361! seems like an attempt to estimate an upper bound on the number of games where nothing is captured.
On Wed, Aug 9, 2017 at 2:34 PM, Gunnar Farnebäck <gun...@lysator.liu.se> wrote: > 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 about how the game’s rules affect the calculation) is outdated since early 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 >
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