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Final Answers
© 2000-2020   Gérard P. Michon, Ph.D.

Joy  of  Go

Smart people in search of a challenging
board game might try a game called Go
.
Hans Berliner  (1929-2017)
The New York Times  (2003-02-06)
  • A brief history of Go.
  • The board  (standard goban).  361 intersections of lines in a 19 by 19 grid.
  • 361 stones.  181  black pieces and  180  white ones  (usually lenticular).
  • Go bowls (gosu).  Japanese wooden bowls.  Baskets from China.
    Rules of the Game of Go :
  • Komi:  Points received by  White  as compensation for starting  second.
  • Score   =   (surrounded territory)  +  (captured stones)  +  komi.
  • Liberty:  A  chain  of stones is captured when all its  liberties  vanish.
  • Rules of ko:  Japanese and Chinese rules differ in the rare case of  triple ko.
  • Playing Go on unusual boards.  Big or small,  rectangular or not...  5 by 5 goban
  • Combinatorics of Go.  Enumerating legal Go configurations.
  • Nalimov tables.  How  Go  has been  solved  for small grids.
    Playing Go.  Concepts, Tactics and Strategy :
  • Opening moves  (fuseki).  What to play first  (and why).
  • Mistakes to avoid.  What not to do and why not to do it.
  • Shapes:  Some localized patterns which skilled players are all familiar with.
  • Ladders and loose ladders.  Repeatedly prevent increase in opponent's  air.
  • Nets.  Loose limits which make captures inescapable.  Elementary reading.
  • Snapback.  A sacrifice may allow a greater capture in return.
  • Eyes and eye-shapes  are the keys to life-and-death problems.
  • Seki.  Shared life.  Configurations that would backfire if you touch them.
  • Tesuji.  Finding key moves.
  • Joseki.  The Go term for a standard sequence of moves worth memorizing.
  • Framework  (moyo)  to consolidate and/or defend against  invasions.
  • Invasions.  Challenging the opponent's claim to a territory.
  • Endgame.  Squeezing the most of the situation when the end is near.
    Go Players and the World of Go :
  • Kyu  (k)  &  dan  (d).  Pro dan or  ping  (p).  Pecking order in Go.
  • Competitions:  Amateur and professional tournaments.
  • Championships and champions:  Past and present stars of the  Go  world.
  • Machines that play Go.  In March 2016,  AlphaGo  beat  Lee Sedol,  9p.
  • Go jargon:  A short glossary of  Go  words indispensable in English.
 Michon
 
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  19 by 19 Goban

On this site, see also:

Related Links (Outside this Site)

Sensei's Library   |   700 Japanese Go terms   |   English glossary
Yellow Mountain Imports  (YMI) :  About Go Equipment.
Life in 19 x 19 :  Go-related forums.
Japanese Go Gear and Folklore  by  Kevin Michael  (Pinterest collection).
Bookmarkshomepage  and  Go bestiary  of  Harry Fearnley, 1k  (2002).
Go Bestiary  &  Questions de règles  by  Denis Feldmann, 3d  (French).
 
Current ELO Ratings of Go players   |   Go databases (go4go.net)
International Go Federation  |  Nihon Ki-in  (Japan Go Association,  1924).
Top  10  reasons to play GoAmerican Go Association  (AGA,  1935).
Hanguk Kiwon  (Korea Baduk Federation,  1945).
Kansai Ki-in  (Kansai Go Association,  1950).
Celebrities who have played Go   (British Go Association1953).
European Go Federation  (EGF,  1957).
Chinese Weiqi Association  (Chinese Go Association,  1962).
Fédération Française de Go  (FFG,  1970)   =   French Federation of Go.
New-Zealand Go Society  (NZGS, 1982).
Taiwan Chi Yuan  (Taiwan Go Association,  2000).

Go Servers :

Pandanet Internet Go Server  (IGS).  Established in 1992.
KGS  (Bill Shubert, 2000).  American Go Foundation.
OGS  (Nov. 2005).  Merged with Nova.gs on 2013-10-19.  Browser-based.
Tygem Baduk  (Korean)  &  Tygem Go  (English).  MS Windows download.
WBaduk.  World Internet Baduk  (Korea).  Most active Go server.
Dragon Go Server  (DGS)  from Sweden.  Turn-based  (correspondence).

Go Vendors :

Yellow Mountain Imports (YMI)   |   WorldWise Imports   |   Brybelly
Kuroki GoishiTen  (KGT,  Mr. Kuroki)   |   Slate & Shell  (books)
Yutopian  &  Kiseido  (Richard Bozulich)   |   Jzool.com

Wikipedia :   Go   |   Rules of Go   |   List of Go terms   |   Go equipment
Go & mathematics   |   Games played with Go equipment   |   List of Go organizations

Introduction to Baduk (23:26)  Shawn Ray, 4d  =  Clossius  (#1, 2014-07-15).
Learn Go in 15 minutes (13:39)  TheDuddha2  (2012-05-31).
Learn to Play Go  -  A Guide for Beginners (23:15)  In Sente  (2016-02-13).
Back to basics - Fundamental play (41:08)  by  Dwyrin  (2015-06-27).
First lecture - 5-kyu Game Review (1:04:19)  by  Nick Sibicky  (#1, 2012-04-01).
Playing on the 9 x 9 Board  (23:46, 20:58)  by  Jonathan L. Hop  (2014-02-20).
Go/WeiQi/Baduk Tutorial  (8:24, 9:57, 9:29, 8:43Goshawk Heron  (Apr. 2008).

Blbliography :

Go:  A Complete Introduction to the Game
by  Cho Chikun, 9p  with  Richard Bozulich  (1988, 1997, 2018).
Mathematical Go Endgames:  Nightmares for the Professional Go Player
by  Elwyn Berlekamp, 10k  &  David Wolfe, 1d  (1994, 2012).

