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- #! /bin/sh
- # This is a shell archive, meaning:
- # 1. Remove everything above the #! /bin/sh line.
- # 2. Save the resulting text in a file.
- # 3. Execute the file with /bin/sh (not csh) to create:
- # README
- # opt1
- # opt2
- # opt3
- # opt4
- # opt5
- # opt6
- # opt7
- # This archive created: Mon Jan 20 18:43:13 1992
- export PATH; PATH=/bin:/usr/bin:$PATH
- if test -f 'README'
- then
- echo shar: "will not over-write existing file 'README'"
- else
- cat << \SHAR_EOF > 'README'
- Path: milton!usenet.coe.montana.edu!rpi!usc!cs.utexas.edu!qt.cs.utexas.edu!yale.edu!jvnc.net!darwin.sura.net!europa.asd.contel.com!uunet!mcsun!sun4nl!cwi.nl!tromp
- From: tromp@cwi.nl (John Tromp)
- Newsgroups: rec.games.go
- Subject: supposedly optimal play on small go-boards
- Message-ID: <5135@charon.cwi.nl>
- Date: 14 Jan 92 13:35:43 GMT
- Sender: news@cwi.nl
- Organization: CWI, Amsterdam
- Lines: 343
-
- Recently, I got interested in discovering optimal play in go.
- That is, assuming the best play by both black and white, by how
- many points can black win the game? Since I have little hope of
- answering this question for the usual 19x19 board, or even the 9x9 one,
- I'll restrict my attention to board sizes smaller than 9x9.
-
- The answer of course depends on the exact scoring rules used.
- The rules I use here are to count empty territory + prisoners, as
- the program mgt does it.
- Hopefully other readers will comment on changes in the outcome caused
- by different scoring rules (e.g. chinese).
-
- Attached to this message is a shar file containing 7 files in mgt format.
- The first 6, on board sizes ranging from 1x1 through 6x6 represent what
- I believe to be optimal play, while the 7th is just a possible play on
- a 7x7 board, in which either white or black is likely to have missed a
- better move.
- Those lacking the mgt program can also follow the lines by numbering both
- axes of the board alphabetically.
-
- The outcomes I get are:
-
- boardsize 1x1 2x2 3x3 4x4 5x5 6x6 7x7
- margin for black 0 0 8 1 24 3 8
-
- The first two are rather silly but included anyway for completeness.
- Note that on the 3x3 and 5x5 boards, black effectively dominates the whole
- board by playing in the center and thus wins by nxn-1. In the games, I have
- let white play as long as black is forced to reply.
-
- I would like to have your opinion on these games, in particular
- suggestions for better lines in the 7x7 game. The 8x8 board may
- also be amenable to such analysis due to the symmetry. Still, it's not
- so obvious that one should start dividing the center, which in this
- case is relatively far from the edge.
-
- Happy analysis!
-
- -John Tromp, ~10 kyu (tromp@cwi.nl)
-
-
-
-
-
- Path: milton!nntp.uoregon.edu!cs.uoregon.edu!mips!think.com!wupost!waikato.ac.nz!comp.vuw.ac.nz!canterbury.ac.nz!math!wft
- From: wft@math.canterbury.ac.nz (Bill Taylor)
- Newsgroups: rec.games.go
- Subject: Optimal play on small go-boards.
- Message-ID: <1992Jan20.182631.3508@csc.canterbury.ac.nz>
- Date: 20 Jan 92 05:26:30 GMT
- Organization: Department of Mathematics, University of Canterbury
- Lines: 59
- Nntp-Posting-Host: math.canterbury.ac.nz
-
- tromp@cwi.nl (John Tromp) posted an article "supposedly optimal play on small
- go-boards" on 14 Jan 92.
-
- I was hoping there would be some replies, but none so far, so here's mine.
-
- John writes
- > The outcomes I get are:
- >
- > boardsize 1x1 2x2 3x3 4x4 5x5 6x6 7x7
- > margin for black 0 0 8 1 24 3 8
-
- He is using (empty spaces + prisoners) scoring, which is in fact neither
- Chinese nor Japanese. My comments will be directed mainly toward Chinese scoring,
- (as suggested by John), i.e. 1 point for all intersections filled or surrounded,
- (ignoring prisoners), which I understand is also official American scoring now
- as well. (It has been official here in N.Z. for many years). With this we get
-
- boardsize 2x2 3x3 4x4 5x5 6x6
- margin for black 1 9 2 25 4
-
- with the same moves as given by John. These figures are all one point more to
- black, (as is the case in 50% of normal games; interestingly for these small
- boards this happens in ALL cases, black always gets the last move.)
- a b
- Only the case 2x2 needs a little extra comment. The full
- game should go (aa bb ba pass pass). Thus black is ahead a @ - .
- by one point, as in the diagram. White cannot improve with | |
- capture ab, otherwise black plays ba (NOT aa !), then b @ - O
- aa ba ab aa pass, and white cannot play, by the (Chinese
- and American) no-repeat rule. These comments, and the cases 3x3 and 4x4, were
- given by James Davies, in his article "the Chinese rules of go", in GO WORLD
- of about late '77 or early '78.
-
- The 4x4 case needs a little checking, but is fairly straightforward; (as Davies
- points out, this is in fact a zero-point tie in Japanese). The 3x3
- and 5x5 cases are very simple, and could sensibly end after only one move, of
- course (especially the 3x3). The 6x6 case is more interesting; the line
- given by John is correct, as given in an introductory go book whose name
- I've unfortunately forgotten (if anyone has seen this book I'd be grateful for
- an email on this !). John gives cc dd dc cd bd be ed ee de ce fe ef ec bc bb
- ad ab ac fd df ff. This gives 4 (Chinese) to black, the best result. The moves
- for black are all forced (ignoring trivial symmetries); but White has some
- interesting options that give the same final score with correct play. You
- might have some fun checking out the variant where white plays mirror-go for
- as long as he can, and black must find the correct way to break out of it.
