and bias towards modern players. Moves played compared with computer choices The idea of this approach is to compare the moves played by humans to top engine moves, with the rationale that players more likely to choose these moves are also stronger. Early efforts A computer-based method of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006. A similar project was conducted for World Champions in 2007–08 using Rybka 2.3.2a (then-strongest chess program) and a modified version of Guid and Bratko's program "Crafty". CAPS (Computer Aggregated Precision Score) is a system created by Chess.com that compares players from different eras by finding the percentage of moves that matches that of a chess engine. Markovian model In 2017, Jean-Marc Alliot of the Toulouse Computer Science Research Institute (IRIT) presented a new method, based on a Markovian interpretation of a chess game. Starting with those of Wilhelm Steinitz, all 26,000 games played since then by chess world champions have been processed by a supercomputer using the Stockfish chess engine (rated above 3310 Elo). These predictions have proven not only to be extremely close to the actual results when players have played concrete games against one another, but to also fare better than those based on Elo scores. The results demonstrate that the level of chess players has been steadily increasing. Magnus Carlsen (in 2013) tops the list, while Vladimir Kramnik (in 1999) is second, Bobby Fischer (in 1971) is third, and Garry Kasparov (in 2001) is fourth. Subjective lists Many prominent players and chess writers have offered their own rankings of players. Bobby Fischer (1964 and 1970) In 1964, Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, and Reshevsky. He considered Morphy to be "perhaps the most accurate", writing: "In a set match he would beat anyone alive today." In 1970, Fischer named Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tal, Spassky, Reshevsky, Svetozar Gligorić and Bent Larsen the greatest chess players in history. Irving Chernev (1974) In 1974, popular chess author Irving Chernev published an article titled Who were the greatest? in the English magazine CHESS. He followed this up with his 1976 book The Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca, 2. Alekhine, 3. Lasker, 4. Fischer, 5. Botvinnik, 6. Petrosian, 7. Tal, 8. Smyslov, 9.