Threefold repetition

In chess, the threefold repetition rule states that a player may claim a draw if the same position occurs three times during the game. The rule is also known as repetition of position and, in the USCF rules, as triple occurrence of position. ^[1] Two positions are by definition "the same" if the same types of pieces occupy the same squares, the same player has the move, the remaining castling rights are the same and the possibility to capture en passant is the same. The repeated positions need not occur in succession. The reasoning behind the rule is that if the position occurs three times, no real progress is being made and the game could hypothetically continue indefinitely.

The game is not automatically drawn if a position occurs for the third time – one of the players, on their turn, must claim the draw with the arbiter. The claim must be made either before making the move which will produce the third repetition, or after the opponent has made a move producing a third repetition. By contrast, the fivefold repetition rule requires the arbiter to intervene and declare the game drawn if the same position occurs five times, needing no claim by the players.

Similar rules exist in other abstract strategy games such as xiangqi and shogi (cf. sennichite ) whereas in Go, repetition of any previous board position is completely disallowed in the first place.

Internet chess servers differ in their handling of draw by repetition. For example, Lichess adheres to the FIDE Laws of Chess, whereas Chess.com draws the game immediately upon a position's third occurrence.

Statement of the rule

The relevant rules in the FIDE laws of chess are summarized as: ^[3]

The game is a draw if a position occurs (at least) three times during the game. (Intervening moves do not matter.) It must be claimed by the player with the turn to move. The claim is made:

(a) If the position is about to appear for the third time, the player making the claim first writes their move on their scoresheet and notifies the arbiter that they intend to make this move.

or

(b) If the position has just appeared for the third time, the player with the move can claim the draw.

Positions are considered the same if

(1) the same player has the move,

(2) pieces of the same kind and color occupy the same squares, and

(3) the possible moves of all the pieces are the same.

Under (3) above, positions are not considered to be the same if:

(a) in the first position, a pawn could have been captured en passant (by the en passant rule, in the subsequent positions, the pawn cannot be captured en passant anymore), or

(b) either player has lost a right to castle, i.e. either king or one of the rooks has been moved, in between repetitions of the position.

Although a threefold repetition usually occurs after consecutive moves, there is no requirement that the moves be consecutive for a claim to be valid. The intermediate positions and moves do not matter – they can be the same or different. The rule applies to positions, not moves.

Perpetual check is no longer specifically mentioned in the rules of chess; such a situation will eventually resolve to a draw either by repetition, fifty-move rule or (most commonly) by agreement.

If the claim for a draw is incorrect, the opponent is awarded an extra two minutes, the written move if being a legal move must be played and the game continues. ^[4] Unreasonable claims may be penalized under rule 11.5, which forbids distracting or annoying the opponent. ^[5] Even if the claim is incorrect, any draw claim is also a draw offer that the opponent may accept. ^[6]

The fivefold repetition rule was introduced in 2014 providing for a mandatory draw in the event of a fivefold repetition.

9.6 If one or both of the following occur(s) then the game is drawn:

9.6.1 the same position has appeared, as in 9.2.2 at least five times.

Examples

1972 World Championship

The seventeenth ^[7] and eighteenth ^[8] game of the 1972 World Championship match in Reykjavik between Bobby Fischer and Boris Spassky were declared draws because of threefold repetition. The twentieth game was drawn after an incorrect claim (see incorrect claims below).

Fischer versus Petrosian, 1971

Fischer vs. Petrosian, 1971

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 30.Qe2, 32.Qe2 and 34.Qe2

In the third game ^[9] of the 1971 Candidates Final Match in Buenos Aires between Bobby Fischer and Tigran Petrosian, Petrosian (with a better position) accidentally allowed the position after 30.Qe2 (see diagram) to be repeated three times. Play continued:

30... Qe5

31. Qh5 Qf6 (31... Qxf4 32. Qxf7+ also leads to threefold repetition)

32. Qe2 (second time) Re5

33. Qd3 Rd5?

and then Fischer wrote his next move

34. Qe2 (third time) ½-½

on his scoresheet , which is the third appearance of the position with Black to move, and he claimed a draw. ^[10] At first Petrosian was not aware of what was going on. Incidentally, this was the first time a draw by threefold repetition had been claimed in his career. ^{[11] [12] [13]} This also illustrates that the intermediate moves do not need to be the same – just the positions.

