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Reversi

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This article is about the board game. For the card game, see Reversis.

Reversi
Othello, a modern variation of Reversi
Years active1883; 141 years ago (1883)
(or earlier)—present
GenresBoard game
Abstract strategy game
Mind sport
Players2
Setup time< 10 seconds
Playing time1–60 minutes
ChanceNone
Age range8+
SkillsStrategy, tactics, observation
SynonymsOthello

Reversi is a strategy board game for two players, played on an 8×8 uncheckered board. It was invented in 1883. Othello, a variant with a fixed initial setup of the board, was patented in 1971.

Basics

There are sixty-four identical game pieces called disks, which are light on one side and dark on the other. Players take turns placing disks on the board with their assigned color facing up. During a play, any disks of the opponent's color that are in a straight line and bounded by the disk just placed and another disk of the current player's color are turned over to the current player's color. The objective of the game is to have the majority of disks turned to display one's color when the last playable empty square is filled.

History

Othello was one of Nintendo's first arcade games, and was later ported to a dedicated home game console in 1980.

Original version

Englishmen Lewis Waterman[1] and John W. Mollett[citation needed] both claim to have invented the game of Reversi in 1883, each denouncing the other as a fraud. The game gained considerable popularity in England at the end of the 19th century.[2] The game's first reliable mention is on 21 August 1886 edition of The Saturday Review. Later mention includes an 1895 article in The New York Times, which describes Reversi as "something like Go Bang, [...] played with 64 pieces."[3] In 1893, the German games publisher Ravensburger started producing the game as one of its first titles. Two 18th century continental European books dealing with a game that may or may not be Reversi are mentioned on page fourteen of the Spring 1989 Othello Quarterly, and there has been speculation, so far without documentation, that the game has older origins.[citation needed]

A Japanese publication in 1907 titled World Games Rules Complete Collection (世界遊戯法大全) describes the board game Reversi with the same rules as Othello where the first four pieces go in the center in a diagonal pattern and the player who cannot make a move simply passes.[4]

Othello

A modern plastic Othello set

The modern version of the game—the most regularly used rule-set, and the one used in international tournaments—is marketed and recognized as Othello. It was patented in Japan in 1971[5] by Goro Hasegawa [ja] (legal name: Satoshi Hasegawa), then a 38-year-old salesman.[6] Hasegawa initially explained that Othello was an improvement on Reversi,[7] but from around 2000, he began to claim that he invented it in Mito regardless of Reversi.[8] Hasegawa also claims that the origin of Reversi/Othello dates back 5,000 years.[9]

Hasegawa established the Japan Othello Association in March 1973, and held the first national Othello championship on 4 April 1973 in Japan.[10] The Japanese game company Tsukuda Original launched Othello in late April 1973 in Japan under Hasegawa's license, which led to an immediate commercial success.[11][12][13][14][15]

The name was selected by Hasegawa[15] as a reference to the Shakespearean play Othello, the Moor of Venice, referring to the conflict between the Moor Othello and Iago, and more controversially, to the unfolding drama between Othello, who is black, and Desdemona, who is white. The green color of the board is inspired by the image of the general Othello, valiantly leading his battle in a green field. It can also be likened to a jealousy competition (jealousy being the central theme in Shakespeare's play, which popularized the term "green-eyed monster"), since players engulf the pieces of the opponent, thereby turning them to their possession.[16]

Othello was first launched in the U.S. in 1975 by Gabriel Industries and it also enjoyed commercial success there. Sales have reportedly exceeded $600 million. More than 40 million classic games have been sold in over 100 countries.

Hasegawa's How to play Othello (Osero No Uchikata)[17] in Japan in 1974, was published in 1977 in an English translation entitled How to Win at Othello.[18]

Kabushiki Kaisha Othello, which is owned by Hasegawa, registered the trademark "OTHELLO" for board games in Japan; Tsukuda Original registered the trademark in the rest of the world. All intellectual property regarding Othello outside Japan is now owned by MegaHouse, the Japanese toy company which acquired Tsukuda Original's successor PalBox.[19]

Rules

Each of the disks' two sides corresponds to one player; they are referred to here as light and dark after the sides of Othello pieces, but any counters with distinctive faces are suitable. The game may for example be played with a chessboard and Scrabble pieces, with one player letters and the other backs.

The historical version of Reversi starts with an empty board, and the first two moves made by each player are in the four central squares of the board. The players place their disks alternately with their colors facing up and no captures are made. A player may choose to not play both pieces on the same diagonal, different from the standard Othello opening. It is also possible to play variants of Reversi and Othello where the second player's second move may or must flip one of the opposite-colored disks (as variants closest to the normal games).