 
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The Ancient Game of Go

Go  is one of the most played board game in the World  (second only to the game of  Xiangqi,  or  Chinese chess).  It's more popular than  Chess  or  Shogi  (Japanese chess).  According to a survey by the International Go Federation (2016) more than 46 million people know how to play Go and there are more than 20 million active players.
 
The game was invented well before  1100 BC  in China,  where it was originally called  Yi.  The current Chinese term is  Weiqi  (pronounced way-tchee).  It became one of only four  fine arts  (music, painting, calligraphy and Go).  The size of the earliest  gobans  is unknown.
 
As the game reached the West through Japan,  we use mostly the Japanese term for it  (Go or Igo).  The Chinese name  (Weiqi)  and the Korean one  (Baduk or Paduk)  are sometimes used to stress minor cultural differences in rules or  physical dimensions.
 
In principle,  Go  could be played on a grid of any shape or size using the same  basic rules  (which  Edward Lasker  considered so natural that they'd be used by extraterrestrials too).  Finding the  best strategy  for Go is a mathematical problem which has been solved only for some  tiny boards,  including the 5 by 5 square.
 
Go  is still far more popular in the Orient than elsewhere,  but its prestige in the West has been spearheaded by many occidental celebrities and scientists.  It was reportedly the only hobby of  Paul Erdös (1913-1996)  the most prolific mathematician of all time  (with the possible exception of  Euler).  Notorious Western mathematicians or scientists who have played  Go  include,  in chronological order of birth:
 
 Alan Turing  Emanuel Lasker (1868-1941),  Lise Meitner (1878-1969),  Albert Einstein (1879-1955; Nobel 1921),  Paul Dirac (1902-1984; Nobel 1933),  Claude Chevalley (1909-1984),  Alan Turing (1912-1954),  Paul Erdös (1913-1996),  Philip W. Anderson (b.1923; Nobel 1977),  John Nash (1928-2015; Nobel 1994),  Hans Berliner (1929-2017),  Roger Penrose (1931-),  John H. Conway (1937-2020)  and  Elwyn Berlekamp, 10k (1940-2019).
 
In the Orient,  Go  is widely regarded as one of Mankind's greatest cultural achievements and it's part of a well-rounded education  (sometimes,  sadly,  a substitute thereof).  From rules simple enough for a child emerge rich structures which have been studied for millennia.
 
The first feature documentary about  Go  was released in 2017 after four years of shooting in China, Korea, Japan and the US.  It documents the struggles of young Americans  competing for the first two professional Go titles awarded outside of Asia  (2012-08-04).  The crew visited the ailing  Go Seigen (1914-2014)  as he turned 100.  The film has a great title:

 The Surrounding Game

The Surrounding Game (1:37:37)  by  Will Lockhart  &  Cole D. Pruitt   |   Trailer (2:20)   |   Press Kit


AlphaGo - The Movie (1:30:27)  DeepMind   (2020-03-13)
Exerpted from the promotional litterature of that documentary: 
"On March 9, 2016, the worlds of Go and artificial intelligence collided in South Korea for an extraordinary best-of-five-game competition, coined The DeepMind Challenge Match.  Hundreds of millions of people around the world watched as a legendary Go master took on an unproven AI challenger for the first time in history."

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Go  Equipment


(2018-11-16)   The Go board is also called  Goban.
9x9 or 13x13 boards are sometimes used.  The standard size is 19 by 19.

The grid consists of lines which are about  1 mm  wide.  Players put stones at the  points  (or  nodes)  where those lines intersect.

A few such nodes,  including the center point  (tengen  or Heaven's soul)  are singled out as  star points  using small disks  (about  4 mm  in diameter)  at locations which depend on the size of the board,  as shown below:

 9 by 9 Goban  13 by 13 Goban  19 by 19 Goban

For the 9 by 9 board,  the above is the most common configuration.  I'm told that boards have been made with either one or four star-points instead of five  (omitting either the center or the other four points).  Digitally,  you may encounter a  9 by 9 goban with 9 star-points.

The Japanese name for  star-points  is  hoshi  (star).  In a Korean context,  they're called  flower-points,  since the Korean term is  hwa jeom  (flower).

It's sometimes said that traditional Korean boards had flower designs at the star-points,  but I couldn't find any evidence for that...

Star-points have no special rôle in game-play;  they're mostly convenient landmarks.  When  handicap stones  are called for,  they're customarily put on star-points.  However,  some rule-sets allow the weaker player to put the granted  (black)  handicap stones at any locations on the empty board,  as part of the first move  (before letting  White  play).

Disallowing  even  sizes for  rectangular gobans  ensures the existence of a playable center point,  which gives Black one trivial move which can't possibly be mirrored by White  (even before any stone is captured).

Physical standard Go boards aren't quite square:  They're usually about  7%  or  8%  longer than they're wide  (purportedly,  to compensate for visual foreshortening in over-the-board play).  The wood grain is oriented along the length;  from one player side to the other  (across the width).  In the US,  grid cells are commonly specified as  7/8''  (22.23 mm)  by  15/16''  (23.81 mm).  So,  the  nominal  aspect ratio  for  US  grids  is :

15 / 14   =   1.07142857...

That corresponds to the following viewing angle  q  from vertical:

q  =  arccos (14/15)  =  21° .

However,  the board should always be displayed as perfectly square in all situations which call for orthogonal viewing  (q = 0)  as is the case for Go positions printed in a book or displayed on a computer screen.

Go is played by placing round stones on a grid whose size must match the diameter of the stones:  Chinese stones simply won't fit on a Korean board.  Conversely,  Korean stones may look too skinny on a Chinese board.

