The following text is an essay by Herman Hiddema. Comments are very welcome. If you have comments, please add them to the forum for this page (The "discuss page" link in the menu above), put them at the bottom in the discussion section, or if you want to put your comments in the text, please indent them by preceding them with a >
|Table of contents|
When it comes to board games, go and chess are two of humanity's foremost intellectual pursuits. Both have rich histories, enthusiastic playing populations and a wealth of written material on every facet of the game. It is therefore only natural that people compare these games. This essay strives to separate fact from fiction, to present a balanced view of the similarities and differences of go and chess, and to make some statement about the relative difficulty of these games. All opinions are my own, and I realize that I may well be wrong.
This essay is written from a western perspective. One of the realities in the west is that chess is much more well known than go. In the west, go is a newcomer, barely through its first century. Chess players, unlike go players, will not generally have to explain what this strange board game is that they are playing. Many go players have experienced first-hand the curiosity of people unfamiliar with the game of go. It is no more than natural, in such situations, to explain that this is a strategic board game "like chess, but different".
This essay is also written from a go perspective. Since chess is much better known, and has a playing population far in excess of that of go, a sizable part of the text deals with explaining certain basic facts about go. It does not explain chess basics as deeply, as the public is assumed to be more familiar with that. The author is a reasonably strong go player, but not so accomplished a chess player. If you find errors caused by a lack of understanding of chess, please feel free to let the author know.
One of the basic assumptions underlying this essay is that in both go and chess, top players are similar. They have dedicated their lives to studying their game, playing it at the very highest levels under a lot of competitive stress. There is no reason to believe that either game will attract inherently smarter people than the other, and so it is assumed that top achievements in go and chess are similar in how hard they are to accomplish.
Rules form the core of any game. Everything else —strategy, tactics, skill and competition— starts with the rules. It is often mentioned as an advantage to the game of go the the rules are so elegant and simple. The "Logical Rules of Go" comprise just 10 rules to completely and unambiguously describe the game. http://homepages.cwi.nl/~tromp/go.html
Despite these simple rules however, the goal of the game is sometimes hard to grasp. Although theoretically the goal is quite simple, many starting players find it hard to grasp conceptually. Catalin Taranu, one of the few western born professional Go players, has this to say on the issue:
The main reason for this seemingly strange inability to grasp a goal that is nevertheless well-defined, is the fact that chess has a knock-out winning condition. Once you checkmate your opponent, the game is over. Period. In go on the other hand, the game basically ends by mutual agreement. There comes a point in the game where making any further moves is either detrimental or pointless. At that point players will pass, indicating that they see no way to further increase their score. When both players have passed, the game is counted and the winner is determined. Passing however, requires a basic tactical insight in the game. A player must recognize that further plays are pointless or detrimental to be able to pass at the right moment. Thus go requires that a player understands some very basic tactics before really understanding the goal of the game. A sort of catch 22 of the rules of go. (Note: This problem is particularly strong with Japanese style territory rules, where life and death are actually part of the rules, and understanding them a requirement for successfully finishing a game)
Once a player understand these basics however, the strategy of the game of go quickly becomes obvious. It is easy to visualize the walling in of empty points, and many beginners will thus simply start building lines of stones around areas. Although not a particularly good strategy, it does allow the beginning go player to easily formulate a plan. In chess, we may compare this with a beginner tendency to try and capture pieces, completely ignoring positional play. Again, not a particularly good strategy, but at least it is a plan.
Both go and chess have a long and rich history. The history of go is somewhat older, starting at least 2500 years ago. The history of chess extends some 1500 years at least, with the current rules (Western Chess) being some 500 years old. In go, there is no similar concept of "current rules". The rules have remained basically unchanged for its entire history.
This longer history might give go a bit of an advantage when it comes to development of theory. Quite ancient texts already show an advanced level of understanding of the strategy of go. Theoretical developments in go made huge leaps forwards from the 17th century onward, when the Japanese shogunate formalized the study and teaching of go into a number of state-sponsored go academies. Members of these "Go houses" were able to dedicate themselves full-time to study of the game.
Further leaps forward were made in the first half of the 20th century. The so-called shin-fuseki (new opening) movement coincides with the development of hypermodernism in chess. Curiously, both shinfuseki and hypermodernism deal with new understanding of controlling the center of the board.
It seems safe to say that top Go players read deeper (more moves ahead) than top chess players. When asked about depth of reading, Kasparov once said that generally he reads 6-10 ply ahead, while occasionally reading as far as 24-28 ply ahead (the term ply refers to a single play by one player, in go terminology this is generally simply dubbed a move, but since in chess a move usually refers to two physical moves, one by each player, I will use the term ply here to avoid confusion). Only in very limited situations, such as certain endgames with many forced moves, are players able to read further ahead than this. In go, a similar thing is true. Generally, players will not read very deeply, but in important situations, they will go a lot deeper. Kitani Minoru, known to have good reading skill, was able to read some 40 ply ahead in a complicated tactical fight. (ref: TheTreasureChestEnigma). Again, in limited specific situations like ladders, where there are many forced moves, players can read much deeper, sometimes easily reading over 100 moves ahead (eg: LongestLadderProblem).