For the specific game of Othello, the game begins with four disks placed in a square in the middle of the grid, two facing light-side-up, two dark-side-up, so that the same-colored disks are on a diagonal. Convention has this such that the dark-side-up disks are to the north-east and south-west (from both players' perspectives), though this is only marginally consequential: where sequential openings' memorization is preferred, such players benefit from this. The dark player moves first.

a b c d e f g h
1 a1 b1 c1 d1 e1 f1 g1 h1 1
2 a2 b2 c2 d2 e2 f2 g2 h2 2
3 a3 b3 c3 d3 e3 f3 g3 h3 3
4 a4 b4 c4 d4O e4X f4 g4 h4 4
5 a5 b5 c5 d5X e5O f5 g5 h5 5
6 a6 b6 c6 d6 e6 f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
Starting position

Dark must place a piece (dark-side-up) on the board and so that there exists at least one straight (horizontal, vertical, or diagonal) occupied line between the new piece and another dark piece, with one or more contiguous light pieces between them. For move one, dark has four options shown by translucently drawn pieces below:

a b c d e f g h
1 a1 b1 c1 d1 e1 f1 g1 h1 1
2 a2 b2 c2 d2 e2 f2 g2 h2 2
3 a3 b3 c3 d3x e3 f3 g3 h3 3
4 a4 b4 c4x d4O e4X f4 g4 h4 4
5 a5 b5 c5 d5X e5O f5x g5 h5 5
6 a6 b6 c6 d6 e6x f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
Where dark may play

Play always alternates. After placing a dark disk, dark turns over (flips to dark, captures) the single disk (or chain of light disks) on the line between the new piece and an anchoring dark piece. No player can look back to the previous status of disks when playing moves. A valid move is one where at least one piece is reversed (flipped over).

If dark decided to put a piece in the topmost location (all choices are strategically equivalent at this time), one piece gets turned over, so that the board appears thus:

a b c d e f g h
1 a1 b1 c1 d1 e1 f1 g1 h1 1
2 a2 b2 c2 d2 e2 f2 g2 h2 2
3 a3 b3 c3 d3X e3 f3 g3 h3 3
4 a4 b4 c4 d4X e4X f4 g4 h4 4
5 a5 b5 c5 d5X e5O f5 g5 h5 5
6 a6 b6 c6 d6 e6 f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
After dark play

Now light plays. This player operates under the same rules, with the roles reversed: light lays down a light piece, causing a dark piece to flip. Possibilities at this time appear thus (indicated by transparent pieces):

a b c d e f g h
1 a1 b1 c1 d1 e1 f1 g1 h1 1
2 a2 b2 c2 d2 e2 f2 g2 h2 2
3 a3 b3 c3o d3X e3o f3 g3 h3 3
4 a4 b4 c4 d4X e4X f4 g4 h4 4
5 a5 b5 c5o d5X e5O f5 g5 h5 5
6 a6 b6 c6 d6 e6 f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
Where light may play

Light takes the bottom left option and reverses one piece:

a b c d e f g h
1 a1 b1 c1 d1 e1 f1 g1 h1 1
2 a2 b2 c2 d2 e2 f2 g2 h2 2
3 a3 b3 c3 d3X e3 f3 g3 h3 3
4 a4 b4 c4 d4X e4X f4 g4 h4 4
5 a5 b5 c5O d5O e5O f5 g5 h5 5
6 a6 b6 c6 d6 e6 f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
After light play

Players take alternate turns. If one player cannot make a valid move, play passes back to the other player. When neither player can move, the game ends. This occurs when the grid has filled up or when neither player can legally place a piece in any of the remaining squares. This means the game may end before the grid is completely filled. This possibility may occur because one player has no pieces remaining on the board in that player's color. In over-the-board play this is generally scored as if the board were full (64–0).

Examples where the game ends before the grid is completely filled:

a b c d e f g h
1 a1O b1O c1O d1O e1O f1O g1O h1O 1
2 a2O b2O c2O d2O e2O f2O g2O h2O 2
3 a3O b3O c3O d3O e3O f3O g3O h3O 3
4 a4O b4O c4O d4O e4O f4O g4O h4 4
5 a5O b5O c5O d5O e5O f5O g5 h5 5
6 a6O b6O c6O d6O e6O f6O g6 h6X 6
7 a7O b7O c7O d7O e7O f7O g7O h7 7
8 a8O b8O c8O d8O e8O f8O g8O h8O 8
a b c d e f g h
Vlasáková 1 – 63 Schotte (European Grand Prix Prague 2011)
a b c d e f g h
1 a1 b1X c1X d1X e1X f1X g1X h1X 1
2 a2 b2O c2O d2O e2O f2O g2 h2X 2
3 a3O b3O c3O d3O e3O f3O g3O h3X 3
4 a4O b4O c4O d4O e4O f4O g4O h4X 4
5 a5O b5O c5O d5O e5O f5O g5O h5X 5
6 a6O b6O c6O d6O e6O f6O g6O h6X 6
7 a7O b7O c7O d7O e7O f7O g7O h7X 7
8 a8 b8O c8O d8O e8O f8O g8 h8 8
a b c d e f g h
Vecchi 13 – 51 Nicolas (World Othello Championship 2017, Ghent)
a b c d e f g h
1 a1 b1 c1 d1 e1O f1 g1 h1 1
2 a2 b2 c2 d2 e2O f2O g2 h2 2
3 a3O b3O c3O d3O e3O f3O g3O h3X 3
4 a4 b4 c4O d4O e4O f4O g4 h4X 4
5 a5 b5 c5O d5O e5O f5 g5 h5X 5
6 a6 b6 c6 d6 e6 f6 g6 h6 6
7 a7 b7 c7 d7 e7 f7 g7 h7 7
8 a8 b8 c8 d8 e8 f8 g8 h8 8
a b c d e f g h
Hassan 3 – 61 Verstuyft J. (European Grand Prix Ghent 2017)