The  correct  way to specify board dimensions doesn't depend on the width of the lines in the grid:  Grid cells should be measured center-to-center  (or,  equivalently,  left-edge to left-edge).  The best way to measure cell size with a ruler is to measure  n  cells  left-edge to left-edge  and divide by  n.  (n = 18  for a full goban,  if your ruler is long enough.)  Likewise,  a border goes from the  middle  of the outermost line to the edge of the field  (thus,  the playing field is exactly equal to its number of cells plus the two borders).

With this out of the way,  the width of the lines isn't crucial:  Thin or bold lines affect looks but are utterly irrelevant to playability.  The usual line width is most commonly specified as either  1 mm  or  1/32''  (0.8 mm).

The diameter of the stones must  absolutely  be less than the smaller cell dimension and  preferably  also not exceed  twice  any border width  (or else,  an outermost stone would overhang,  which is unsightly).

Goban dimensions and matching stone diameters,  all in millimeters  (mm).
OriginStone ØGrid CellBorderPlaying Field
China 22.5 mm23.3324.22440470
US 20.6 mm22.2223.8117.7817.46436464
Japan 20.0 mm21.523430460
Korea 18.2 mm20.3720.5014.6713.50396400
Border includes half a line-width.  Thus :   18 cells  +  2 borders  =  field   (exactly).

At my local  Koreatown  supermarket,  the only goban for sale is a folding board made out of  composite wood.  The grid cells measure  20.37 mm  by  20.50 mm  (center to center)  with a line width of about  1 mm.  The total  (solid)  length is  400 mm  and the  (folding)  width is  396 mm  (which is more squarish than usual).  For $15,  they sell a box of glass stones with sturdy plastic bowls and lids  (I counted only 139 white stones and 133 black ones; the bowls clearly can't contain much more).  Those stones have a diameter of  18.2 mm  and a thickness of roughly  7½ mm  (size 28 or so).  They're lenticular but asymmetrical  (the bottom flattens out in the middle).

That cheap Korean set replaced the long-lost Go equipment which I had as a teenager.  I added stick-on  rubber feet of the proper thickness  to prevent the board's hinges from scratching tables  (staggering them to preserve foldability,  disregarding the Xiangqi board on the reverse side).  I used a  black Sharpie  to make the line at the fold match the visibility of the other lines and I sprayed the playing surface with several coats of polyurethane  (carefully sanding between coats).    Just a joke!

Another very good deal on a budget are the magnetic travel sets from  Yellow Mountain Import  (YMI).  There are two models of different sizes.  Both include plastic stones with magnets on the bottom and a convex shape on top.  The bowls and lids fit inside the folded board which serves as a case.  The retail cardboard box protects the playing surface in travel or storage.

Magnetic Go Sets from YMI  (dimensions in mm)
PriceStone ØGrid CellBoardClosed Box
$33 16.8 mm17.9217.9235035036918848
$20 12 mm13.8413.8427027028514537
Dimensions for the smaller set are estimates based on manufacturer's data  &  photos.

The larger set is an excellent compromise between playability and portability.  It weighs  1.5 kg.  My set came with  exactly  181  stones of each color.  None of them are faulty,  although half a dozen white stones have noticeably weaker magnets.

In a pinch,  a foldable goban can  stay folded  for a quick game on a  9 by 19  rectangular grid  (171 nodes)  which has about the same complexity as a more traditional  13 by 13  goban  (169 nodes)  albeit with a different  feel.

Wood used in traditional or commercial gobans:

Part of the mystique of thick traditional floor gobans are the  kogushi  cuts facing the players,  showing many tree-rings,  embodying years of wisdom.

Kaya  is the gold standard for gobans.  Other types of wood are used because of the drastic shortage of kaya and its prohibitive price.  Choices are mostly oriental woods,  with the notable exceptions of  maple  and  yellow cedar.

  • KayaTorreya nucifera.  700- to 1000-year-old trees.
    The traditional wood for demanding single-slab floor gobans  (as opposed to tableboards without feet,  for tabletop use).  Kaya trees are protected;  only the wood of dead trees can be used,  which makes it scarce and expensive.
  • Katsura  (arbre au caramel).  Cercidiphyllum japonicum.  Dark hardwood.
  • Yellow cypress,  Nootka cedar  (cyprès de Nutka).  Cupressus nootkatensis.
    The  Seattle Go Center  has recently  relined  its original yellow-cypress boards,  after more than  20  years of intensive use  (for $180 per board).
  • Kauri   (kaori).  Agathis australis.  Harder than  kaya  and more affordable.
  • Sugar maple  (érable).  Acer saccharum.  A good occidental alternative.
  • Dragon spruce, shin-kaya   (épicéa de Chine).  Picea asperata.
    Promoted as a replacement for  kaya  (now called  old kaya,  by contrast).
  • Hiba cedar,  asunaro   (thujopsis).  Thujopsis dolabrata.
    Will crack over time if slabs are too thick.  For thin table-gobans only.
  • Hinoki cypress  (cyprès du Japon).  Chamaecyparis obtusa.  Likewise.
  • Bamboo  (technically, not wood but  grass).  Composite  bamboo gobans are successful in the West because of the low price and Asian  mystique.  Purists,  like myself,  may find the grain of bamboo boards too distracting.

Goban   |   Sensei's Library (SL)   |   Dimensions   |   Averaging
 
Shinkaya Go Board sound test (9:17)  by  jtgravity  (2014-10-10).
Pro 13x13 game (54:25)  by  Nick Sibicky  (#279, 2017-12-25).


(2018-11-17)   Biconvex stones
A full set consists of  181  black pieces and  180  white ones.

In premium sets,  the black stones are designed to be slightly larger  (e.g.,  21.2 mm  average,  with a strict maximum of  21.5 mm)  than the white ones  (e.g.,  20.7 mm,  with a maximum of  21 mm).  That difference of  0.5 mm  is purported to make both kinds of stones appear the same size.