-
- As for the 7x7, I suspect John's answer of 8 (Chinese 9) is wrong. John gives
- a line starting dd ee ed de cd , then continuing much as in the 6x6 case, giving
- the result above. However I suspect black's 3rd move is wrong. With the more
- aggressive 3rd move, ce, we get, for the whole game, in its most simple
- variant; dd ee ed de ce cf be bf fe ff fd bd cd ae bc ad ac af gf fg ge dg gg.
- Black wins by 15 (14 Japanese); but white may resist more strongly at various
- places, and it then becomes quite hard to check that black can maintain this
- result. I suspect that a fully detailed analysis would cover several pages to
- be reasonably convincing !
-
- Anyway, all players are urged to try for themselves, and post their comments
- for us to see.
- ----------------------Pleasant plonking!------Bill Taylor--------------------
-
- SHAR_EOF
- fi
- if test -f 'opt1'
- then
- echo shar: "will not over-write existing file 'opt1'"
- else
- cat << \SHAR_EOF > 'opt1'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[1]
- Comment[Black: 0 + 0 = 0
-
- White: 0 + 0 = 0
-
- White wins by 0.]
- )
- SHAR_EOF
- fi
- if test -f 'opt2'
- then
- echo shar: "will not over-write existing file 'opt2'"
- else
- cat << \SHAR_EOF > 'opt2'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[2]
- Comment[A supposedly optimal game.]
- ;
- Black[aa]
- ;
- Comment[Black: 0 + 0 = 0
-
- White: 0 + 0 = 0
-
- White wins by 0.]
- White[bb]
- )
- SHAR_EOF
- fi
- if test -f 'opt3'
- then
- echo shar: "will not over-write existing file 'opt3'"
- else
- cat << \SHAR_EOF > 'opt3'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[3]
- Comment[A supposedly optimal game.]
- ;
- Black[bb]
- ;
- White[bc]
- ;
- Black[cb]
- ;
- White[ab]
- ;
- Comment[Black: 6 + 2 = 8
-
- White: 0 + 0 = 0
-
- Black wins by 8.]
- Black[ba]
- )
- SHAR_EOF
- fi
- if test -f 'opt4'
- then
- echo shar: "will not over-write existing file 'opt4'"
- else
- cat << \SHAR_EOF > 'opt4'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[4]
- Comment[A supposedly optimal game.]
- ;
- Black[bb]
- ;
- White[cc]
- ;
- Black[cb]
- ;
- White[bc]
- ;
- Black[ac]
- ;
- White[db]
- ;
- Black[bd]
- ;
- White[ca]
- ;
- Black[cd]
- ;
- White[dc]
- ;
- Comment[Black: 2 + 0 = 2
-
- White: 1 + 0 = 1
-
- Black wins by 1.]
- Black[aa]
- )
- SHAR_EOF
- fi
- if test -f 'opt5'
- then
- echo shar: "will not over-write existing file 'opt5'"
- else
- cat << \SHAR_EOF > 'opt5'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[5]
- Comment[A supposedly optimal game.]
- ;
- Black[cc]
- ;
- White[cd]
- ;
- Black[dc]
- ;
- White[bc]
- ;
- Black[bb]
- ;
- White[ad]
- ;
- Comment[Black: 21 + 3 = 24
-
- White: 0 + 0 = 0
-
- Black wins by 24.]
- Black[be]
- )
- SHAR_EOF
- fi
- if test -f 'opt6'
- then
- echo shar: "will not over-write existing file 'opt6'"
- else
- cat << \SHAR_EOF > 'opt6'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[6]
- Comment[A supposedly optimal game.]
- ;
- Black[cc]
- ;
- White[dd]
- ;
- Black[dc]
- ;
- White[cd]
- ;
- Black[bd]
- ;
- White[be]
- ;
- Black[ed]
- ;
- White[ee]
- ;
- Black[de]
- ;
- White[ce]
- ;
- Black[fe]
- ;
- White[ef]
- ;
- Black[ec]
- ;
- White[bc]
- ;
- Black[bb]
- ;
- White[ad]
- ;
- Black[ab]
- ;
- White[ac]
- ;
- Black[fd]
- ;
- White[df]
- ;
- Comment[Black: 11 + 0 = 11
-
- White: 6 + 2 = 8
-
- Black wins by 3.]
- Black[ff]
- )
- SHAR_EOF
- fi
- if test -f 'opt7'
- then
- echo shar: "will not over-write existing file 'opt7'"
- else
- cat << \SHAR_EOF > 'opt7'
- (
- ;
- GaMe[1]
- VieW[]
- SiZe[7]
- Comment[A supposedly optimal game.]
- ;
- Black[dd]
- ;
- White[ee]
- ;
- Black[ed]
- ;
- White[de]
- ;
- Black[cd]
- ;
- White[ce]
- ;
- Black[be]
- ;
- White[bf]
- ;
- Black[fe]
- ;
- White[ff]
- ;
- Black[fd]
- ;
- White[bd]
- ;
- Black[bc]
- ;
- White[ae]
- ;
- Black[ac]
- ;
- White[gf]
- ;
- Black[ad]
- ;
- White[be]
- ;
- Comment[Black: 20 + 0 = 20
-
- White: 11 + 1 = 12
-
- Black wins by 8.]
- Black[ge]
- )
- SHAR_EOF
- fi
- exit 0
- # End of shell archive
-