Oh, I made a mistake. Total length of typical game is very long in go, because Tessa has one programmed rule as an exeption to randomness. That is, she does not fill her own eyes. Without this limitation, typical go game length is practically unlimited. On Dec 14, 2011 7:45 AM, "Jouni Valkonen" <[email protected]> wrote:
> Most of the random go games are around 500 moves long. As there are on > average 10-360 possibilities for branching, there we can easily calculate > total number of games. If we know the math. Note that longer than 500 move > games are rare and they can be ignored. > > My Tessa will give you fair statistical sample of the most common games. > http://valkonen.kapsi.fi/tessa.php?board=19 > > From this data it is possible to calculate total number of games. I > already tried it, but it overflew my calculator. > > I think that it is something in order of 500^100 — 500^300. But anyway it > is very possible and simple to calculate if you are fluent with large > numbers, where exponent is a function (I am not). > > Note that that this method cannot be applied to chess because random games > do not end there, because there are illogical expections in the chess > rules: I.e. letting king to be captured is illegal, without obvious reason. > > Chess rules should contain as an objective to capture opponent king. Then > it would be possible to run simulation how long are typical chess games. > That is, how long on average it takes that king is captured. This would > give the total length of typical game and thus total depth of the game. But > even then, chess is too complex came to calculate the complexity of the > game. > > But statistical method is applicable to go very well, because go rules are > logical and simple. > > This method can be applied also for smaller boards. However Tessa won't > solve 3×3 board complexity accurately, because there are no super kou rule > and anyway it cannot handle an ending kou very well, but makes mistakes. > > —Jouni > On Dec 14, 2011 5:34 AM, "Peter Drake" <[email protected]> wrote: > >> Thanks -- and apologies for missing the Wikipedia page myself. >> >> I ran into this in discussing a claim that "the number of digits in the >> number of 19x19 Go games is larger than the number of chess games", which >> did not sound credible to me. I realize that Go is many orders of magnitude >> larger than Chess, but surely not THAT much. >> >> Peter Drake >> http://www.lclark.edu/~drake/ >> >> >> >> On Dec 13, 2011, at 5:35 PM, Jeff Nowakowski wrote: >> >> On 12/13/2011 07:57 PM, Peter Drake wrote: >>> >>>> An exercise for the combinators and combinatrices out there: >>>> >>>> How many different 2x2 Go games are there? >>>> >>>> An unnamed source claims 386,356,909,593, but I don't find this >>>> credible. >>>> >>> >>> I found a source for this via Wikipedia: >>> http://en.wikipedia.org/wiki/**Go_and_mathematics<http://en.wikipedia.org/wiki/Go_and_mathematics> >>> >>> Which refers to a 1999 article from rec.games.go by John Tromp: >>> http://groups.google.com/**group/rec.games.go/browse_**thread/thread/** >>> 161ff6e5922e1124/**c90e5b4a61ea0602?lnk=st<http://groups.google.com/group/rec.games.go/browse_thread/thread/161ff6e5922e1124/c90e5b4a61ea0602?lnk=st> >>> >>> >>> A game therefore involves at most 56 >>>> non-passing moves (as one more would violate superko). >>>> >>> >>> Now consider how many permutations you get by re-arranging the moves. On >>> Tromp's solving 2x2 page he links to a program and says: >>> >>> "This program solves the game of Go played on a 2x2 board using area >>> rules and positional superko. It demonstrates the enormous importance of >>> good move ordering in exhaustive alpha beta search. With the given ordering >>> of passing last, as many as 19397529 nodes are searched, up to a depth of >>> 58. But putting passes first requires the search of only 1446 nodes, to a >>> depth of no more than 22. Minimax, which doesn't depend on move ordering, >>> takes over a week while searching a few trillion nodes." >>> >>> http://homepages.cwi.nl/~**tromp/java/go/twoxtwo.html<http://homepages.cwi.nl/~tromp/java/go/twoxtwo.html> >>> >>> ______________________________**_________________ >>> Computer-go mailing list >>> [email protected] >>> http://dvandva.org/cgi-bin/**mailman/listinfo/computer-go<http://dvandva.org/cgi-bin/mailman/listinfo/computer-go> >>> >> >> ______________________________**_________________ >> Computer-go mailing list >> [email protected] >> http://dvandva.org/cgi-bin/**mailman/listinfo/computer-go<http://dvandva.org/cgi-bin/mailman/listinfo/computer-go> >> >
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