  • Goldstone.  Red and blue.  (Semi-precious  aventurine glass.)
  • Yunzi.  (Some lead?)
  • Shell and Slate.
  • Jitsuyo (standard) and Yuki (snow) grades.
  • Glass.
  • Melamine resin.
  • Ceramic  (porcelain).
  • Bakelite.
  • Urea resin.
  • Plastic.

 Come back later, we're
 still working on this one...

The thickness of stones of size   33 + n   is   (9.2 + 0.3 n) mm ,  if  n ≥ 0.  For sizes below  33,  see the following table:

Sizes
SizeThickness
3810.7 mm
3710.4 mm
3610.1 mm
339.2 mm
328.8 mm
318.4 mm
308.0 mm
287.5 mm
257.0 mm

Yunzi stones (Yunzi)
Semi-precious Exotic Go Stones (10mm x 21.5mm, 180 per set).
 
Yunnan Weiqi Factory (8:40)  Traditional manufacture,  narrated in Chinese  (2006-08-01).
Unboxing Kurokigoishiten Clamshell Go Stones (29:11)  by  Chris Walljasper  (2017-01-26).
My Go Equipment (13:56)  by  Nick Sibicky  (#180, 2016-03-07).


(2018-12-14)   Go bowls  (gosu)  and  deep lids.
Special straps secure lids for travel.  Lids hold  prisoners  during games.

Stay away from flat or shallow lids,  which are inadequate.

To carry two bowls full of stones,  it's recommended to have special straps to secure the lids and a carrying bag with two compartments.

Wooden go bowls come in two styles,  named after two famous Go rivals:

  • Go Seigen bowl.  Chinese style.  Large diameter.
  • Kitani bowl.  Japanese style.

Those terms were coined by Go lecturer and  3p  retired professional  Janice Kim (1969-) who is now a professional poker player based in San Francisco.

 Come back later, we're
 still working on this one...

Guide to wooden Go Bowls "Go Seigen" and "Kitani" Shapes   (Yellow Mountain Imports).
Bamboo bowls and lids with straps and carrying bags (Yellow Mountain Imports, $30).

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The rules of Go

Concise Rules  and  Official Rules  (American Go Association, 1991).
The Chinese Rules of Go  (Rules of Weiqi)  edited by  Fred Hansen  (1992).
Differences between Chinese and Japanese rules of Go  (2010, 2012).
New-Zealand rules of Go   |   Tromp-Taylor rules of Go
Comparison of Some Go Rules  (British Go Association).


(2019-01-10)   Komi
Extra points awarded to  White  for the disadvantage of playing second.

The rules specify that  Black  always goes first.  Placing the first stone is an advantage which can be compensated by the award to white of a certain number of points called  komi.

The  komi  is either awarded by a fixed rule adopted by the organizer of the game  (and/or agreed upon by both players)  or it can be put up for bidding.

Examples of institutional komis are 5.5, 6.5 or 7.5. 

When komi is up for bid,  each player announces at the beginning of the tournament what komi he is willing to accept for playing white or give the other player for the privilege of playing black.

 Come back later, we're
 still working on this one...


(2018-12-15)   The object of a game of Go is to maximize the final score.
Score  =  (surrounded territory)  +  (captured stones)  +  komi

A game may end for one of the following reasons:

  • One of the player resigns  (thereby losing without the need for a tally).
  • Both players agree to end the game.  This happens when both pass consecutively.  Formally,  the player who first passed must pass again for the game to end.
  • The players have exhausted their initial supply of stones.

At that point,  the position on the board is evaluated to determine the number of intersections surrounded by each player.  There are two ways to count that:

  • By area (Chinese).  Surrounded points plus number of stones on the board.
  • By territory (Japanese).  Surrounded points minus number of stones captured by opponent.

The two methods give the same result if the two players have played the same number of moves  (since a stone is put in play with every move,  either on the board or as prisoner when passing). The scores may be different but the score  difference  is the same.

 Come back later, we're
 still working on this one...

How to Score a Game of Go   (WikiHow).
 
Counting the Final Score in Go/Baduk/Weiqi (6:39)   BadukChannelAmerica  (2009-09-10).
How to count the final score in Go (7:34)  by  Stephanie Yin, 1p  (NYIG, 2018-06-04).
The Shortest Game (42:54)  by  Nick Sibicky  (#199, 2016-06-07).


(2018-11-17)   Chains,  Liberties,  Captures  and  Eyes.
A chain of stones is captured when all its liberties are taken away.

Give me liberty, or give me death!
Patrick Henry (1736-1799)  on  23 March 1775.

 Come back later, we're
 still working on this one...

A chain which has only one liberty left is said to be  in atari.  It could be captured on the opponent's next move.

Liberty   |   Rule of Capture   |   Atari


(2018-11-18)   The Ko Rule
A move cannot be played if it repeats a previous situation.

The  Chinese  Superko rules do not allow  any  repeat position.

 Come back later, we're
 still working on this one...

Ko rule   |   Ko fight
 
Kato Masao vs. Cho Chikun - Triple Ko, 1975 (1:04:19)  by  Nick Sibicky  (#200, 2016-06-13).


 5 by 5 goban (2018-12-13)   Playing Go on boards of all sizes and shapes.
Rectangles or any irregular shapes:  Small,  large...  or  infinite.

While the Baroque rules of Chess could only have been created by humans,
the rules of Go are so elegant, organic and rigorously logical that if intelligent life exists elsewhere in the Universe,  they almost certainly play Go.

