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Complexity of Go
Keywords: Theory
HarryWang OK, I cannot help it to notice there are no page in sensei here to discuss the mathematical nature of GO.
I copied this following part from personally, I know that a un-pruned GO game tree is 361! = xxx × 10 ^ 71. Most GO games seems to end with less than 300 moves. so I guess the average GO game tree is 300! But how to prune the GA grame tree. I am facinated to know from wiki: "It is commonly said that no game has ever been played twice. This may be true: On a 19×19 board, there are about 3^361×0.012 = 2.1×10^170 possible positions, most of which are the end result of about (120!)^2 = 4.5×10^397 different (no-capture) games, for a total of about 9.3×10^567 games. Allowing captures gives as many as 10^(7.49×10^48) possible games, most of which last for over 1.6×10^49 moves! (By contrast, the number of legal positions in chess is estimated to be between 10^43 and 10^50, and physicists estimate that there are not more than 10^90 protons in the entire universe.)" unkx80: Since the page title is also a common term in computer science, I shall also mention something about the computational power required for perfect computer Go players. The game of Go on a general n by n board is a computationally difficult problem. It is known to be an EXPTIME-complete[1] problem, which means that it is very computationally expensive for a computer to solve any position perfectly. In fact, Go endgames is already known to be PSPACE-hard. The implication is that there is are some go problems which are completely infeasible for computer Go programs to solve perfectly, particularly by using brute force searching.[2] Hence, programs for Go have to rely on heuristics, which gives imperfect answers to problems. Even on the normal 19 by 19 board, which has 361 points, current computer Go players are still very weak compared to current computer chess (both Chinese and International) players. While International chess programs like X3D Fritz can draw with grandmasters like Garry Kasparov, current Go programs are probably not even amateur Dan strength. References: [1] It is EXPTIME-complete under the simple ko rule. Deciding if a ladder works is PSPACE-hard. -- Rafael Caetano [2] Rafael: Those complexity classes are about worst-case complexity. The complexity of the general problem is as high as the complexity of its worse specific instance. For example, the kind of ladder problems which require lots of time and space to solve are highly artificial, and probably a tiny fraction of all possible ladder problems. Still they are ladder problems, so the complexity of the general ladder problem is said to require lots of time and space. See also: This is a copy of the living page "Complexity of Go" at Sensei's Library. ![]() |