Capablanca versus Lasker, 1921

Capablanca vs. Lasker, 1921

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 34...h5, 36...Kf8 and 38...Kf8

As noted above, one of the players must claim a draw by threefold repetition for the rule to be applied, otherwise the game continues. In the fifth game ^[14] of the 1921 World Chess Championship match in Havana between José Raúl Capablanca and Emanuel Lasker, the same position occurred three times, but no draw was claimed. After 34...h5 (see diagram), the moves were:

35. Qd8+ Kg7

36. Qg5+ Kf8 (second time)

37. Qd8+ Kg7

38. Qg5+ Kf8 (third time)

The game continued; Lasker blundered and resigned on move 46. Capablanca repeated the position to gain time on the clock (i.e. get in some quick moves before time control). ^[15] (Capablanca went on to win the match and became world champion.)

Two games between Alekhine and Lasker, 1914

Alekhine vs. Lasker Moscow 1914 a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h Position after 16.Qg6

Lasker vs. Alekhine St. Petersburg 1914 a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h Position after 21.Qd4, 23.Kg1 and 25.Kg1

The game ^[16] between Alexander Alekhine and world champion Emanuel Lasker in Moscow 1914 ended in a short draw. After 16.Qg6 (see diagram) the players agreed to a draw because Alekhine can force the threefold repetition, for example 16...Qe8 17.Qxh6+ Kg8 18.Qg5+ Kh8 19.Qh6+ ^[17] (under repetition of position).

In the first game ^[18] between the two players in the St. Petersburg tournament 1914, ^[19] Alekhine, this time with the black pieces, after 21.Qd4 (see diagram), forced a draw by threefold repetition using a similar process. ^[20]

Portisch versus Korchnoi, 1970

Portisch vs. Korchnoi, 1970

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 21...Qb5 with Portisch in a better position

A famous draw for threefold repetition occurred in the fourth ^[22] game ^[23] between Lajos Portisch and Viktor Korchnoi in Belgrade in the Russia (USSR) vs Rest of the World 1970 match. After 21...Qb5 (see diagram), in a clearly better position, ^[24] Portisch allowed this position to repeat three times and was criticized by teammate Bobby Fischer for allowing it. ^[25] If Portisch had won the game, the match would have been a tie. Play continued:

22.Bf1 Qc6

23.Bg2 Qb5 (second time)

24.Bf1 Qc6

25.Bg2 ½-½

allowing Black to claim the threefold repetition with 25...Qb5.

Kasparov versus Deep Blue, 1997

Kasparov vs. Deep Blue, 1997

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 49...Kb4

In the game ^[26] between Garry Kasparov and Deep Blue in New York 1997, the game ended with a draw by agreement, because after 49...Kb4 (see diagram) if White plays 50.g8=Q, Black can force perpetual check and claim a draw after 54.Kb1 by threefold repetition: ^[27]

50...Rd1+

51.Ka2, Kb2 or Kc2 Rd2+

52.Kb1 (second time) Rd1+

53.Ka2, Kb2 or Kc2 Rd2+

54.Kb1 (third time)

Khamparia vs Bo, 2018

Khamparia vs Bo, 2018

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 60...Rc1, 62...Rc1, 68...Rc1, 73...Rc1 and 75...Rc1

To detect fivefold repetitions can be challenging for the arbiter. In the game Akshat Khamparia vs Li Bo, Budapest 2018, Li twice requested a draw, saying simply "repetition". Both times the request was rejected because it was not made correctly according to the threefold repetition rule. Li was later checkmated. Li discussed the result and eventually said "five". The arbiter was able to verify fivefold repetition at moves 60, 62, 68, 73 and 75. ^[28] Had the fivefold repetition rule not been in effect, the result would have stood, as no correct claim for threefold repetition had been made. Under the fivefold repetition rule, however, the fifth occurrence of a position immediately terminates the game, and subsequent moves become irrelevant. The result was therefore overturned, and the game was declared a draw. ^{[28] [29]}

