Abstract. Who is the best chess player of all time? Chess players are often interested in this question that has never been answered author- itatively, because it requires comparison between chess players of dif- ferent eras who never met across the board. In this paper, we attempt such a comparison based on the evaluation with a chess playing program of games played by the world chess champions in their championship matches. We slightly adapted the program Crafty for this purpose. Our analysis also takes into account the di®erences in players' styles to ac- count for the fact that calm positional players have in their typical games less chance to commit gross tactical errors than aggressive tactical play- ers. To this end, we designed a method to assess the di±culty of positions. Some of the results of this computer analysis might appear quite surpris-ing. Overall, the results can be nicely interpreted by a chess expert.
Introduction
Who was the best chess player of all time? This is a frequent and interesting question, to which there is no well founded, objective answer, because it requires comparison between chess players of di®erent eras who never met across the board. With the emergence of high quality chess programs a possibility of such an objective comparison arises. Despite this fact, computers were so far mostly used as a tool for statistical analysis of players' results. However, such statistical
analyses often do not re°ect true strengths of the players, nor do they re°ect their quality of play. It is common that chess players play against opponents of di®erent strengths and also that the quality of play changes in time. Furthermore, in chess a single bad move can decisively in°uence the ¯nal outcome of a game, even if all the rest of the moves are excellent. Therefore, the same result can be achieved through play of completely di®erent quality. The most complete and resounding attempt made to determine the best chess player in history has recently been put forward by Je® Sonas, who has become a leading authority in the ¯eld of statistical analysis in chess during past years. Sonas devised a specialized rating scheme, based on tournament results from 1840 to the present . The rating is calculated for each month separately, with
player's activity taken into account. A player's rating, therefore, starts declining when he is no longer active, which di®ers from the classic FIDE rating.
Introduction
Who was the best chess player of all time? This is a frequent and interesting question, to which there is no well founded, objective answer, because it requires comparison between chess players of di®erent eras who never met across the board. With the emergence of high quality chess programs a possibility of such an objective comparison arises. Despite this fact, computers were so far mostly used as a tool for statistical analysis of players' results. However, such statistical
analyses often do not re°ect true strengths of the players, nor do they re°ect their quality of play. It is common that chess players play against opponents of di®erent strengths and also that the quality of play changes in time. Furthermore, in chess a single bad move can decisively in°uence the ¯nal outcome of a game, even if all the rest of the moves are excellent. Therefore, the same result can be achieved through play of completely di®erent quality. The most complete and resounding attempt made to determine the best chess player in history has recently been put forward by Je® Sonas, who has become a leading authority in the ¯eld of statistical analysis in chess during past years. Sonas devised a specialized rating scheme, based on tournament results from 1840 to the present . The rating is calculated for each month separately, with
player's activity taken into account. A player's rating, therefore, starts declining when he is no longer active, which di®ers from the classic FIDE rating.
Chess Books and Prerequisites
One of the principal ways in which a chess player picks up knowledge is through reading chess books, or via other chess media (software, videos, etc.). It is often debated as to which are the most instructive, good for beginners, most unique, etc. So it is important to understand how this dynamically growing set of material can be comprehended, especially which material either requires (or is better understood) by learning other material first. This knowledge is similar to
understanding prerequisites for high school or college courses. Just because a book contains lots of information that you don’t know, it doesn’t necessarily mean that it will be extremely helpful in making you better at this point in your chess development. As an analogy, take a student from Spanish I and put him in Spanish IV, or a middle school student studying social studies and put him in graduate school microeconomics. In both cases it is easy to see that the student is now
in an environment where there is lots of unknown information, but it will not be very helpful to him. Much more subtle is the case of chess books, because any intelligent adult can pick up a well written chess book and both understand the material and see that it contains information he does not currently know. The problem is that, unlike Spanish IV, he may not be able to
tell that the material, while understandable, is not the right kind of information that will help take him to the next level. This information may even be somewhat counterproductive if the student misperceives that it IS helpful For example let’s consider Jeremy Silman’s excellent book How to Reassess Your Chess. In my opinion, this book is slightly more advanced than his other similar great work, The Amateur’s Mind. Both deal with fairly advanced positional and planning subjects – certainly not advanced to a Grandmaster, but advanced for beginning adults - in the sense that these players are still making basic tactical mistakes and will get diminishing returns for studying positional and planning niceties. It would not be possible to fully use these books without having (mis-)absorbed some of the basic positional ideas and thinking guidelines they intend to correct. So, for example, you might first read a text like Pachman’s Modern Chess Strategy or even Nimzovich’s classic My System to learn about positional ideas before you read TheAmateur’s Mind to see how beginning and intermediate players often
One of the principal ways in which a chess player picks up knowledge is through reading chess books, or via other chess media (software, videos, etc.). It is often debated as to which are the most instructive, good for beginners, most unique, etc. So it is important to understand how this dynamically growing set of material can be comprehended, especially which material either requires (or is better understood) by learning other material first. This knowledge is similar to
understanding prerequisites for high school or college courses. Just because a book contains lots of information that you don’t know, it doesn’t necessarily mean that it will be extremely helpful in making you better at this point in your chess development. As an analogy, take a student from Spanish I and put him in Spanish IV, or a middle school student studying social studies and put him in graduate school microeconomics. In both cases it is easy to see that the student is now
in an environment where there is lots of unknown information, but it will not be very helpful to him. Much more subtle is the case of chess books, because any intelligent adult can pick up a well written chess book and both understand the material and see that it contains information he does not currently know. The problem is that, unlike Spanish IV, he may not be able to
tell that the material, while understandable, is not the right kind of information that will help take him to the next level. This information may even be somewhat counterproductive if the student misperceives that it IS helpful For example let’s consider Jeremy Silman’s excellent book How to Reassess Your Chess. In my opinion, this book is slightly more advanced than his other similar great work, The Amateur’s Mind. Both deal with fairly advanced positional and planning subjects – certainly not advanced to a Grandmaster, but advanced for beginning adults - in the sense that these players are still making basic tactical mistakes and will get diminishing returns for studying positional and planning niceties. It would not be possible to fully use these books without having (mis-)absorbed some of the basic positional ideas and thinking guidelines they intend to correct. So, for example, you might first read a text like Pachman’s Modern Chess Strategy or even Nimzovich’s classic My System to learn about positional ideas before you read TheAmateur’s Mind to see how beginning and intermediate players often
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