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: 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).
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:
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:
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."
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:
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 nominalaspect ratio
for US grids is :
15 / 14 = 1.07142857...
That corresponds to the following viewing angle
q from vertical:
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).
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).
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.
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.
Kaya.
Torreya 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.
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).
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.
(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.
(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.
(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.
(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.
A chain is defined to be dead when all its liberties are flooded by the other color.
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).
(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).
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.
(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:
Play Go : Tactics & Strategy
(2018-12-20) Openings (fuseki).
What to play first.
(2018-12-05) A ladder is a sequence of ataris in a regular pattern.
A 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.
(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.
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
1p
30
2p
40
3p
50
4p
70
5p
90
6p
120
7p
150
8p
200
9p
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.
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.
Dame. Vacant 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.
(See node.) Intersection of two lines in the usual goban grid.
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 (empty, free, unoccupied). Said of a node with no stone on it.
Weiqi Chinese name for Go.
Formerlywei-ch'i. Pronounced way-tchee.
