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The traditional board game go 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 martial arts, for example karate. A rating calculated on the basis of game results is something less part of the traditional way of thinking. There is no universally applied system. It is generally agreed that the number of distinct levels of skill in go is as many as 50.
There are three main types of rank , kyu (級,급) which is 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.
Kyu (pronounced like the letter "Q") ranks are for beginners, and start at around 30 kyu (30k), and proceed numerically downward as strength increases to 1k.
A 1k player is one rank weaker than a 1 dan (1d). Also called shodan in Japanese, the 1d rank is achieved when all elementary and essential go concepts are mastered.
Dan ranks ascend numerically with strength, to a normal high of 6 or 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 the insight of a 6 dan pro (normally able to give a 6 dan amateur at least two stones).
A professional rank is currently only attained through competition in Japan, China or Korea through one of the professional go associations, most notably, the Nihon Ki-in. 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 perform 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 most 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 take a decision whether to continue based on their chances of a career in go, versus going 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 abolished quite recently, and the Korean system has also been changed in the past few years.
The game 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. Tactical means such as good shape, tesuji, life and death are throughly understood by professionals. Pros mostly have similar levels of pure technical skill. They differ more in positional judgement: deep evaluation of future game positions and a vast variety of tactical and even strategic means to obtain that imagined future position are prerequisites of professional players. It is of basic importance for a player to know whether s/he is behind or has the advantage, because it influences the risk aversion and subsequently the chosen stategies.
The knowledge of josekis patterns is a by-product of years of study and playing Go and 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 only 100 moves later.
In China, Japan, and Korea, there are two distinct ranking sets, one for professional players (who receive a fee for each game they play, bonuses for winning, and fees for other related activities) and one for amateur players. In the Japanese professional ranking system, distinction between ranks was traditionally considered to be 1/3 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). Within 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 online versus real-life player groups) often result in divergent playing strengths for the same rank level. 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 pro-/demote after a won/lost game. [Image:http://www.gobond.nl/images/dan-kyu2.gif|right| Kyu-Dan-classes]
As in other sports where you cannot 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 quite used in Go (e.g. ). 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:
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).
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.
In Go the 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 exluded 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.
An empirical table of winning chances over rating differences can be found here :
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.
Number of games included in statistics: 137872 (date: 09/2004)
Notation: Nw - number of wins
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.
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.
Number of games included in statistics: 137872
Notation: Nw - number of wins
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.
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. Theoretical best play could result in the strength of an imaginable 13 dan, according to measurements of standard deviations among professional games. Taking 20 kyu and 9 dan as endpoints makes Go until now the deepest game.
A rating difference of 2900 ELO points from Nihon Ki-in
What the list on the right below can not show is the asymptotic shape of the skill improvement over time. 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 an evening, s/he might take a 1/2-1 year to 10 kyu and 4 years to 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 from there it might take a very enthousiast player more then 10 years to obtain this level. The level reflects levels of abstraction of the game, knowledge of varieties of problem solution skills, correctness of evaluation resulting in the capability to chose better tactics and strategic plans from the growing rage.
[Image:http://www.gobond.nl/images/dan-kyu2.gif|right| Kyu-Dan-classes]
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