Opening line

Pirc Defense line

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 11.Nxd8

An Austrian Attack line from the Pirc Defence has been analyzed out to a draw by threefold repetition. After the moves 1.e4 d6 2.d4 Nf6 3.Nc3 g6 4.f4 Bg7 5.Nf3 c5 6.Bb5+ Bd7 7.e5 Ng4 8.e6 fxe6 9.Ng5 Bxb5! 10.Nxe6 Bxd4! 11.Nxd8 (see diagram) Black can force perpetual check and so the draw by the following moves:

11...Bf2+

12.Kd2 (first time) Be3+

13.Ke1 Bf2+

14.Kd2 (second time) Be3+

15.Ke1 Bf2+

16.Kd2 (third time)

15...Bf2+ is only a twofold repetition, as White lost their castling right only after 12.Kd2. Threefold repetition will be in effect on the next occurrence of the position.

Grandmaster draws

Carlsen vs. Nakamura, 2021

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 2...Ke7, 4...Ke7 and 6...Ke7

A grandmaster draw is characterised as a short draw between high-level players, typically intended to hold position without the expenditure of mental energy. As short draws by agreement are sometimes frowned upon or outright banned in tournaments, some players circumvent such rules by playing out lines known to end in threefold repetition draws. The Berlin draw in the Ruy Lopez is one of the more commonly used lines, while Magnus Carlsen and Hikaru Nakamura finished out a dead rubber at the Magnus Carlsen Invitational with a variation of the Bongcloud Attack – Nakamura admitted that with both players secure in passage to the next round of the tournament he saw no value in attempting to force the win.

Repeating a position to gain time

Players sometimes repeat a position once not in order to draw, but to gain time on the clock (when an increment is being used) or to bring themselves closer to the time control (at which point they will receive more time). Occasionally, players miscount and inadvertently repeat the position more than once, thus allowing their opponent to claim a draw in an unfavourable position. The game ^[30] between Ponomariov and Adams in Wijk aan Zee 2005 may have been an example of this. ^[31]

Incorrect claims

Even top players have made incorrect claims of a draw under this rule. The Karpov–Miles game is an example of the right to castle having to be the same in all positions. The Fischer–Spassky game is an example that it must be the same player's move in all three positions.

Karpov versus Miles, 1986

Karpov vs. Miles, 1986

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 22.Nb5

The clause about the right to castle is a subtle but important one. In a game ^[32] between grandmasters Anatoly Karpov and Tony Miles in Tilburg 1986, Karpov had less than five minutes remaining on his clock in which to finish a specified number of moves or forfeit the game. He claimed a draw by repetition after checking his scoresheet carefully, whereupon it was pointed out to him that in the first occurrence of position, Black's king had had the right to castle, whereas in the second and third it had not. Tournament rules stipulated that a player be penalized with three minutes of their time for incorrect claims, which left Karpov's flag on the verge of falling. By then, Miles had taken the draw. (Miles should have readily accepted a draw in that position, but Karpov was close to losing the game because of time control.) After 22. Nb5 (see diagram) play continued:

22... Ra4 (Black loses queenside castling right)

23. Nc3 Ra8

24. Nb5 (first time only, Black lost queenside castling right) Ra4

25. Nc3 Ra8

26. Nb5 (second time only, Black lost queenside castling right) ½-½

Black was able to castle queenside the first time the arrangement of pieces in the diagram occurred, but not when the arrangement was repeated.

Fischer versus Spassky, 1972

Fischer vs. Spassky, 1972

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 48.Kc3, 50.Ne1 and 54...Nd4 (different turn)

In the twentieth game ^[33] of the 1972 World Chess Championship between Bobby Fischer and Boris Spassky, Fischer called the arbiter Lothar Schmid to claim a draw because of threefold repetition. Spassky did not dispute it and signed the scoresheets before the arbiter ruled. ^[34] After the draw had been agreed, it was pointed out that the position had occurred after White's forty-eighth (see diagram) and fiftieth moves, and again after Black's fifty-fourth move. So the claim was actually invalid because it was not the same player's turn to move in all three instances, but the draw result stood. ^{[35] [36]}

