The traditional board game go (igo, baduk, or weiqi) has a number of national, regional and online systems of measuring levels of skill, as ranks and ratings. A go rank is comparable to a rank in some Asian-originated martial arts. A rating rigorously calculated on the basis of game results is less traditional (common on go servers). There is no universally applied system, but within most systems and at most levels, one handicap stone is given as the difference between each level. On this basis there are more than 40 distinct levels.

Go ranks

There are three main types of rank: kyu (級,급) (gup in Korean), dan (段,단), and professional dan. The means of awarding each of those ranks, and the corresponding levels of strength, vary from country to country and between online go servers.

Kyu (pronounced like the letter "Q" and abbreviated as 'k') ranks are for beginners, and start at around 30 kyu (30k), and proceed numerically downward as strength increases to 1 kyu. Grades below 30 kyu may have limited usefulness in teaching young children, since there are discernible differences in level; a player playing a first game of go is likely to be in the range of 40 to 30 kyu. Players in the weak kyu ranges often progress very quickly, especially young children, and may not attain stable rank until they reach single digit kyu (SDK, 9k to 1k).

One rank higher than a 1 kyu player is a 1 dan (1d), also called shodan in Japanese (roughly, "entry-level expert"). The 1 dan rank is achieved when all elementary and essential go concepts are mastered, implying a general competence in the game. This usually requires a number of years of playing seriously, though exceptionally talented players have risen from first exposure to the game to shodan in a year. Recognition as a dan player is the ambition of most club-level players (average club standard can be taken to be around 4 or 5 kyu).

Dan ranks ascend numerically with strength, to a normal high of 7 dan. A very few amateurs have proved very strong, even against professionals, though they do not have an official, professional rank. The conventional wisdom is that such players may achieve some of the insight of a pro, though perhaps not the detailed knowledge.

In the kyu and amateur dan ranks, the difference in ranks is a good guide to how many handicap stones may be given to adjust the game for a more even struggle. For example, a 3k player would normally give a 7k player four handicap stones. When the difference in ranks is only one, then no handicap stones are used. When ranks are equal, it is common to give a point advantage (komi) of 6.5 (Japanese rules) or 7.5 (Chinese or AGA rules) to the player using the white stones to compensate for moving second.

Beginners often play the first few games on 99 or 1313 boards. Then, each handicap stone will compensate a difference of several ranks. Given 5 handicap stones on a 99 board, even a beginner is hard to defeat.

Professional strength

Professional ranks are at a standard that requires devoted study, not just competition play. The existing systems, for historical reasons, consist of nine levels, also called dan. The differences between professional levels are much smaller: perhaps of the order of three handicap stones between an average 1p and a prime 9p. To distinguish between amateur 5 dan and pro 5 dan the former is often written 5d and the latter 5p; this is not generally used as an abbreviation beyond the Internet, where it is common, but not universal.

A professional rank is currently only attained through competition in Japan, China or Korea through one of the professional go associations, most notably, the Hanguk Kiwon (Korea) or Nihon Ki-in (Japan). The highest professional rank is 9 dan pro, or 9p. There are currently over one hundred people who have the rank of 9p, though many of them no longer play competitively, due to age. A further distinction is that some 9p players regularly hold titles, some won some titles, some entered the title leagues and many 9p never had the luck to achieve any of above.

Qualification as a professional depends on the country. In China a few amateurs are given the 1p grade as probationers, on the basis of success in amateur tournaments. In Japan student professionals are called insei, and have to play in internal insei competitions to qualify; mostly they are adolescents, and must decide whether to continue based on their chances of a career in go, or go to university. Insei rarely take part in amateur events, but some of the top amateurs are ex-insei. In South Korea four amateurs become professional every year, at the top of a ferocious league system of 80 aspirant pros. Once within the professional system, promotion is based on game results. The Japanese Oteai system, dating back to 1924, was reformed in 2004 to alleviate some rank inflation that had crept in over the years. Today's system uses various benchmarks; for example, winning certain tournaments or a certain number of games, to be promoted a rank. The Korean system has also been similarly changed in the past few years. A professional's rank may rise, but never fall.