Edward Lasker (1885-1981)  International chess-master (IM
Founder of the  American Go Association  (1935) 

Go  can be played on any  undirected graph  (henceforth called  grid)  not just the square grids of  traditional gobans.  When so generalized,  it's preferable to call the possible locations of the stones  nodes  (which is the general graph-theoretic term)  rather than  points,  which I don't recommend even for standard Go  (there's a needless risk of confusion with the related  points  used to compare scores at the end of the game).  I don't recommend the term  intersection  either,  because it's a polysyllabic word which properly describes  nodes  only for the usual rectangular grids.

Without loss of generality,  the Go grid can be restricted to  simple  undirected graphs  (which is to say that there's at most one edge between two nodes in the grid).  The game would be the same on other graphs,  since multiple  liberties  between two nodes would disappear exactly like a single one would.  Likewise,  graph loops are utterly irrelevant  (any liberty from a node to itself vanishes as soon as it's occupied).  The grids need not be planar graphs.

In that context,  Go  is just a coloring game played on the  grid  with three colors;  black, white and vacant  (there's an obvious generalization to more than two players,  which is largely uninvestigated). 

Flooding :

One advantage of expressing the rules of Go in a way which can apply to any graphs is that there's no tempatation to appeal to our intuitive knowledge of planar grids,  which could be misleading.

Arguably the best way to do so is to introduce the concept of  flooding  with a simple  recursive  definition:

A node is  flooded  by one clor when it's  either

  • Occupied by a stone of that color  or
  • Adjacent to a node flooded by that color.

To the uninitiated,  a proper recursive definition like this may look circular because we're defining a concept in terms of itself.  This isn't so because we could introduce an artificial distinction between various  levels  of flooding by Black  (say)  with nodes occupied by a black stone being  flooded at level zero.  The stones black-flooded at level n+1 are then defined as nodes which are not flooded at level n but are adjacent to such a node.  No circularity there.  The above recursive definition is retrieved if we just call  flooded,  without further qualifier,  nodes which are flooded at  some  unspecified level.

chain  is defined to be  dead  when all its liberties are flooded by the other color.

 Come back later, we're
 still working on this one...

Periodic Rectangular Grids  (with various topologies) :

A restricted generalization of  Go  suitable for human players involves the grids which are obtained from familiar rectangular boxes by  gluing  ar least one pair of sides.  For example,  we obtain an  horizontal cylinder  by considering that the bottom line of a regular goban  also  appears just above the top line  (which implies that the top line also appears just below the bottom line).

We may also  glue  the sides with a  twist.  Doing so for the top and bottom of a rectangular goban is like putting above the top line the bottom line  back to front.

Gluing two opposite sides of rectangles with such a twist is like drawing the grid of a  Moebius strip.  If we glue both pairs of sides without any twist,  we obtain a grid drawn on the surface of a  torus.  If  one  gluing involves a twist,  the underlying  topology  is that of a  Klein bottle.  (Gluing  cannot  be done consistently with  two  twists.)

Solved examples :

On a 1 by 1 board,  The single node has no liberties and neither player can legally put a stone on it.

On a 2 by 2 board,  Black plays first  (as usual)  in the lower-left corner  (WLG).  Then,  white can pass, play on an adjacent node,  or on the opposite corner:

  • If White passes,  Black plays on the opposite corner to end 5 points ahead.
  • If White plays on an adjacent node,  Black captures and ends 5 points ahead.
  • If White plays the opposite corner,  Both players are better off passing,  which leaves an even board  (otherwise,  the opponent captures two stone and control the whole board).

 Come back later, we're
 still working on this one...

Behing the rules of Go  by  Charles Matthews  (NRICH, May 2002 / Feb. 2011).
 
Go without bordersPlaying Go on a 19 x 19 Torus (14:39)  Michaela Gallucci  (2018-12-11).


(2019-01-08)   Combinatorics of Go
Enumerating the number of legal Go configurations.

This is usually done without considering the limited number of stones and discarding the actual  reachability  of a given board configuration  (whether there exist or not an actual game which can reach that configuration).  The only constaraint is that every  chain  on the board must have at least one  liberty.

For example,  in the case of the  2 x 2  board,  there are  N = 4  nodes.  That yields  3N = 81  raw  configurations  (legal of not)  which is just the number of assigning one of three states  (black, white or vacant)  to each of the  N  nodes.  From that,  we must subtract the 2N = 16  configurations without  any  vacant nodes  (in which case case no chain can possibly have any liberty).  The only other type of illegal configuration is formed by one stone in a corner, surrounded by two opponents  (so it doesn't have any liberties)  with the fourth stone being vacant  (we've already tallied configurations without any vacant node).  There are  8  such configurations  (the lone stone can be of one of two colors in one of four bpossible corners).  So,  the number of  legal  configurations is:

57   =   81  -  16  -  8

That precise enumeration  (A094777)  was completed by  John Tromp  (with  Michal Koucky)  for all square board up to 19 by 19  (2016-01-21).

123456
157126752431816541429514874162567386502084877
78
83677847847984287628595990966953618170260281935463385
9
103919148791293834318983090438798793469   =   1.0392 1038
1011121314
9.6498 1046 7.9347 1056 5.7774 1067 3.7250 1079 2.1267 1092
1516171819
1.0751 10106 4.8131 10120 1.9079 10136 6.6972 10152 2.0817 10170

This is to say that the number of legal configurations on a 13 by 13 goban is nearly equal to our current estimate of the number of elementary particles in the observable Universe.  The number of legal configurations on a 19 by 19 board is vastly more than the  square  of that.


 5 by 5 goban (2018-12-29)   Nalimov tables for endgames or small grids.
How Go was solved for a 5 by 5 goban.

The  Nalimov  approach can be used,  which requires no more than one byte of computer storage for each reachable situation  and a time proportional to the number of such situations.

