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A medical doctor by profession, Tarrasch may have been the best player in the world in the early 1890s. He scored heavily against the aging Steinitz in tournaments, (+3-0=1), but refused an opportunity to challenge for the world title in 1892 because of the demands of his medical practice. Soon afterwards, Tarrasch drew a hard-fought match against Steinitz' challenger Mikhail Chigorin (+9-9=4). Tarrasch also won four major tournaments in succession: Breslau 1889, Manchester 1890, Dresden 1892, and Leipzig 1894.

However, after Emmanuel Lasker became world chess champion in 1894, Tarrasch could not match him. Fred Reinfeld wrote: "Tarrasch was destined to play second fiddle for the rest of his life." For example, Lasker scored much better against common opponents, e.g. vs. Chigorin, Tarrasch had +2 over 34 games while Lasker scored +7 in 21; vs. Akiba Rubinstein Tarrasch was -8 without a single win, while Lasker scored +2-1=2; vs. David Janowski Tarrasch scored +3 compared to Lasker's huge +22; vs. Géza Maróczy, Tarrasch was +1 over 16 games while Lasker scored +4-0=1, vs. Richard Teichmann Tarrasch scored +8-5=2, while Lasker beat him all four tournament games. However, Tarrasch had a narrow plus score against Harry Nelson Pillsbury of +6-5=2, while Lasker was even +5-5=4. However, Tarrasch remained a powerful player, demolishing Frank Marshall in a match in 1905 (+8-1=8), and winning Ostend 1907 over Schlechter, Janowski, Marshall, Burn, and Chigorin.

There was no love lost between the two masters. The story goes that when they were introduced at the opening of their 1908 championship match, Tarrasch clicked his heels, bowed stiffly, and said, "To you, Dr. Lasker, I have only three words, check and mate" ... then left the room. When Lasker finally agreed to a title match in 1908, he beat Tarrasch convincingly +8-3=5.

Tarrasch continued to be one of the leading players in the world for a while. He finished fourth in the very strong Saint Petersburg tournament of 1914, behind only World Champion Lasker and future World Champions José Raúl Capablanca and Alexander Alekhine, and ahead of Marshall, Ossip Bernstein, Rubinstein, Nimzowitsch, Blackburne, Janowski, and Gunsberg. His win against Capablanca in the 19th round, though much less famous than Lasker's win against Capablanca the round before, was essential to enable Lasker to achieve his famous come-from-behind victory over Capablanca in the tournament. This tournament was probably Tarrasch's swan song, because his chess career was not very successful after this, although he still played some highly regarded games.

Tarrasch was a very influential chess writer, and was called Praeceptor Germaniae, meaning "Teacher of Germany." He was editor of the magazine Deutsche Schachzeitung in 1897 and wrote several books, including Die moderne Schachpartie and Three hundred chess games. Although his teachings became famous throughout the chess world, until recently his books had not been translated into English.

He took some of Wilhelm Steinitz's ideas (e.g. control of the center, bishop pair, space advantage) and made them more accessible to the average chess player. In other areas he departed from Steinitz. He emphasized piece mobility much more than Steinitz did, and disliked cramped positions, saying that they "had the germ of defeat."

Tarrasch stated what is known as the Tarrasch rule, that rook should be placed behind passed pawns — either yours or your opponent's. Andrew Soltis quotes Tarrasch as saying

Clash with hypermodern school

He was a great target of the hypermodern school, led by Richard Réti, Aron Nimzowitsch, and Savielly Tartakower, all of whom criticized his ideas as dogmatic. However, many modern masters regard Tarrasch's actual play as not dogmatic. For example, Tarrasch annotated his victory on the Black side of the Advance French against Paulsen (Nuremberg 1888):