So top go players are apparently able to read about 1.5 times as far ahead as top chess players. Why is this?
As there is no reason to assume that a top go player is inherently smarter than a top chess player, this can only mean that in go, despite the larger board, reading ahead is actually easier. The increased reading depth may well be an inherent result of the visual nature of human thought. In chess, when you move a piece, two things usually change. One square becomes empty, another becomes occupied. Occasionally, a third change occurs, the removal of an opposing piece. In go on the other hand, most move just add a stone to the board, making only one change. Occasionally, the move may capture one or more opposing stones, resulting in two or more changes. To visualize the position after a certain number of moves is thus often easier in go than it is in chess, because it involves fewer visual changes. Indeed, it is well known in go that those situations where correct play requires an "under the stones" move, a move played on a position previously occupied by stones that have since been captured, are notoriously difficult for most players.
Chess was once regarded as one of the bastions of Artificial Intelligence. For a computer to play chess well, it was surmised, surely it must do something approaching human thought. Not so, it has been shown. Strong chess programs do not need a particularly deep understanding of the game. Simple brute force evaluation of millions of positions, in combination with opening and endgame tables, has allowed the computer to defeat the best players humanity has produced.
In go, the computer has not as of yet performed a similar feat, which again leads many people to believe that for a computer to play go well, it must somehow approach human thought. Go programs have long been struggling to reach even an average level of play. Recent developments in go playing programs however, have a similarity to what happened in chess. Programs utilizing "Monte Carlo UCT" techniques, which basically amounts to simulating millions of random games extremely fast, have finally broken the "average player" barrier. Such programs do not try to understand the game at all, but instead try focusing on what computers do best: Doing lots of simple calculations really really fast. Although it may be some time yet before the computer defeats the world champion, there seems little doubt that with enough time, it will eventually happen.
Update: as of March 2016, it is the case that a computer has defeated the Go world champion. https://techcrunch.com/2016/03/15/google-ai-beats-go-world-champion-again-to-complete-historic-4-1-series-victory/
The argument is sometimes made that go is more difficult than chess, because it has a broader rating range. A rating range in this context is defined in how many distinguishable levels of play there are between the strongest player and an absolute beginner. We might for example define that two players have a distinguishable level of play if one of them scores, on average, two points out of every three games they play (other numbers work equally well, but lets stick with these). In chess, a 67% score against another player is roughly equivalent to 150 Elo rating points. If we consider someone with an Elo rating of 500 as an absolute beginner, then there are about 15 distinguishable levels of play in chess. In go, a 67% score is roughly equivalent to one kyu or dan rank (except at the very top). If we consider someone who is 30 kyu as an absolute beginner, then there are about 40 distinguishable levels of play in go, almost three times as many. So it is true that go has this broader rating range. But what does that mean?
Consider the average length of a game. In chess, the norm is about 40 moves (80 ply), in go it is about 120 moves (240 ply). Which means that a go player has about three times as many opportunities to "make a difference". So a much smaller difference in skill may get inflated because the stronger player has more time to make that difference count. Indeed, consider the scenario where chess was not played on single board, but where in fact the players played three boards simultaneously, and where any positive score (3-0, 2.5-1.5 or 2-1) means victory for a player. In such a setup, the stronger player could score, on three different matchups, 2-1, 1.5-1.5 and 1.5-1.5 (one victory, two draws) or 2-1, 1-2, 2-1 (two victories, one loss) and still be considered to have achieved a 67% score overall despite winning only 5-4 if all separate boards are counted. In this scenario, a much smaller difference in skill will already express itself as a distinguishable level of skill.
So we can say that go as a whole is deeper in the sense that it has more moves, but that each individual move is probably roughly equally difficult. Finding the best move from a given position is thus probably about equally challenging in both chess and go. It would be interesting to see statistics about how many different moves top players consider before deciding on one. All in all, the increased length means that Go is harder to play perfectly, more moves give more opportunity for error, but I see no reason to assume that the difference in skill between top players and beginners is any different in go than it is in chess, or that top level playing skill is any harder to achieve in either game.
Dieter: Very well crafted article. A few remarks:
Thank you :-)
Herman: I think that even with a simple, well defined goal like that used in the stone counting teaching method, beginners still run into the problem that they need to understand when to pass, as illustrated by stone counting teaching method/ filling the board. No matter how you formulate the goal, it is still pretty much an "end by mutual agreement". I do think that a simplified goal is certainly better than the vague "you surround territory, but you don't need to capture dead stones", where we're basically asking beginners to understand life and death as a condition to understanding when to pass. I also think that the "knockout" goal can be considered an advantage of capture go.