History of the rule

Pest vs. Paris

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 19.Nc5, 21.Nc5, 23.Nc5, 25.Nc5 and 27.Nc5

The rule has been variously formulated at different times in chess history. In Tim Harding's MegaCorr database (a collection of correspondence chess games), the notes to a game between the cities of Pest and Paris played between 1842 and 1845 state that a sixfold repetition was necessary to claim a draw. The game went: 1.e4 e5 2.Nf3 Nf6 3.Nxe5 d6 4.Nf3 Nxe4 5.d4 d5 6.Bd3 Bd6 7.0-0 0-0 8.c4 Be6 9.Qc2 f5 10.Qb3 dxc4 11.Qxb7 c6 12.Bxe4 fxe4 13.Ng5 Bf5 14.Nc3 Qd7 15.Qxd7 Nxd7 16.Ngxe4 Bc7 17.Re1 Rab8 18.Re2 Nb6 19.Nc5 (see diagram) Bd6 20.N5e4 Bc7 21.Nc5 Bd6 22.N5e4 Bc7 23.Nc5 Bd6 24.N5e4 Bc7 25.Nc5 Bd6 26.N5e4 Bc7 27.Nc5 and now instead of taking the sixfold repetition draw with 27...Bd6 28.N5e4 Bc7, Paris diverged with 27...Bd3 and went on to lose the game.

The first use of such a rule was in a tournament in London in 1883, but was stated vaguely: "... if a series of moves be repeated three times the opponent can claim a draw." The rules for the first official World Chess Championship 1886 match between Wilhelm Steinitz and Johannes Zukertort stated: "... if both players repeat the same series of moves six times in succession, then either player may claim a draw." In two of the games the same position was repeated three times. The rule was modified soon afterward to be based on positions instead of moves, and for three repetitions. ^[37] Draws by this method used to be uncommon. ^[38]

The first edition of the FIDE rule from 1928 already defines the threefold repetition rule without considering castling and en passant capture rights. ^[42] To additionally consider castling and en passant capture rights was implicitly introduced in 1975 ^[44] and explicitly worded in 1985. ^[46] Prior to that, a 1964 FIDE interpretation established the same. ^[47]

Pillsbury versus Burn, 1898

Pillsbury vs. Burn, 1898

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Position after 42...Qe3, 46...Kg7 and 50...Kg7

In this 1898 Vienna tournament game ^[48] between Harry Pillsbury and Amos Burn, the same position occurred three times, but no draw could be claimed under the rules at the time. The tournament was played under the rules of Bilguer's Handbuch des Schachspiels (1843, with later editions), in which the three-fold rule was stated as the repetition of moves or a sequence of moves, not a position. After 42...Qe3 (see diagram), the game continued:

43.Qb2 Kh6

44.Qc2 Kh7

45.Qb2 Kg8

46.Qc2 Kg7 (second time)

47.Qb2 Kh7

48.Qc2 Kh6

49.Qb2 Kh7

50.Qc2 Kg7 (third time)

51.Qb2

Under modern rules, Black could claim a draw by informing the arbiter of their intention to play 50...Kg7, producing the same position as had occurred after 42...Qe3 and 46...Kg7. Alternatively, after 51.Qb2, Black could claim a draw immediately because White has repeated the position after 43.Qb2 and 47.Qb2. Burn went on to win the game. ^[49]

Other games

Main articles: Sennichite and Xiangqi § Rules

In many abstract strategy games there are rules to cover repetition of position. In some games this results in a draw, in others it is forbidden to repeat a position.

Currently, shogi employs a fourfold repetition (千日手 sennichite) rule, which is required to end in a draw. Each player must have the same pieces in hand as well as the same position on the board. The result is a draw. However, a fourfold repetition with perpetual checks is illegal, and results not in a draw but in a loss by the checking player.

In Xiangqi, rules about repetitions vary between different sets of rules, but generally perpetual attacks (長打), including perpetual check, perpetual threatmate, and perpetual chase, are forbidden.

Arimaa does not allow threefold repetition of the same position with the same player to move.