Using black/white symmetry,  we only have to consider the board configurations where Black has to move.  With a playing grid of N nodes  (N=361 for the standard goban)  the number of situations to evaluate is certainly less than  3  to the power of  N.  Divide that by  8  for a square grid if we analyze it using the  8 symmetries of the square.

To save on storage requirements  (at the cost of greater programming complexity and clever address encoding)  we need only consider boards with no more than  N/2  stones of either color.  Using  H  to denote the largest integer not exceeding  N/2,  the total number of such situations is:

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 19 by 19 Orthodox Opening

Play Go :   Tactics  &  Strategy


(2018-12-20)   Openings   (fuseki).
What to play first.

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Fuseki   |   Shinfuseki   |   Chinese fuseki   |   Go opening theory
 
Fuseki overview (18:10)  by  theduddha2  (2012-09-03).
Go Opening Strategies (9:47)  by  Stephanie Yin, 1p  (NYIG, 2018-04-30).
Traditional Opening Theory (1:13:59)  by  Nick Sibicky  (#42, 2013-07-13).
Opening Basics (25:19)  by  Jonathan Hop  (Sunday Go Lessons, 2014-02-21).
The High Chinese Opening (20:28)  by  Jonathan Hop  (Sunday Go Lessons, 2014-02-21).
The Oldest Game, c. AD 280 (27:57)  by  Nick Sibicky  (#229, 2016-12-10).


(2018-12-16)   Things to Avoid

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Seven things to avoid when playing Go (42:54)  by  theduddha2  (2013-04-27).
Top 8 Go mistakes in June (32:06)  by  Stephanie Yin, 1p  (NYIG, 2018-07-16).
Top 9 Go mistakes in July (25:00)  by  Stephanie Yin, 1p  (NYIG, 2018-08-20).
Top Go mistakes in August (22:05)  by  Stephanie Yin, 1p  (NYIG, 2018-09-10).


(2018-11-16)   Shapes
The power of local patterns.

Shapes  are elementary stone configurations which are occasionally used to describe more complex situations.

  • Bamboo joint
  • Table
  • Mouth
  • Hane
  • Dumpling shape
  • Tiger's Mouth
  • Empty Triangle
  • 1-space Jump
  • 2-space Jump
  • Knight's Move  (keima). 
  • Large knight's Move  (ogeima). 
  • Elephant's Jump

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6 good shapes and 6 bad shapes.  The lists of Victor Chow  (1976-).
 
Basic Shapes in the game of Go (15:21)  by  Jonathan Hop  (Sunday Go Lessons, 2014-02-20).
Good and bad shapes (14:52)  by  theduddha2  (2012-06-27).
The Good the Bad and the Ugly  (1:20:18  |  56:57)  by  Nick Sibicky  (April 2013).
Making better shapes (58:50)  by  Nick Sibicky  (2014-12-13).


(2018-12-05)   ladder  is a sequence of  ataris  in a regular pattern.
loose ladder  guides the growth of a chain so its  air  never increases.

If you don't know ladders, don't play Go.

Most commonly,  the term  ladder  is applied to the simplest case described below,  which is most commonly encountered.  Because this pattern is so well known,  even to beginners,  it's rarely acted out  (see famous exception in the footnotes)  but serves as a threat which calls either for a clever answer  (tesuji)  or a  tenuki  abandonning the stone(s) in  atari  early on.

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Ladder   |   Ladder-breaker   |   Loose ladder  (yurumi shicho)
 
Lee Sedol's 2003 Ladder Game  (18:38 | 21:55 | 7:41)  by  Nick Sibicky  (#9, 2012-07-08).
Lee Sedol's 2003 Ladder Game Redux (58:56)  by  Nick Sibicky  (#205, 2016-07-15).


(2018-12-05)   Nets.  Inescapable captures.
Traps which the opponent can't slip through.

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Net (geta)   |   Knight's net
Nets and Ladders (10:15)  by  Jonathan Hop  (Sunday Go Lessons, 2016-03-11).
Ladders and Nets (19:08)  Michael Gallucci  (#E4, 2016-03-07).


(2019-01-05)   Snapback
A sacrificed stone may allow greater captures.

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Snapback (31:36)  Jim Plays Go  (#15, 2016-03-26).


(2018-12-12)   Eyes and Eye-shapes.  Life and death problems.
Elementary reasons why a group is  alive  or  dead.

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Eye shapes

The shape formed by the vacant nodes you are surrounding tells whether or not you can carve two eyes in it.

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Eye shapes   |   Alive
 
Life and Death (21:11)  by  Shawn Ray, 4d  (#2, 2014-07-16).
Life and Death:  Living eye-shapes (30:33)  TheDuddha2  (2013-10-29).
Life and Death:  Dead eye-shapes (14:42)  TheDuddha2  (2013-11-08).


(2018-12-12)   Seki   (shared life).
Configurations where neither player can play without losing.

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Seki   |   Alive


(2019-01-07)   Tesuji
Finding nice moves.

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Tesuji
 
Get Strong at Tesuji (27:09)  Michaela Gallucci  (2018-12-07).
Tesuji Time (44:20)  by  Nick Sibicky  (#204, 2016-07-11).


(2018-12-19)   Joseki
Some common sequences of moves.

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Must-know 4-4 josekis (1:01:00)  by  Nick Sibicky  (#6, 2012-04-04).
Five 3-4 dan joseki mistakes (16:15)  by  Stephanie Yin, 1p  (NYIG, 2018-11-13).
Common Star-Point Joseki, for 19k-10k (9:50)  by  Ryan Li, 1p  (NYIG, 2018-07-02).
Common 3-4 Point, High Approach Joseki, for 1d-2d (12:42)  by  Ryan Li, 1p  (NYIG, 2018-09-17).


(2019-01-09)   Framework   (moyo).
A staked zone to be consolidated and/or defended against  invasions.

