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I am a student of physics. I have learnt some basic group theory, and I am wondering if there is any ideal solution for a given Chess game (like solving Rubik's cube). I know the no. of permutations are enormous that computation becomes almost impossible to do such a thing. But I am interested in knowing if there is any Group theory based solution being researched and developed.

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    $\begingroup$ I don't think group theory is very applicable because not all of the moves in chess are invertible like they are for a Rubik's cube. $\endgroup$
    – Dan Rust
    Feb 12, 2014 at 1:41
  • $\begingroup$ No clue what a group theory solution is but Chess is solvable by Zermelo's algorithm. Too bad we will never have computational power to apply it and know what is the solution... $\endgroup$ Feb 12, 2014 at 1:42
  • $\begingroup$ Oh, I didn't see that through ! Thanks !! $\endgroup$
    – user35952
    Feb 12, 2014 at 1:43
  • $\begingroup$ You may want to read Christian Ewerhart's articles (2000 and 2002) on Games and Economic Behavior, both articles are on the game of chess. $\endgroup$ Feb 12, 2014 at 1:47
  • $\begingroup$ As pointed out, chess will never be solved mathematically. However, by incorporating intelligent positional evaluation, opening books and endgame tablebases, modern day engines would be able to crush deep blue and older supercomputers even though they have much less processing power. $\endgroup$ Feb 12, 2014 at 1:53

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For games like checkers, yes this has been solved using computers - you can guarantee at least a tie; however, for chess, there are far too many moves to be solved at this point in time because the number of strategies that must be calculated go up exponentially. It IS possible to solve it using game theory, but it is far too complicated to be done with current technology levels.

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  • $\begingroup$ "with current technology levels." or future as well... $\endgroup$ Feb 12, 2014 at 1:44
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    $\begingroup$ @SergioParreiras Can you recommend a source? Exponential technological growth as well as emerging technologies (quantum, organic computers for example) seems to guarantee that power will come $\endgroup$
    – David P
    Feb 12, 2014 at 2:09
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    $\begingroup$ While this answer is factually correct, I do not think it really satisfies the condition that the OP has put in the question, which are the particular applications of group theory to the potential solution of chess. $\endgroup$
    – Dan Rust
    Feb 12, 2014 at 2:14
  • $\begingroup$ @DavidPeterson: maybe with new algorithms but if we use force brute (i.e. Zermelo's algorithm), the Handbook of Game Theory (vol I, I think) has a chapter on Chess where they say the game tree of chess has an order or magnitude higher than the number of electrons in the universe (I don't know much physics so I have no clue how can we estimate the later). If this is true, we will never have enough memory to input the game tree (all possible moves). Sorry for the long comment... $\endgroup$ Feb 12, 2014 at 2:15
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    $\begingroup$ @SergioParreiras because I don't think it constitutes an answer. It's possible that someone working in the crossover of algebra and game theory could offer a definitive answer which I can not. It's only an uninformed hunch that group theory might not be very applicable, at least not in the same way that it informs us of the solutions of the Rubik's cube. $\endgroup$
    – Dan Rust
    Feb 12, 2014 at 2:20

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