In Go, a player may not make a move which repeats a previous position, as would occur if a player were to immediately recapture a stone in a ko situation. Creating ko threats is an important strategic consideration in Go.

References

1. Article 14K.2 in "US CHESS FEDERATION'S OFFICIAL RULES OF CHESS 7TH EDITION" (PDF). The United States Chess Federation. Retrieved 12 July 2020.
2. "FIDE Laws of Chess taking effect from 1 January 2018". FIDE. Retrieved 2 July 2020.
3. Rules 9.2.1 and 9.2.2 in FIDE Laws of Chess ^[2]
4. Rule 9.5.3 in FIDE Laws of Chess ^[2]
5. Rule 11.5 and 12.6 in FIDE Laws of Chess ^[2]
6. Rule 9.1.2.3 in FIDE Laws of Chess ^[2]
7. "Spassky vs. Fischer, 17th game, 1972". Chessgames.com. Retrieved 2020-07-03.
8. "Fischer vs. Spassky, 18th game, 1972". Chessgames.com. Retrieved 2020-07-03.
9. "Fischer vs. Petrosian, 1971". Chessgames.com. Retrieved 2020-07-03.
10. Different sources give different moves near the end. Plisetsky & Voronkov and Kasparov give 32...Re5 33.Qh5 Rd5. ChessGames.com and Chess Life (11/1971 and 12/1971) give 32...Re5 33.Qd3 Rd5. The December 1971 Chess Life also discusses how the intermediate moves were different, and that Petrosian seemed unaware that he was going to allow a three-fold repetition.
11. ( Plisetsky & Voronkov 2005 :283–84)
12. ( Kasparov 2004 :422–23)
13. ( Byrne 1971 :682)
14. "Capablanca vs. Lasker, 1921". Chessgames.com. Retrieved 2020-07-03.
15. ( Kasparov 2003 :266–67)
16. "Alekhine vs.Lasker, 1914". Chessgames.com. Retrieved 2020-07-02.
17. ( Hooper & Whyld 1992 )
18. "Lasker vs. Alekhine, 1914". Chessgames.com. Retrieved 2020-07-03.
19. "St. Petersburg (1914)". Chessgames.com. Retrieved 2020-09-07.
20. ( Bott & Morrison 1966 :14)
21. Fischer, Johannes (14 April 2020). "USSR vs. Rest of the World, 1970: Lajos Portisch comments". Chessbase. Archived from the original on 15 September 2020. Retrieved 15 September 2020.
22. "Lajos Portisch comments on the controversy surrounding his draw against Viktor Kortschnoi in their fourth and last game." per ChessBase article ^[21]
23. "Lajos Portisch vs Viktor Korchnoi (1970)". Chessgames.com. Retrieved 2020-09-16.
24. "22. Bf1 White steers for a repetition and a draw. Modern engines evaluate the position as clearly better for White." per ChessBase article ^[21]
25. ( Brady 1973 :163)
26. "Kasparov vs. Deep Blue, 1997". Chessgames.com. Retrieved 2020-07-03.
27. ( Hsu 2002 :251–52)
28. Saltamara, Efstathia (September 2018). "FIDE Arbiter's Magazine" (PDF). FIDE. p. 8. Archived (PDF) from the original on 6 October 2019. Retrieved 26 August 2020.
29. The PGN of the game is contained in the following FIDE rating page "PGN Chess Game First Saturday GM May 2018 (HUN)". FIDE. Retrieved 3 August 2020.
30. "Ponomariov vs. Adams, 2005". Chessgames.com. Retrieved 2020-07-03.
31. ( Friedel 2005 )
32. "Karpov vs. Miles, 1986". Chessgames.com. Retrieved 2020-07-03.
33. "Fischer vs. Spassky, 20th game, 1972". Chessgames.com. Retrieved 2020-07-03.
34. ( Gligorić 1972 :119)
35. ( Alexander 1972 :137–38)
36. Alexander says that it appears that the arbiter approved the draw but Gligorić says that Spassky signed the scoresheet before the arbiter could rule on the claim.
37. ( McCrary 2004 )
38. ( Brace 1977 :236)
39. "AUTHORISED EDITION OF THE OFFICIAL CODE COMPILED BY THE FEDERATION INTERNATIONALE DES ECHECS" (PDF). CCA - Chess Arbiters’ Association Britain. Retrieved 9 July 2020. By recurrence of position when the same position occurs three times in the game, and the same person is Player on each occasion, and if such Player claim the draw before the position is altered by further play, otherwise no claim can be sustained.
40. "Laws historic". CCA - Chess Arbiters’ Association Britain. Retrieved 9 July 2020.
41. "CCA Britain". CCA - Chess Arbiters’ Association Britain. Retrieved 9 July 2020.
42. Par 15.C in FIDE Laws of Chess 1928 ^[39] from "1931 - 1st FIDE Laws (BCF version)" on the Laws historic page ^[40] of the CCA Britain. ^[41]
43. "Fide Laws of Chess 1975, translation" (PDF). CCA - Chess Arbiters’ Association Britain. Retrieved 9 July 2020. The position is considered the same if pieces of the same kind and colour occupy the same squares and if the possible moves of all the pieces are the same.
44. Article 12.3 in Fide Laws of Chess 1975 ^[43] from "1975" of the Laws historic page ^[40] of the CCAB ^[41]
45. "Laws of Chess 1985" (PDF). CCA - Chess Arbiters’ Association Britain. Retrieved 9 July 2020. The position is considered the same if pieces of the same kind and colour occupy the same squares and if the possible moves of all the pieces are the same, including the right to castle or to take a pawn en passant.
46. Article 10.5 (b) in Fide Laws of Chess 1985 ^[45] from "1985" of the Laws historic page ^[40] of the CCAB ^[41]
47. ( Harkness 1967 :49)
48. "Pillsbury vs. Burn, 1898". Chessgames.com. Retrieved 2020-07-03.
49. ( Giddins 2012 :166–67)

