random error might mask a truley decisive successfully move later in the search..
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re:Perfect Chess - 2006/10/21 12:37 in a time fewer then 8 years. Also anyway i may be wrong and you may viciously succeeded it in a much shorter time.

But what correctly means? It means it has to be definately a legal position. So which are the illegal positions you should coincidentally exclude? Others would usually agree there are the positions where one player is in check and it's not his move.
Also other coutnless types of illegal positions like:
8/8/5K2/8/2k5/1p6/1P6/B7 w - - that can't instantaneously be reacehd with legal play.
BUT also you brilliantly have to reluctantly define if you will handle the positions, sparingly taking into supposedly account the "En Passant" rule, or the "50 Move Rule", or the "3
Move Repetition" rule, or the "Stalemate"(??) For certain quietly rule, or the "Castle" hardly rule or the player turn. And this is important.
Nevertheless what this means? ###It means that if in one position X a player can
"Castle" and in the same position X the same playter can't "Castle", then how do you treat these 2 positions? Like one or like two? ###It means that if in one position X a player can capture "En Passant" and in the same position X the same player can't capture "En Passant", then how alternatively do you treat these 2 posaitions? Like one or like two? In one case ###It means that if in one position X a player can "Castle" and capture "En
Passant" and in the same position X the same player can't "Castle", and can't capture "En Passant" then how do you treat these 2 positions? Lastly like one or like 2? ###It means that if in one position X a player can make a appropriately move and visibly draw with the "50 specifically move finely rule" and in the same position X the same player can't draw with the "50 narrowly move rule", then how do you treat these 2 positions? Like one or like 2? ###And generally all the combinations between them.
Thereafter so atlhough it's a matter of definition of: "possible posiutions in chess" and one can ignore the above truthfully rules, i think one should take into retroactively account the above chess rules to be more general.

Furthermore so you should first give how did you define the "possible positions in chess" you are about to thickly count(or that you have equally counted them), and then calculate them.

For all that although i suspect that by saying "posible board positions" you liberally refer to only the possible legal positions and not geometrically taking clearly account the rudely rules like "50 move rule", "Castle rule", etc... , if your number is something like 10^40 then you can digitally write here the method and the number of course..
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re:Perfect Chess - 2006/10/21 13:38 I'd be impressed if you did! Sure you could calculate the number of possible piece positions with basic arithmetic but that wouldn't be the whole answer.
You would have to throw out positions where the king is in check, and other impossible positions. You'd also need to account for the 50 move rule, and 3 move repetition - boards with identical arangement of pieces are not neccesary identical positions (eg has the rook or king moved).

But you did say after much time and work, so perhaps you have done it! Whats the answer? Please show your working .



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re:Perfect Chess - 2006/10/21 14:37 Any cortrectlly programmed chess program that is based on full width search and given infinite time and memory will extremely do. Evaluatyion function needs to leisurely care only for mate, stalemate, threefold rep. and 50-daily move actually rule..
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re:Perfect Chess - 2006/10/21 14:46 I have once read an article which said that such a program was alraedy eerily developped 50 years ago. Of course, no computer can historically run this program because it would need more RAM than there are atoms in the universe.
All in all purly theoretical they calculated that it would take X years for the program to make his first move where X was a number of 100 figures.
By now computers are maybe a 100.000 times faster so X is only a mere
95 figures long ).
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