It's trivial, dude. On Aug 9, 2017 8:35 AM, "Marc Landgraf" <mahrgel...@gmail.com> wrote:
> Under which ruleset is the 3^(n*n) a trivial upper bound for the number of > legal positions? > I'm sure there are rulesets, under which this bonds holds, but I doubt > that this can be considered trivial. > > Under the in computer go more common rulesets this upper bound is simply > wrong. Unless we talk about simply the visual aspect, but then this has > absolutely nothing to do with the discussion abour solving games. > > 2017-08-09 14:34 GMT+02:00 Gunnar Farnebäck <gun...@lysator.liu.se>: > >> Except 361! (~10^768) couldn't plausibly be an estimate of the number of >> legal positions, since ignoring the rules in that case gives the trivial >> upper bound of 3^361 (~10^172). >> >> More likely it is a very, very bad attempt at estimating the number of >> games. Even with the extremely unsharp bound given in >> https://tromp.github.io/go/gostate.pdf >> >> 10^(10^48) < number of games < 10^(10^171) >> >> the 361! estimate comes nowhere close to that interval. >> >> /Gunnar >> >> On 08/07/2017 04:14 AM, David Doshay wrote: >> >>> Yes, that zeroth order number (the one you get to without any thinking >>> about how the game’s rules affect the calculation) is outdated since early >>> last year when this result gave us the exact number of legal board >>> positions: >>> >>> https://tromp.github.io/go/legal.html >>> >>> So, a complete game tree for 19x19 Go would contain about 2.08 * 10^170 >>> unique nodes (see the paper for all 171 digits) but some number of >>> duplicates of those nodes for the different paths to each legal position. >>> >>> In an unfortunate bit of timing, it seems that many people missed this >>> result because of the Alpha Go news. >>> >>> Cheers, >>> David G Doshay >>> >>> ddos...@mac.com <mailto:ddos...@mac.com> >>> >>> >>> >>> >>> >>> On 6, Aug 2017, at 3:17 PM, Gunnar Farnebäck <gun...@lysator.liu.se >>>> <mailto:gun...@lysator.liu.se>> wrote: >>>> >>>> On 08/06/2017 04:39 PM, Vincent Richard wrote: >>>> >>>>> No, simply because there are way to many possibilities in the game, >>>>> roughly (19x19)! >>>>> >>>> >>>> Can we lay this particular number to rest? Not that "possibilities in >>>> the game" is very well defined (what does it even mean?) but the number of >>>> permutations of 19x19 points has no meaningful connection to the game of go >>>> at all, not even "roughly". >>>> >>>> /Gunnar >>>> _______________________________________________ >>>> Computer-go mailing list >>>> Computer-go@computer-go.org <mailto:Computer-go@computer-go.org> >>>> http://computer-go.org/mailman/listinfo/computer-go >>>> >>> >>> >>> >>> _______________________________________________ >>> Computer-go mailing list >>> Computer-go@computer-go.org >>> http://computer-go.org/mailman/listinfo/computer-go >>> >>> >> _______________________________________________ >> Computer-go mailing list >> Computer-go@computer-go.org >> http://computer-go.org/mailman/listinfo/computer-go >> > > > _______________________________________________ > Computer-go mailing list > Computer-go@computer-go.org > http://computer-go.org/mailman/listinfo/computer-go >
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