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University of Ljubljana, Faculty of Computer and Information Science,
Artificial Intelligence Laboratory, Ljubljana, Slovenia.
In this paper we attempt to get some answer to the questions formulated in the header, through a computer analysis of the individual chess moves played by the players. Strong chess engines and increasingly powerful computer hardware provide us with opportunities to observe more than just pure game results. As we all know, a single mistake may ruin a well-played game. Game results do not necessarily reflect well the quality of play – that is for sure. Besides, quality of play seems to have improved greatly with the emergence of huge databases of chess games and very strong chess engines.
In this article, we briefly present results of computer analysis of chess games played in the latest Candidates Tournament in London, using the chess engine Houdini 1.5a (64 bit) at search depth of 20 plies. In our previous studies (see e.g. the Chessbase.com article Using chess engines to estimate human skill) we demonstrated that (fallible) chess engines can produce quite reliable rankings of the players. Possibly surprisingly, it turns out that different engines at different search depths produce the same or at least very similar rankings. The method is briefly described below. While the method could be debated, it can nevertheless give us some insights about the quality of play in the games analysed.
According to the 20-ply Houdini, Magnus Carlsen achieved the best computer score at the FIDE Candidates Tournament 2013. Probably the greatest surprise is an excellent computer score by Alexander Grischuk, who finished the tournament with less that 50% points in the tournament table! According to the analysis, Vladimir Kramnik also played at a very high level.
FIDE Candidates 2013 computer scores:
(lower scores indicate the better quality of play)
The results suggest that the quality of play demonstrated by the Candidates is very high indeed. In particular, Carlsen’s score is the second best score achieved in an individual tournament or match of all the top-level tournaments and matches that we have analysed to the present day.
Let us note that both Carlsen’s and Kramnik’s computer score greatly deteriorated in the last few rounds. After Round 10 their scores were both under 3.00, which is truly remarkable: we will see that shortly, as we will compare the results in the graph above to the achievements of the 15 classical world champions at the peaks of their careers – in the World Chess Championship matches.
In the graph below, we see corresponding results obtained with the same program at the same level of search (i.e. Houdini at 20 plies).
The comparison of the world chess champions
(lower scores indicate the better quality of play)
The results suggest that in terms of the computer scores, Vishy Anand and Vladimir Kramnik did best of all the players in the World Chess Championship matches. It should be noted that several players achieved rather similar scores.
By comparing the two graphs we can observe that the top three 2013 Candidates (Carlsen, Grischuk, and Kramnik) achieved even better computer scores than were the average scores of any of the fifteen “classical” world champions in the “classical” World Championship matches!
What about the champions’ achievements in their individual World Championship matches? Here is the Top-10 list of individual achievements, using the same program at the same depth of search:
| Player | World Championship match | Player's score |
| Kramnik | Kramnik-Leko, 2004 | 3.43 |
| Kasparov | Kasparov-Anand, 1995 | 4.35 |
| Anand | Kramnik-Anand, 2008 | 4.49 |
| Anand | Anand-Gelfand, 2012 | 4.81 |
| Capablanca | Lasker-Capablanca, 1921 | 5.48 |
| Anand | Anand-Topalov, 2010 | 5.59 |
| Karpov | Karpov-Kasparov, 1984 | 5.71 |
| Kramnik | Kasparov-Kramnik, 2000 | 5.76 |
| Botvinnik | Botvinnik-Petrosian, 1963 | 5.84 |
| Kasparov | Kasparov-Kramnik, 2000 | 5.85 |
The top 10 scores in the “classical” World Championship matches
(lower scores indicate the better quality of play)
The best quality of play (as judged by Houdini 1.5a at 20-ply search) was therefore demonstrated by Kramnik in his World Championship match against Leko. As noted above, both Carlsen and Kramnik were on the way to achieve an even better score in the first ten rounds of the FIDE Candidates Tournament.
The method used to obtain the results presented in this article is described in the following scientific paper:
M. Guid and I. Bratko:Using Heuristic-Search Based Engines for Estimating Human Skill at Chess. ICGA Journal, Vol. 34, No. 2, pp. 71-81, 2011. [Available as PDF]. An interested reader may also find more information in the Chessbase.com article Using chess engines to estimate human skill.
Here is a summary of the method (see the above paper for explanations):
The analysis of each game starts at move 12.
The chess engine evaluates the best moves (according to the computer) and the moves played by the player.
All engine’s evaluations are obtained at the same depth of search.
The score is then the average difference between evaluations of the best moves and the moves played.
If the player’s mistake (as seen by the engine) at particular move is greater than 3.00, the score for this particular move becomes 300 “centipawns” (to avoid unreasonably high penalties for gross mistakes).
Moves where both the move played and the move suggested by the computer had an evaluation outside the interval [-2.00, 2.00], are discarded. (In clearly won positions players are tempted to play a simple safe move instead of a stronger, but risky one. Such “inferior” moves are, from a practical viewpoint, perfectly justified. Similarly, in lost positions players sometimes deliberately play an objectively worse move.)
In the graphs above, all the scores are given in “centipawns”.
We would like to emphasize that the scores obtained by the program only measure the average differences between the players' choices of move and the computer's choice. Several studies have shown that these scores that are relative to the chess engine used have good chances to produce sensible rankings of the players.
A valid comment regarding the computer scoring method is that it does not take into account the complexity of positions. As a consequence, players that tend to prefer simple positions are a priori more likely to commit less errors and therefore obtain better computer scores. To qualify the computer score results from the perspective of complexity, we add the average complexity estimates of individual player's games. These complexity estimates were computed by the method described in the scientific paper M. Guid and I. Bratko: Computer analysis of world chess champions. ICGA Journal, Vol. 29, No. 2, pp. 65-73, 2006.
Again, the chess engine Houdini 1.5a (64-bit) was used to compute the complexity estimates, this time (in accordance with the algorithm) performing search to various depths in the range between 2 and 15 plies.
The average complexity estimates of individual player's games in the World Championship matches (left) and in the FIDE Candidates 2013 (right). The lower scores indicate tendency towards simple positions.
These results confirm previous observations that Capablanca’s outstanding score in terms of low average differences in computer evaluations between the player’s moves and the computer’s moves should be interpreted in the light of his playing style that tended towards low complexity positions.
It is worth noting that according to the results demonstrated in the graph above, Aronian dealt with the most complex positions (on average) of all the Candidates. On the other hand, Carlsen’s outstanding computer score (the estimated quality of play) does not in any way seem to be the consequence of the level of complexity of positions that occurred in his games.
The authorsMatej Guid has received his Ph.D. in computer science at the University of Ljubljana, Slovenia. His research interest include computer game-playing, automated explanation and tutoring systems, heuristic search, and argument-based machine learning. Some of his scientific works, including the Ph.D. thesis titled Search and Knowledge for Human and Machine Problem Solving, are available on Matej's Research page. Chess has been one of Matej's favourite hobbies since his childhood. He was also a junior champion of Slovenia a couple of times, and holds the title of FIDE master. |
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Ivan Bratko is professor of computer science at University of Ljubljana, Slovenia. He is head of Artificial intelligence Laboratory, Faculty of Computer and Information Science of Ljubljana University, and has conducted research in machine learning, knowledge-based systems, qualitative modelling, intelligent robotics, heuristic programming and computer chess (do you know the famous Bratko-Kopec test?). Professor Bratko has published over 200 scientific papers and a number of books, including the best-selling Prolog Programming for Artificial Intelligence. Chess is one of his favourite hobbies. |
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