1. e4 e6 2. d4 d5 3. e5 c5 4. c3 Nc6 5. Nf3 Qb6 6. Bd3 cxd4 (Tarrasch gives this an exclamation mark, and points out that 6 ... Bd7 allows 7. dxc5 with a good game. However, most accounts credit Nimzovitch with such anti-dogmatic hypermodern inventiveness when he played 7. dxc5 against Gersz Salwe almost a quarter of a century later (Karlsbad 1911) in this game [1]) 7. cxd4 Bd7 8. Be2 Nge7 9. b3 Nf5 10. Bb2 Bb4+ 11. Kf1 Be7 12. g3 a5 13. a4 Rc8 14. Bb5 Nb4 15. Bxd7+ Kxd7 16. Nc3 Nc6 17. Nb5 Na7 18. Nxa7 Qxa7 19. Qd3 Qa6 20. Qxa6 bxa6 21. Kg2 Rc2 22. Bc1 Rb8 23. Rb1 Rc3 24. Bd2 Rcxb3 25. Rxb3 Rxb3 26. Bxa5 Rb2 27. Bd2 Bb4 28. Bf4 h6 29. g4 Ne7 30. Ra1 Nc6 31. Bc1 Rc2 32. Ba3 Rc4 33. Bb2 Bc3 34. Bxc3 Rxc3 35. Rb1 Kc7 36. g5 Rc4 37. gxh6 gxh6 38. a5 Ra4 39. Kg3 Rxa5 40. Kg4 Ra3 41. Rd1 Rb3 42. h4 Ne7 43. Ne1 Nf5 44. Nd3 a5 45. Nc5 Rc3 46. Rb1 Nxd4 47. Na6+ Kd8 48. Rb8+ Rc8 49. Rb7 Ke8 50. Nc7+ Kf8 51. Nb5 Nxb5 52. Rxb5 Ra8 53. f4 a4 54. Rb1 a3 55. f5 a2 56. Ra1 Ra4+ 57. Kh5 Kg7 58. fxe6 fxe6 59. Rg1+ Kh8 60. Ra1 Kh7 61. Rg1 a1=Q 62. Rg7+ Kh8 0-1

Contribution to opening theory

A number of chess openings are named after Tarrasch, with the most notable being:

• The Tarrasch Defense, Tarrasch's favorite line against the Queen's Gambit.
• The Tarrasch Variation of the French Defence (3.Nd2), which Tarrasch considered refuted by 3...c5, although this is certainly not thought so today.
• The Tarrasch Variation of the Ruy Lopez, also sometimes known as the Open Defence (1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 Nxe4).

In the game Tarrasch versus Allies, Black seems to be holding here (at least against immediate catastrophe), because the black queen guards against Qb7+ (followed by Kxa5 Ra1#), while the black rook on c8 defends against Rxc5#. Tarrasch played the ingenious interference move 31.Bc7! (known as a Plachutta interference because the pieces both move orthogonally). This blocks off both defences, and whatever piece captures becomes overloaded. That is, if 31...Rxc7, the rook is overloaded, having to look after both the key squares, since the queen is blocked from b7. So White would play 32.Qb7+ Rxb7, deflecting the rook from defence of c5, allowing 33.Rxc5#. But if Black plays instead 31...Qxc7, the queen blocks off the rook's defence of c5 and becomes overloaded: 32.Rxc5+ Qxc5 deflects the queen from defence of b7, allowing 33.Qb7+ Kxa5 34.Ra1#. Black actually resigned after this move.

In the game against Walbrodt, Tarrasch played rather poorly, and his opponent had the better of it for a long time. But the game is redeemed by the following startling combination:

34.Rxd4 seems obvious, because 34...cxd4 allows 35.Bxd4 winning the queen. But Black has a seemingly strong counterattack which had to be foreseen ...34...Nxg3 35.Nxg3 Rxg3+ 36.hxg3 Rxg3+ 37.Kf1! Rxd3 and now the startling 38.Rg4!! with devastating threats of 39. Rf8+ mating and Bxe5 not to mention cxd3 to follow. Black resigned.