The player with the most pieces on the board at the end of the game wins. An exception to this is that if a clock is employed then if one player defaults on time that player's opponent wins regardless of the board configuration, with varying methods to determine the official score where one is required.

In common practice over the Internet, opponents agree upon a time-control of, typically, from one to thirty minutes per game per player. Standard time control in the World Championship is thirty minutes, and this or something close to it is common in over-the-board (as opposed to internet) tournament play generally. In time-defaulted games, where disk differential is used for tie-breaks in tournaments or for rating purposes, one common over-the-board procedure for the winner of defaulted contests to complete both sides' moves with the greater of the result thereby or one disk difference in the winner's favor being the recorded score. Games in which both players have the same number of disks their color at the end (almost always with a full-board 32–32 score) are not very common, but also not rare, and these are designated as 'ties' and scored as half of a win for each player in tournaments. The term 'draw' for such may also be heard, but is somewhat frowned upon.

What are generally referred to as transcript sheets are generally in use in tournament over-the-board play, with both players obligated to record their game's moves by placing the number of each move in an 8×8 grid. This both enables players to look up past games of note and tournament directors and players to resolve disputes (according to whatever specific rules are in place) where claims that an illegal move, flip or other anomaly are voiced. An alternative recording method not requiring a grid is also in use, where positions on a board are labeled left to right by letters a through h and top to bottom (far-to-near) by digits 1 through 8 (Note that this is the opposite of the chess standard, with numerals running upward away from the side (White) that has a through h left to right, and also that the perspective may be that of either player (with no fixed standard)), so that the very first move of a game may be (based upon standard starting setup) d3, c4, f5 or e6. This alternate notational scheme is used primarily in verbal discussions or where a linear representation is desirable in print, but may also be permissible as during-game transcription by either or both players.

Tournament play using ordinary sets rather than a computer interface—where this cannot be an issue—have various ways of handling illegal moves and over- or underflipping (flips that should not be made but are or should be but are not). For example, permitting either player (perpetrator or its opponent) to make a correction going back some fixed number of moves (after which no remedy is available) is one procedure that has been used.

Significant variants of the game, such as where the starting position differs from standard or the objective is to have the fewest pieces one's color at the end, are sometimes—but rarely—played.

Brightwell Quotient

Invented by the British mathematician and three times runner-up at the World Championship and five times British Champion Graham Brightwell, this is the tie-breaker that is now used in many tournaments including the W.O.C. If two players have the same number of points in the thirteen-round W.O.C. Swiss, the tie is resolved in favour of the player with the higher Brightwell Quotient.

The Brightwell Quotient (BQ) is calculated as follows:[20]

  1. A constant c is calculated. It is the integer nearest to (number of squares on the board) divided by (number of rounds in the tournament).
  2. If any of the player's opponents have withdrawn in the course of the tournament, or if a player has been paired against bye, ignore such games for the moment.
  3. Calculate the total number of disks scored by the player in all games not covered by step 2 and add c times the sum of points scored by all of the player's opponents, except those who have withdrawn.
  4. For each game against an opponent who has withdrawn, and each bye received, add half the number of squares on the board plus (c times the player's own tournament score) to the result calculated in step 3. The number resulting is the player's BQ.

Computer opponents and research

Main article: Computer Othello

Good Othello computer programs play very strongly against human opponents. This is mostly due to difficulties in human look-ahead peculiar to Othello: The interchangeability of the disks and therefore apparent strategic meaninglessness (as opposed to chess pieces for example) makes an evaluation of different moves much harder. This can be demonstrated with blindfold games, as the memorization of the board demands much more dedication from the players than in blindfold chess.

