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>"Machines reaching a level of play that is consistently better than humans" and "the game is solved" are two completely different statements and it isn't parti

>"Machines reaching a level of play that is consistently better than humans" and "the game is solved" are two completely different statements and it isn't particularly useful to conflate them. Very good point >We will likely never be able to solve Go in the formal sense. I'm not sure if it would be precise to say chess will be solved either. The number of outcomes in a 50-move chess game approaches Graham's Number--a number larger than the number of atoms in the observable universe. In a 100-move game, the number would be many orders of magnitude than an already incomprehensibly large number. So chess also will probably in a precise definition of the word, also never be solved. Edit: It's kind of mind boggling to think about every atom in the universe representing one position in a game of chess and there not being enough atoms in the universe to represent each one.

laxd 10y ago
> It's kind of mind boggling to think about every atom in the universe representing one position in a game of chess and there not being enough atoms in the universe to represent each one. Chess players mentions this a lot. And then they consider chess a sport. For a sport, it shure is a mind boggingly low number of game states :) (ps: I don't mean to start an uninteresting sport-or-not debate. It is what it is.)
RexetBlell 10y ago
The number of outcomes in a 50-move chess game does not even come close to the Graham's Number. 10^(number of outcomes in a 50-move chess games) also does not come close.
- prezjordan 10y ago
  Even 10^10^10... (repeat this the number of outcomes in a 50-move chess game) does not come close to Graham's number.
  - wallace_f 10y ago
    Thanks, I was wrong about that. I swore I read that somewhere, turns out it was on a chess forum--not a source I should have committed to long-term memory. I did find this interesting statement about Graham's number (unsure of the veracity): > Graham's number is greater than all of the Planck lengths in the universe. There literally isn't room in the universe to write it out in numerical form. Edit: It looks like we confused Graham's Number for Shannon's number: https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number But according to the Wiki on Shannon's number, a the number of possible outcomes in chess does still far exceed the number of atoms in the universe: >Allis also estimated the game-tree complexity to be at least 10123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable universe, to which it is often compared, is estimated to be between 4×10^79 and 4×10^81.
    - CJefferson 10y ago
      This is a bad kind of argument. There are more 16x16 sudoku boards, and ways of dealing a deck of cards, than there are atoms in the Universe too, but Sudoku and many card games are easy for computers to solve.
      - wallace_f 10y ago
        Well, you should volunteer on the Stockfish engine and show everyone how it's done. I don't believe your comparison between fundamentally different games is sufficient to support your conclusion that an extremely large number of calculations does not pose a challenge for computer programs to solve. Rather, to the best of my knowledge, to support your conclusion what you would need to do is to prove there exists a method or formula for reducing the number of permutations to a manageable number while still coming to an optimal solution. Apparently if Sudoku is easy to solve, that exists in Sudoku, but it certainly does not yet exist in the realm of human knowledge in chess. The fact is that Sudoku and many card games are easy to solve, while chess is in fact a much, much more challenging problem for a computer program, and there are a lot of very smart people that have worked on that problem.

laxd 10y ago

> It's kind of mind boggling to think about every atom in the universe representing one position in a game of chess and there not being enough atoms in the universe to represent each one. Chess players mentions this a lot. And then they consider chess a sport. For a sport, it shure is a mind boggingly low number of game states :) (ps: I don't mean to start an uninteresting sport-or-not debate. It is what it is.)

RexetBlell 10y ago

The number of outcomes in a 50-move chess game does not even come close to the Graham's Number. 10^(number of outcomes in a 50-move chess games) also does not come close.

prezjordan 10y ago
Even 10^10^10... (repeat this the number of outcomes in a 50-move chess game) does not come close to Graham's number.
- wallace_f 10y ago
  Thanks, I was wrong about that. I swore I read that somewhere, turns out it was on a chess forum--not a source I should have committed to long-term memory. I did find this interesting statement about Graham's number (unsure of the veracity): > Graham's number is greater than all of the Planck lengths in the universe. There literally isn't room in the universe to write it out in numerical form. Edit: It looks like we confused Graham's Number for Shannon's number: https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number But according to the Wiki on Shannon's number, a the number of possible outcomes in chess does still far exceed the number of atoms in the universe: >Allis also estimated the game-tree complexity to be at least 10123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable universe, to which it is often compared, is estimated to be between 4×10^79 and 4×10^81.
  - CJefferson 10y ago
    This is a bad kind of argument. There are more 16x16 sudoku boards, and ways of dealing a deck of cards, than there are atoms in the Universe too, but Sudoku and many card games are easy for computers to solve.
    - wallace_f 10y ago
      Well, you should volunteer on the Stockfish engine and show everyone how it's done. I don't believe your comparison between fundamentally different games is sufficient to support your conclusion that an extremely large number of calculations does not pose a challenge for computer programs to solve. Rather, to the best of my knowledge, to support your conclusion what you would need to do is to prove there exists a method or formula for reducing the number of permutations to a manageable number while still coming to an optimal solution. Apparently if Sudoku is easy to solve, that exists in Sudoku, but it certainly does not yet exist in the realm of human knowledge in chess. The fact is that Sudoku and many card games are easy to solve, while chess is in fact a much, much more challenging problem for a computer program, and there are a lot of very smart people that have worked on that problem.