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Defending Moyos (53:12)  by  Nick Sibicky  (#273, 2017-11-06).
More Defending Moyos (1:09:32)  by  Nick Sibicky  (#274, 2017-11-13).


(2018-12-11)   Invasions
How to invade.

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Introduction to Invasions (19:11)  Michael Gallucci  (2015-10-13).


(2018-12-21)   Endgame

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Counting and Endgame Workshop (30:58)  by  Nick Sibicky  (#231, 2016-12-21).

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People  &  Places


(2018-11-20)   Ranks and Titles
The  dan  and  kyu  system was introduced in  Go  before the martial arts.

The basic system was introduced in Japan early in the  Elo period  by  Hon'inbo Dosaku (1645-1702)  the strongest player of his era,  by far.

Originally,  the difference in ranks was supposed to be the number of handicap stones which is to be awarded to the weaker player to make the game balanced.  That only applies to kyus and amateur dans  (see below)  when that difference is not too large  (for one thing,  a game is rarely played with more than  9  handicap stones).  The modern dan system for top professional players is entirely different.

Amateur beginning and intermediate ranks go from 30th kyu (30k for a beginner barely knowing the rules) to  1k.

Kyu ranks merely mark progress in learning and can be self-awarded or handed out by one's Go teacher in an educational environment.  Beyond  first kyu  (1-kyu or 1k)  one is considered an expert and may be awarded a  dan  rank based on an institutional evaluation and/or results in tournaments,  starting with  first dan  (1-dan or 1d).  Unlike the kyu scale where a lower number indicates a stronger player,  the dan number increases with the strength a player demonstrates.

It's usually considered that there ought to be a difference of  two  handicap stones between a  1k  player and a  1d  player.  This gave birth to the unofficial existence of a zeroth rank in the two scale  (0k = 0d)  with a difference of one stone above or below the extreme rank of either scale.  The formula for the number of stones between a  k-kyu  and a  d-dan  player is thus extremely simple:

# of handicap stones   =   k + d

To that traditional handicapping system can be substituted a rough equivalent based on  Elo ratings  obtained results in actual matches.  This is what's used internally for correspondence games through the  DGS  online system.  They consider that a difference of 100 Elo points correponds to a one-stone handicap.  There's no mathematical reason why this should be so and it isn't,  but close enough.  We've adopted their system at face value for kyu levels in the following table.  Following the viewpoint advocated by the New-Zealand Go association  (as expounded above)  we've allowed for a lareger gap of two stones  (200 Elo points)  between 1 kyu and 1 dan.  Finally, we have accepted an assessment due to the legendary  cho Chikun  who said that there's a difference of 7 stones  (700 Elo points)  between 1 dan among amateurs and 1 dan among professionals.  The estimated Elo rating between two rungs of the professional ladder  (30 Elo points)  is consistent with the received wisdom that a difference of three ranks amounts to a little bit less than one stone of handicap.

Unlike an Elo rating which varies with the result of each game,  the dan rank  (and/or professional status)  of a player is awarded for life.

Unified Scale of Go Ranks
AmateurProEloColor Notes or relevant advice:
 8d9p3140 
8p3110
7p3080
6p3050
5p3020
4p2990
3p2960
2p2930
1p2900
7d 2800
6d2700
5d2600
4d2500
3d2400
2d2300
1d2200Shodan
0k0dTickling shodanOne stone below  1d  or one stone above  1k.
1k2000Red Belt
2k1900Brown
Belt
3k1800
4k1700Purple
Belt
5k1600
6k1500Blue Belt
7k1400
8k1300
9k1200Green
Belt
10k1100
11k1000
12k900Orange
Belt
13k800
14k700
15k600
16k500Yellow
Belt
17k400
18k300
19k200
20k100
21k0White
Belt
22k-100
23k-200Stake territory with loose jumps.
24k-300Open on corner lines 3, 4 or 5  (but not 5 & 5).
25k-400Clueless beginner.
Just knows the rules.
30k
The above belt colors (similar to those in martial arts) are all but unused in Go.

The above table is incompatible with the system used by the  AGA  in North America,  where top amateurs are routinely awarded  8d  and  9d  amateur ranks.

In Japan,  amateur  8 dan  rank is only awarded to  winners  of the World Amateur Go Championship  (WAGC, since 1979)  or national amateur championships of the stature of the Japanese  Amateur Honinbo.

There is fierce competition among young Japanese apprentices  (insei)  to achieve professional status through the rating tournaments held every Saturday and Sunday throughout most of the year.  About  5%  become professionals  (for life)  each year.  Anyone who hasn't achieved professional status by the age of  18  is discouraged from pursuing a Go career.  There are about  400  Go professionals in Japan.  Progression on the professional dan scale depends on the number of games won in professional tournaments.  It takes 30 wins to be promoted from the professional entry-level  1 dan  (1p)  to  2 dan  (2p).  Subsequent promotion require a greater number of new wins  (losses don't count).  A freshly-promoted 8 dan professional player  (8p)  will need  200  more wins to earn the ultimate promotion to 9 dan  (9p).

Number of professional wins needed for promotion from one rank to the next
1p30 2p40 3p50 4p70 5p90 6p120 7p150 8p2009p

In addition,  at the end of every season,  the two players of every rank below 6-dan who earned the most money  (in the top 12 professional tournaments)  among their peers are promoted to the next rank.  Likewise,  the top-earner among 6-dans is promoted to 7-dan.

Fast promotion to 7p,  8p  or 9  may also be obtained from top results in major tournaments.  For example,  Piao Wenyao (1988-)  was promoted directly from  5p  to  9p  in 2011 for winning the 15th LG Cup  in Korea.

The term  10 dan  (Judan)  isn't a proper rank but the honorary title given to the winner of the eponym professional tournament.

