Many Faces of Go has 2052 3x3 patterns. All have a empty point in the center. One value is used for all the illegal patterns, so there are 2051 valid patterns. I use Aja’s idea of including in the pattern the Atari status of zero to four adjacent groups. That’s why it’s more than Álvaro’s 1107.
There is no reason to iterate over all patterns. Just iterate over the ones that are identical through rotation or symmetry. One easy way to find the canonical pattern is to calculate hashes for all rotations and reflections and choose the smallest one as the pattern ID. I use a table to map the pattern IDs to a set of consecutive index, 0-1251. David From: Computer-go [mailto:computer-go-boun...@computer-go.org] On Behalf Of Jim O'Flaherty Sent: Tuesday, November 03, 2015 11:35 AM To: computer-go@computer-go.org Subject: Re: [Computer-go] Number of 3x3 patterns Ah. That makes sense. It's a pattern centered on a possible next move. Very cool. Tysvm for explaining. On Tue, Nov 3, 2015 at 1:33 PM, Detlef Schmicker <d...@physik.de> wrote: -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Am 03.11.2015 um 20:24 schrieb Jim O'Flaherty: > I don't see how "leave the center empty" works as a valid case, > assuming this it just any valid 3x3 window on the board. Given bots > playing each other, there can be 9x9 clumps of a stone of the same > color. I can see it being argued there is no computational value in > this specific pattern instance. But, then what are the conditions > of the exceptions to the generalization? And how do you effectively > iterate through the other +20,000 variations (not reduced by > location or color symmetry)? > > So, I'm curious, is there some other assumption about the 3x3 > window other than it be a view into any valid 3x3 space on a Go > board? Sorry, I did not explain the details, the assumption is: I play in the middle, so it must be empty. I thought legal moves might not really reduce the number of 3x3 patterns, as there can be no suicide known from 3x3 patterns, as a capture is always possible. Therefore I wonder, what 14 patterns did not appear in my 40000 games harvested:) > > On Tue, Nov 3, 2015 at 1:04 PM, Álvaro Begué > <alvaro.be...@gmail.com> wrote: > >> I get 1107 (954 in the middle + 135 on the edge + 18 on a >> corner). >> >> Álvaro. >> >> >> >> On Tue, Nov 3, 2015 at 2:00 PM, Detlef Schmicker <d...@physik.de> >> wrote: >> > Thanks, but I need them reduced by reflection and rotation > symmetries (and leave the center empty so 3^8 + 3^5 + 3^3 and than > reduce) > > > > Am 03.11.2015 um 19:32 schrieb Gonçalo Mendes Ferreira: >>>>> If you are considering only black stone, white, empty and >>>>> border, ignoring symmetry, wouldn't it be >>>>> >>>>> 3^9 + 3^6 + 3^4 >>>>> >>>>> 3^9 for patterns away from the border, 3^6 for near the >>>>> sides and 3^4 near the corners, assuming you are also >>>>> interested in the center value. >>>>> >>>>> This makes 20493, then you need to take out illegal >>>>> patterns (surrounded middle stone). So I'd hint it's close >>>>> to 20000. >>>>> >>>>> On 03/11/2015 18:17, Detlef Schmicker wrote: I could not >>>>> find the number of 3x3 patterns in Go, if used all >>>>> symmetrie s. >>>>> >>>>> Can anybody give me a hint, were to find. Harvesting 40000 >>>>> games I get 1093:) >>>>> >>>>> Thanks, Detlef >>>>>> _______________________________________________ >>>>>> 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 >>> >> >> >> _______________________________________________ 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 > -----BEGIN PGP SIGNATURE----- Version: GnuPG v2.0.22 (GNU/Linux) iQIcBAEBAgAGBQJWOQv1AAoJEInWdHg+Znf4GTYQAIATv45HU7fR1S4bfiygapDI IOOnTtHTdjNoqHWGD07Y3MUy8rP24AcWHtEmlH+uwt42HBFXhCW9Hr2ul/Yreofl e/lxcoawYYWs1tPuHEKV8TPQUVM3aHvPREoQgBMbkMlDpKQA1Jj3Q0Kv8T9cUVOW S2URrTyOFrLiEbl4znYJwiH7hVI7q0HKom/XGFYWkfwhvJjDdKDrPbTUyl4IWo2Q v/HdIXC/6WrPSnkeFnkc595w0qTUiXWj+B/0JYMnKvBml3aEsG8W6uT79SdDJ1MN OJ4iW9L08p68Ovxt6Wp+eXopiPZSQ90PxPtI3cfmWrPWhs3/P95mLPg+u0CEt+PH iuMaCM/XR68rWqQhMjRVbJkM+udo0f5iIGwN3xSDQiqfD1OO4Ks60Bdbj2qmKu/B npEMGGeCqQmiyPftCYSdeMTHPScH+CvcL1nZaC4kdW7+aDfrC7JvU3L5nfKhVxMK RfuXdNeX6mVAI2uL+MvFFea1B38qvdBS4y1XCQ8QObQxuxNJJupzQ8fixYGdOotj UzuuXI4pyCzEcWWG+dr58pA35MbEpUWVsw/UMSA96RjevaqAUQ7nyFvNxcBahzE/ PGHRvcdp/c9AtlxKLDCqMd4+XMVWkSzj75jFhJuyRM4hkcszYdzVngWj6D4h9Npk bzUgyQTYpesLVPNtVfjx =Vqlf -----END PGP SIGNATURE----- _______________________________________________ Computer-go mailing list Computer-go@computer-go.org http://computer-go.org/mailman/listinfo/computer-go
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