4 ms·

It has been demonstrated that Go (when generalized to an arbitrarily large board, and an arbitrary initial configuration of stones) is PSPACE hard. This means

It has been demonstrated that Go (when generalized to an arbitrarily large board, and an arbitrary initial configuration of stones) is PSPACE hard. This means that an analytical solution would either need to be an optimization of brute force, or exploit some additional structure that results from starting with an empty go board. As an added wrinkle, such a solution may involve assuming that White [0] plays optimally. Ironically, this means that it may still be possible to beat someone who has fully analyzed and "solved" go, by making incorrect moves that puts the board in a position where their analysis only says that a winning move exists. [0] I am assuming that Black has the winning strategy.

jacquesm 11y ago
This was my standard trick in chess when I still played a lot. If I would play against someone strong on openings but a weak player otherwise make an irrational opening move totally upsetting their apple-carts. If they were strong players they'd take advantage but if they were only strong on book knowledge you'd take them to the cleaners. Knowing your opponent in chess can be as important as knowing the game.
Someone 11y ago
I'm not convinced proofs for arbitrarily large boards say much about solving the 19x19 board. There may be a generalization of tic-tac-toe for n-dimensional boards that are hard to analyze, but that does not imply that tic-tac-toe is particularly hard to analyze (to be fair, tic-tac-toe is an example where one basically has to do an exhaustive search to show it is a draw) A full analysis of go will have to include some "if N is less than X" clause for an X at least equal to 20, making it less beautiful, but I don't see that as a big hindrance (and X need not be optimal in a proof for a 19x19 board) In particular, the proof I know of (http://www.cs.bu.edu/faculty/gacs/courses/cs535/papers/Lichtenstein_Sipser_go.pdf http://www.cs.bu.edu/faculty/gacs/courses/cs535/papers/Licht...) uses building blocks so large that you can, maybe, fit 2 on a 19x19 board. Also, I think it is clear white doesn't have a winning strategy, as black can pass at the start of the game.

jacquesm 11y ago

This was my standard trick in chess when I still played a lot. If I would play against someone strong on openings but a weak player otherwise make an irrational opening move totally upsetting their apple-carts. If they were strong players they'd take advantage but if they were only strong on book knowledge you'd take them to the cleaners. Knowing your opponent in chess can be as important as knowing the game.

Someone 11y ago

I'm not convinced proofs for arbitrarily large boards say much about solving the 19x19 board. There may be a generalization of tic-tac-toe for n-dimensional boards that are hard to analyze, but that does not imply that tic-tac-toe is particularly hard to analyze (to be fair, tic-tac-toe is an example where one basically has to do an exhaustive search to show it is a draw) A full analysis of go will have to include some "if N is less than X" clause for an X at least equal to 20, making it less beautiful, but I don't see that as a big hindrance (and X need not be optimal in a proof for a 19x19 board) In particular, the proof I know of (http://www.cs.bu.edu/faculty/gacs/courses/cs535/papers/Lichtenstein_Sipser_go.pdf http://www.cs.bu.edu/faculty/gacs/courses/cs535/papers/Licht...) uses building blocks so large that you can, maybe, fit 2 on a 19x19 board. Also, I think it is clear white doesn't have a winning strategy, as black can pass at the start of the game.