Bibliography

• Alexander, C. H. O'D. (1972), Fischer v. Spassky, Vintage, ISBN   0-394-71830-5
• Bott, Raymond; Morrison, Stanley (1966), The Chess Player's Bedside Book, Faber & Faber, ISBN   978-0571068647
• Brace, Edward (1977), An Illustrated Dictionary of Chess, Craftwell, ISBN   1-55521-394-4
• Brady, Frank (1973), Bobby Fischer: Profile of a Prodigy (2nd ed.), Dover, ISBN   0-486-25925-0
• Byrne, Robert (December 1971), "Fischer vs Petrosian: A Rocky Start", Chess Life , 26 (12): 680–82
• Friedel, Frederic (2005), Corus 09: Striking with the Albin Counter Gambit, ChessBase.com , retrieved 2005-07-14
• Giddins, Steve (2012), The Greatest Ever Chess Endgames, Everyman Chess, ISBN   978-1-85744-694-4
• Gligorić, Svetozar (1972), Fischer vs. Spassky - The Chess Match of the Century , Simon and Schuster, ISBN   0-671-21398-9
• Harkness, Kenneth (1967), Official Chess Handbook, McKay
• Hooper, David; Whyld, Kenneth (1992), The Oxford Companion to Chess (second ed.), Oxford University Press, ISBN   0-19-866164-9
• Hsu, Feng-hsiung (2002), Behind Deep Blue: Building the Computer that Defeated the World Chess Champion, Princeton University Press, ISBN   0-691-09065-3
• Kasparov, Garry (2003), My Great Predecessors, part I, Everyman Chess, ISBN   1-85744-330-6
• Kasparov, Garry (2004), My Great Predecessors, part IV, Everyman Chess, ISBN   1-85744-395-0
• Korn, Walter; de Firmian, Nick (1990), Modern Chess Openings (13 ed.), McKay, ISBN   0-8129-1730-8
• McCrary, John (2004), "The Evolution of Special Draw Rules", Chess Life (November): 26–27
• Plisetsky, Dimitry; Voronkov, Sergey (2005), Russians versus Fischer, Everyman Chess, ISBN   1-85744-380-2

External links

• FIDE laws of chess
• "Repetition of Position or Moves in Chess" by Edward Winter