The following Japanese names may be applied to holders of a dan rank,  either  in the professional or amateur scale.  Only  shodan  (1 dan)  seems commonly used in English.

123456789
Shodan
(Ichidan)
NidanSandan Yodan
Yondan
Godan RokudanNanadan
Shichidan
HashidanKudan

Zeroth kyu  =  Zeroth dan   |   Go ranks and ratings   |   Go professionals
 
Go ranks compared to martial arts  by  Nadoss  (2013-12-17).   |   Go ranks worldwide variations
Nihon Ki-in promotion system for professionals (since 2003).
 
Ratings and Rankings (25:15)  by  Nick Sibicky  (#126, 2015-06-20).


(2018-12-13)   Go Clubs and Venues

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List of professional Go tournaments.


(2018-12-07)   Go Tournaments

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List of professional Go tournaments.


(2018-11-18)   Go Champions
Stars of the Go world.

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Hon'inbo Dosaku (1645-1702)
Utaro Hashimoto (1907-1994)   |   Minoru Kitani (1909-1975)   |   Go Seigen (1914-2014)
Rin Kaiho (1942-)   |   Otake Hideo (1942-)   |   Kato Masao (1947-2004)
Takemiya Masaki (1951-)   |   Kobayashi Koichi (1952-)   |   Cho Chikun (1956-)
Michael Redmond (1963-)  was the first Westerner to reach  9-dan  (in 2000).
Park Junghwan (1993-)  was the youngest Korean 9-dan, at the age of 17  (in 2010).
Shin Jinseo (2000-) 
 
List of Go players   |   List of top title holders in Go
 
Animation:  History of the world's best Go players (5:03)  by  Abacaba  (2016-03-16).


(2018-12-03)   Robots Playing Go
The stunning rise of  AlphaGo.

In March 2016,  the computer program  AlphaGo  defeated the  9-dan  Korean professional player Lee Sedol (1985-).

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How the Computer Beat the Go Master  by  Christof Koch  (SciAm, 2016-03-19).
 
AlphaGo vs. Fan Hui, 2p (18:24)  Game 1  (2015-10-05).


Continued on  Part 2,  coming soon...

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Essential Go Jargon
Commonly-used Go terms,  in alphabetical order.

In English,  the Go subculture has its own technical jargon,  with many terms borrowed from Japanese.  Here's a subset which no Go player can possibly avoid  (work in progress).

  • Adjacent.   Said of two nodes with an  edge  (grid line)  beween them.
  • Air.   See  liberty.  The set of all the  liberties  of a  chain.
  • Aji.   Potential for development of a  group  (notably,  to secure  territory).
  • Atari,  in Atari  (Korean dansu).  When a  chain  can be captured next.
  • Attach.   Play  adjacent  to an opponent but not to a friendly stone.
  • Baduk  (or  paduk).   Korean name of the game of Go.
  • Capture.  Remove from the board a  chain  of stones with no  air  left.
  • Chain  (or  string).  Maximal  solidly-connected set of stones of one color.
  • Cut
  • Connect.  Put a stone at a node adjacent to two distinct chains of one's own color.
  • DameVacant  node  path-connected  to both colors.
  • Dango  (dumpling shape).  Solid block with no  eyes  and few liberties.
  • Double-hane  (nidan-bane). 
  • Dumpling shape.   See  dango.
  • Edge.   Short line between adjacent  nodes.  (Inherited from  general Go.)
  • Empty.   See  vacant.  (Also termed  free  or  unoccupied.)
  • Extend.  
  • Eye.  
  • Eye in the belly.  
  • Eye space.   A  vacant  portion of the  grid  large enough to host  eyes.
  • Flooding.   A recursive process which determines respective  territories.
  • Framework.   See  moyo.
  • Free.   See  vacant.  (Also called  unoccupied.)
  • Fuseki.   Opening pattern.
  • Group.   Maximal  set of  path-connected stones.  (It needn't be a  chain.)
  • Half-eye.  
  • Hane.  
  • Intersection.   Synonym of  node  or  point [1]  unused in  general Go.
  • Joseki.   Sequence of localized expert moves worth memorizing.
  • Komi.   Agreed-upon compensation  points  for starting second.
  • Ko threat.  
  • Ko  (Korean: pae).  
  • Liberty,  liberties  (air).   Vacant node(s)  adjacent  to any stone of a  chain.
  • Moyo  or  framework.  Zone of influence to either consolidate or defend.
  • Nakade.  
  • Node.   See  point [1].  (Node  is the preferred term in  generalized Go.)
  • Optimal  sequence of moves.   When both players do what's best for them.
  • Path.   Connected set of  nodes  colored alike or  vacant.
  • Pincer.  
  • Point.  The term is best reserved for the second usage below.
    1.   (See  node.)   Intersection of two lines in the usual  goban  grid.
    2.   The unit used to tally  scores  at the end of a game.
  • Prisoner.   Captured  stone  (usually stored in the lid of one's go-bowl).
  • Push.  
  • Reading:   Anticipating  near-optimal  moves implied by a board position.
  • Seki.  
  • Sente,  in sente.  
  • String.   See  chain  (I recommend that latter term.)
  • Squash  (oshi-tsubushi).  
  • Tiger's mouth  (shape).  
  • Tenuki.   Play away  [from the vicinity of the latest moves].
  • Territory.   All nodes  path-connected  to stones of only one color.
  • Tesuji.   Clever play.
  • Unoccupied.   See  vacant.  (Also called  free  or  empty.)
  • Vacant  (emptyfreeunoccupied).   Said of a  node  with no stone on it.
  • Weiqi  Chinese name for Go.  Formerly  wei-ch'i.  Pronounced  way-tchee.

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Baduk Glossary (Korean)

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