Herman: If a player plays 3 matches, with resuls 2-1, 1-2, 2-1, he has won 2 matches, and lost 1, for a score of 2/3 (matches). But if we sum the board points, its 2+1+2 - 1+2+1 = 5-4. So a player capable of winning 55% of games has thereby won 67% of matches. (the same applies to the 2-1, 1.5-1.5, 1.5-1.5 case, where the match scores are 1-0, 0.5-0.5, 0.5-0.5 = 2/3 but again the summed board points are 5-4).
Herman: I may not have put this well. The intention of this section was to show that go is deeper than chess, but that this is almost certainly a result of the number of moves, and that each individual move involves a similar level of difficulty. It would be interesting if there were solid statistics for go and chess to see how many different moves top players consider on each turn, and how deep they calculate each one before (possibly) discarding it. My guess would be that both go and chess players take a similar number of moves into consideration. I assume this number is higher than in 4-in-a-row, where you can never consider more than 7 different moves, and may discard many of them quickly as "losing immediately". (I have now incorporated this into the section in question)
Andy: Is blindfolded go common, that is, no board the players can see is used? Blindfold chess if very common, but I haven't heard of go being played this way. Actually, I take that back. I seem to recall some special coordinate system (AudouardCoordinates) used for this purpose with go. How about a link to that page in the library? Is it widely used for blindfold go?
Herman: Blindfolded go is extremely uncommon, as far as I know. The AudouardCoordinates were invented by Pierre Audouard who is almost entirely blind (and will go blind in the future). There are some blind go players, but they use a special board where they can feel the stones (so they do not need to memorize the position as you would with blindfolded go). What is somewhat common is one color go, where the players know where the stones are, but have to memorize which ones are what color.
Now the implied question here, I assume, is how the availability of blindfolded chess and the absence of blindfolded go reflect on the games, and how it highlights differences or similarities. A very interesting question, I think. I will start with some research that has been done into this in chess:
If you show a strong chess player a position from a game in progress. He can generally memorize it within 5 seconds, and will be able to recreate the position on another board. Show that same strong chess player a position that is completely random, where any piece can be anywhere (including pawns on the first/last line, etc) and he will not be able to do the same thing. What this shows is that chess players do not remember positions, they remember patterns (White has castled here, black has set up an attack on that bishop there, etc). So in effect, the strong chess player is not remembering the position, but quickly analyzes roughly how it was created and remembers that.
Dieter: I believe there is a little bit more to that. The lecture of Jeff Hawkins' "On Intelligence" has taught me our memory is based on prediction and confirmation. A position from a game in progress will look familiar, because many pieces are on a position or in a relation with each other which can be expected. The effort goes into memorizing where prediction is not confirmed. In a random position, no prediction is confirmed, so a whole new reference framework has to be built instantly. Time is another key factor of memory, which is greatly affirmed in your argument.
From my own experience with one color go, go players do the same thing. They do not actually memorize which stones are what color, they memorize what sequence was played and can deduce from that which stones are where.
The problem for go players, and the probable reason that blindfolded go is so rare, is twofold. One problem is the much longer game. A chess player playing blindfolded chess generally needs to remember less than 40 moves (80 ply), a go player will need to remember over 100 (200 ply). The second problem is that go is an additive game, while chess is a subtractive game. In go, the board is slowly filled with stones, making the position more and more complex (from a memorization viewpoint). In chess, the board slowly gets emptier as pieces get captured, making the position simpler (again, from a memorization viewpoint).
Anonymous: Not sure if I am editing this properly. Nice article, but the section on computers and chess/go is completely erroneous. Computers and chess is a very complicated topic. It is not correct that computers can beat the top human players based on brute force calculation of millions of positions. Without exception, every strong computer chess program has enormous amounts of knowledge (databases which may contain the complete moves of tens of millions of recorded games, likely much more than this), as well as heuristics, which were based on human thought processes. It is well known that a computer with just these components will play poorly. In addition, it requires enormous brute-force calculation. As an example, the computer that Kasparov played could look at 200 million moves per second. On average one has 3 minutes to make a move in a tournament game. What is that, 160 trillion moves per turn? And the reason this occurred is that IBM had 15 full-time computer programmers working for 2 years, invested upwards of $50 million dollars, and hired one of the top human chess-players to work with this team. Until this investment of time, money, computer hardware, and the assistance of one of the top go players in the world to work full-time on a go program, one cannot say how good a top go program will be. One cannot remove the element of Western interest (and many other countries) in chess with Western interest in go, and the development of top programs. People also began seriously working on chess programs in the 1960s. I do not know that there have been several decades of work on computer go programs.
Liso: interesting articles could be http://www.go-baduk-weiqi.de/go-bot-go/ and http://www.chess.com/article/view/how-rybka-and-i-tried-to-beat-the-strongest-chess-computer-in-the-world (where stockfish has not database and just with (brute?) force could beat pair <human grand master + computer program rybka>)
Herman: Thanks for the comment! I've made a slight adjustment to the section in question. The point of the section was not really to go into detail on how computers are so good at chess, but to touch on the fact that in both chess and go, the successful approaches seem to be based mostly on what computers do well (brute force calculation, near unlimited recollection of openings and endgames, and things like that) and not on anything similar to how the human mind works.