The game of go requires study from an early age, should one wish to become a strong professional player. In order to qualify as a 1 dan professional (1p), one must have deep resources of game experience and study. Tactically, professionals thoroughly understand good shape , tesuji, and life and death. Pros mostly have similar levels of pure technical skill. They differ more in positional judgement: deep evaluation of future game positions and a great variety of tactical and strategic means to obtain that imagined future position are requirements for professional players. It is of basic importance for a player to know whether they are behind or have the advantage, because it influences the risks that should be taken and subsequently the stategies chosen in a game.

Knowledge of tactical opening patterns (joseki) is a by-product of years of study and playing Go; memorization is not the basis for strong play. Joseki knowledge is far less central in Go than openings are in Chess. The decisive part of the game, resulting in win or loss, may occur 100 moves or more later.

Pro and amateur ranks

In China, Japan, and Korea, there are two distinct ranking sets, one for amateur players and one for professional players (who receive a fee for each game they play, bonuses for winning, and fees for other related activities such as teaching). In the Japanese professional ranking system, distinction between ranks was traditionally considered to be roughly one third of a handicap stone (making the difference 3 pro dan equal to one amateur dan). The strength of new professionals (1 dan) was usually comparable to that of the highest ranked amateurs. Currently the professional ranks are assumed to be more bunched together, covering not much more than two amateur dans; so that pro 1 dans win some games against 9 dans. There are also a number of amateur players acknowledged as having pro 6 dan understanding of the game.

In Taiwan a distinctive system of pro dan ranks is used, with the order reversed (so that 1 dan is the highest, 9 dan the lowest).

In Japan, amateur ranks are only recognised up to 8 dan. Before the year 2001, only amateur ranks up to 7 dan were recognised. 8 dan is also awarded to the winner of the World Amateur Go Championship. Within the European Go Federation, ranks are recognised up to 7 dan. The American Go Association currently recognizes rankings up to 6 dan amateur.

Player pools that do not regularly mix (such as different countries, or sub-groups on online servers) often result in divergent playing strengths compared to the same nominal rank level of other groups. Players asked to give their rank will therefore often qualify it with "in my country" or "on this Internet server".

In Germany and The Netherlands a "classes"-system (German: "Klassen") was established. It comprised a further subdivision into Kyu/Dan halfgrades with classes 18 and 17 = amateur 1 dan with the 17 being on the stronger side. It is still in use for club ladders etc. where you get promoted or demoted after a won or lost game, respectively. [Image:http://www.gobond.nl/images/dan-kyu2.gif|right| Kyu-Dan-classes]

Go rating with ELO

As in other sports where it is not practical to hold an all-against-all championship to establish who is strongest (Chess, statistical Backgammon, physical Racquetbal etc.) a statistical method is employed. The ELO rating system is nowadays often used in Go (see also external links). An average 1 dan should have Go Rating about 2100 and the difference between grades is set to 100. Hence, a rating of 2100 would coincide with an amateur 1 dan who has a 2/3 winning chance against just anyone with a recent rating of 2000 (an average 1 kyu, a recently improved 2 kyu or, e.g. a 1 dan who has lost many games and so rating points).

Similarly the same player only has a 1/3 winning chances against any player with a recent ELO rating 100 points higher than oneself. Here one can see the difference between ranks kyu/dan, being the highest personal achievements and an actual rating. A player having been 3 dan 15 years ago will know the necessary strategies and concepts for teaching weaker players, but when it comes to actual play this person will certainly lose rating points when again entering the tournaments (where the rating points are measured) against players with the same grade.

Winning Probabilities

The rating indirectly represents the probability of winning against other rated players. This probability depends only on the difference between the two players' ratings as follows (based on a normal distribution with a standard deviation of 286):

  rating     probability
 difference  of winning
 ----------  -----------
    400       .919
    300       .853
    200       .758
    100       .637
     50       .569
      0       .500
    -50       .431
   -100       .363
   -200       .242
   -300       .147
   -400       .081

Converting Elo Ratings into Go Ranks

The Elo system can be used establish a Go grade (kyu/dan) by a national promotion commission or implement Go ranks on Go servers (on the internet).

 Points   Go rank
 ------   -------
  1600     3 dan       (this table here is inconsistent in itself & in comparision with text below) 
  1500     2 dan
  1400     1 dan

  2000      1 kyu
  1900      2 kyu
  1800      3 kyu

  1500      6 kyu
  1000     11 kyu
   500     16 kyu
     0     21 kyu

  -100     22 kyu
  -200     23 kyu
  -300     24 kyu   etc. 

Because of the low confidence in (lower) amateur ratings (high fluctuation in the outcome) but high confidence in pro ratings (stable, consistent play), the K-value in the formula

where Rn = new rating, Ro = old rating, S = score, Se = expected score and the constant C is 30 and 20 for players below ELO= 2.400 (e.g. 4 dan) and set C = 10 for players above. For Go, the variance of the Normal Probability Function is set at 100 ELO points and the constant K depends on the rating of the players involved.

In the ELO system the total number of ELO points of the player pool is only changed by changes of the pool and the players itself, e.g. newcomers and improvers. Because Go is a zero-sum, full information game the ELO points won by the winner are the ones lost by the loser and its maximum is the constant K above.

Because of the few played ranked even games between amateurs and professionals, it is difficult to establish a single ELO table where both pools are represented. Using the rough equivalence between handicap stones and rating difference (1 stone = 100 ELO points) a professional 9 dan (9p) would have +/- 2900 ELO points. For the winning chances of amateurs against professionals in even games the following has to be considered.

Winning chances are more than cumulative

On average the rating differences will be congruent with the ranking differences in the same system (same club, country or server). Go is usually played on even because players prefer it and resp. tournaments are organized that way. However, besides that point, the table with the winning chances set over the rating differences will only work in practice up to a small ranking difference correctly (ELO difference of up to 300-400 points.) If players with a higher inequality,, e.g. ELO difference = 900, normally requiring a handicap of 9 stones would meet in an even game, then the chances of the weaker player are not even a mere 0.0006 (0.06%) to win this game, rather they are zero! This can be explained by the fact that the probabilities of risks and gains can be moderated by the stronger player.

While in chess you had to take the full risk and must capture the opponent's king and, more difficult, avoid the possibility of draw, which in Go is excluded by the komi. An average game of Go lasts for 240 moves (= 120 double moves; compared to 50 in chess). There are more opportunities for weaker player to make sub-optimal moves for confirming the result (a loss). The stronger player would win on average with + 140 points (empirically established) in an even game with a person s/he has even chances on 9 stones.

The stronger player gains already with 1/2 points more (cf. komi) a win. By moderating the risk exposure and steering for a lower win in points (not a 50% chance for 140 points), this player increases the probability for this win. This behaviour increases the chance from 99.94% (1-0.06%) to 100%.

The ability of transforming small advantages (e.g. 5 points; eqivalent to the first move or half a grade difference) into sure wins increases much with playing strength. What is true for amateurs with an ELO difference of 900 holds as much for professionals with a smaller ELO difference. That is also the reason why the constant C in the formula above is set smaller for professionals.

Statistics on even games

The table shows statistics on winning a game with the opponent that is one (G+1), two (G+2), three (G+3) and four (G+4) grades stronger than the player whose strength is idicated in the first column. The data were collected from all events included in GoR tournament database.

          G + 1             G + 2             G + 3             G + 4

 G     Nw    Ng   Pw     Nw    Ng   Pw     Nw    Ng   Pw     Nw    Ng   Pw
--- ----------------- ----------------- ----------------- -----------------
20K   670  1950  34.4   422  1251  33.7   151   605  25.0    78   391  19.9
19K   303   769  39.4   136   447  30.4    56   191  29.3    28   126  22.2
18K   438  1005  43.6   230   579  39.7   123   330  37.3    29   122  23.8
17K   392   878  44.6   314   700  44.9    73   207  35.3    29   141  20.6
16K   543  1177  46.1   224   568  39.4    78   238  32.8    43   161  26.7
15K   567  1330  42.6   303   741  40.9   137   347  39.5    49   164  29.9
14K   489  1062  46.0   286   690  41.4    81   219  37.0    55   219  25.1
13K   568  1267  44.8   279   656  42.5   142   336  42.3    46   156  29.5
12K   609  1335  45.6   458  1078  42.5   129   314  41.1    39   183  21.3
11K   770  1653  46.6   323   795  40.6    89   253  35.2    35   150  23.3
10K  1038  2301  45.1   486  1196  40.6   117   432  27.1    72   296  24.3
 9K  1066  2329  45.8   453  1103  41.1   124   397  31.2    41   233  17.6
 8K  1089  2476  44.0   540  1361  39.7   146   449  32.5    52   246  21.1
 7K  1279  2857  44.8   577  1506  38.3   130   433  30.0    47   215  21.9
 6K  1533  3525  43.5   660  1625  40.6   185   573  32.3    57   292  19.5
 5K  1711  3900  43.9   807  2113  38.2   159   565  28.1    73   373  19.6
 4K  2058  4551  45.2   797  2057  38.7   189   690  27.4    55   359  15.3
 3K  2201  5116  43.0   876  2572  34.1   171   796  21.5    42   327  12.8
 2K  2356  5737  41.1   739  2402  30.8   112   652  17.2    28   346   8.1
 1K  2791  7169  38.9   687  2659  25.8   160  1069  15.0    43   508   8.5
 1D  2669  7012  38.1   869  3441  25.3   207  1504  13.8    44   757   5.8
 2D  1976  5752  34.4   683  2981  22.9   156  1291  12.1    19   468   4.1
 3D  1888  5424  34.8   673  3300  20.4   107  1362   7.9     1   136   0.7
 4D  1436  4675  30.7   341  2485  13.7     8   261   3.1     0     0    - 
 5D   918  3231  28.4    35   538   6.5     0     0    -      0     0    - 
 6D   100   664  15.1     0     0    -      0     0    -      0     0    - 

Number of games included in statistics: 137872 (date: 09/2004)

Notation:

         Nw - number of wins
         Ng - number of games
         Pw = Nw/Ng

The zeros in the last line (6 Dans vs. stronger opponents) just show a lack of data of amateur 6 Dans playing on even with 2, 3, 4? stones stronger (professional) opponents. The table as a whole proves the point made above (more than cumulative winning chances), that the winning chances of the weaker player become much smaller, the stronger the average strength of both players is. Confer the decline of winning chances in the 4th column from 20% with weak kyus to a mere 0.7% when Dan players are involved.

Depth of the game

The ELO rating depth also states something about the depth of the game. The total depth of a game is defined by two end points of the range of skills: the total beginner, and the theoretical best play by an infallible creature. The beginner, playing according to the rules, may be set at 30 kyu or weaker. Theoretical best play could conceivably result in the strength of a 13 dan, according to measurements of standard deviations among professional games. Taking 20 kyu and 9 dan as endpoints makes Go the deepest game. A rating difference of 2900 ELO points from Gu Li to a 20 kyu with 100 ELO points, a beginner, is a difference in insight into the game by 29 times the standard deviation.

Table of ranks

What the list on the right below can not show is the asymptotic shape of the skill improvement over time (diminishing returns). It is summarized in the saying "(Go is) Easy to learn and difficult to master". While a beginner could rush through from 35-30 kyu to 20 kyu in a few months - possibly weeks if the player has a mind for the game - the player might take several years to 10 kyu and another half decade to amateur 1 dan. The handicap between these stages would be about 9 stones each, but the time for achieving the levels is not equidistant, even if the effort might have been the same. Few make it to a 5 dan amateur ranking (i.e. ELO 2500 in Europe) and only after great enthusiasm and dedication, taking many, many years. The level reflects levels of abstraction of the game, knowledge of varieties of problem solution skills, correctness of evaluation resulting in the capability to choose better tactics and strategic plans from the growing range.

External Links

• ELO by the EGF
• An empirical table of winning chances over rating differences
• International Comparison of Ranks (external Wiki page)