The first tournament pitting Othello computer programs against human opponents took place in 1980. In it, then world champion Hiroshi Inoue, although he would go on to win the tournament, lost a game against the computer program The Moor. In 1997, the computer Othello program Logistello defeated the reigning human champion, Takeshi Murakami, six games to zero.[21]

Analysts have estimated the number of legal positions in Othello is at most 1028, and it has a game-tree complexity of approximately 1058.[22] Mathematically, Othello still remains unsolved. Experts have not absolutely resolved what the outcome of a game will be where both sides use perfect play. However, analysis of thousands of high-quality games (most of them computer-generated) appears to lead to a reliable conclusion (pending actual proof if true) that, on the standard 8×8 board, perfect play on both sides results in a draw.[23] When generalizing the game to play on an n×n board, the problem of determining if the first player has a winning move in a given position is PSPACE-complete.[24] On 4×4 and 6×6 boards under perfect play, the second player wins.[25] The first of these proofs is relatively trivial, and the second dates to around 1990.

World Othello Championship

The World Othello Championship (WOC), which started in 1977, was first organized by the Japan Othello Association. From 1978 until 2004, the World Othello Championship was organized by the Othello TD group and Anjar Co. In 2005, the World Othello Federation took over the responsibility for the WOC.

From 1977 to 1986, each country could send one player to participate in the WOC. From 1987, each country could send up to three players to participate. 1987, the title WOC team championship started. In 2005, a female championship category was added to the WOC. From 2006, each World Othello Federation member could send a full team of up to four players. In 2016, a youth champion title was added to the WOC.[26] The WOC was cancelled in 2020 and 2021 due to the COVID-19 pandemic.

Year Location World Champion Team Runner-up Female Champion Youth Champion
1977 Tokyo Japan Hiroshi Inoue N/A Norway Thomas Heiberg N/A N/A
1978 New York City Japan Hidenori Maruoka N/A United States Carol Jacobs N/A N/A
1979 Rome Japan Hiroshi Inoue N/A United States Jonathan Cerf N/A N/A
1980 London United States Jonathan Cerf N/A Japan Takuya Mimura N/A N/A
1981 Brussels Japan Hidenori Maruoka N/A United States Brian Rose N/A N/A
1982 Stockholm Japan Kunihiko Tanida N/A United States David Shaman N/A N/A
1983 Paris Japan Ken'Ichi Ishii N/A United Kingdom Imre Leader N/A N/A
1984 Melbourne France Paul Ralle N/A Japan Ryoichi Taniguchi N/A N/A
1985 Athens Japan Masaki Takizawa N/A Italy Paolo Ghirardato N/A N/A
1986 Tokyo Japan Hideshi Tamenori N/A France Paul Ralle N/A N/A
1987 Milan Japan Ken'Ichi Ishii United States United States France Paul Ralle N/A N/A
1988 Paris Japan Hideshi Tamenori United Kingdom United Kingdom United Kingdom Graham Brightwell N/A N/A
1989 Warsaw Japan Hideshi Tamenori United Kingdom United Kingdom United Kingdom Graham Brightwell N/A N/A
1990 Stockholm Japan Hideshi Tamenori France France France Didier Piau N/A N/A
1991 New York City Japan Shigeru Kaneda United States United States France Paul Ralle N/A N/A
1992 Barcelona France Marc Tastet United Kingdom United Kingdom United Kingdom David Shaman N/A N/A
1993 London United States David Shaman United States United States France Emmanuel Caspard N/A N/A
1994 Paris Japan Masaki Takizawa France France Denmark Karsten Feldborg N/A N/A
1995 Melbourne Japan Hideshi Tamenori United States United States United States David Shaman N/A N/A
1996 Tokyo Japan Takeshi Murakami United Kingdom United Kingdom France Stéphane Nicolet N/A N/A
1997 Athens Japan Makoto Suekuni United Kingdom United Kingdom United Kingdom Graham Brightwell N/A N/A
1998 Barcelona Japan Takeshi Murakami France France France Emmanuel Caspard N/A N/A
1999 Milan Netherlands David Shaman Japan Japan Japan Tetsuya Nakajima N/A N/A
2000 Copenhagen Japan Takeshi Murakami United States United States United States Brian Rose N/A N/A
2001 New York City United States Brian Rose United States United States United States Raphael Schreiber N/A N/A
2002 Amsterdam Netherlands David Shaman United States United States United States Ben Seeley N/A N/A
2003 Stockholm United States Ben Seeley Japan Japan Japan Makoto Suekuni N/A N/A
2004 London United States Ben Seeley United States United States Japan Makoto Suekuni N/A N/A
2005 Reykjavík Japan Hideshi Tamenori Japan Japan South Korea Kwangwook Lee Japan Hisako Kinoshita N/A
2006 Mito Japan Hideshi Tamenori Japan Japan Singapore Makoto Suekuni[27] Japan Toshimi Tsuji N/A
2007 Athens Japan Kenta Tominaga Japan Japan France Stéphane Nicolet Japan Yukiko Tatsumi N/A
2008 Oslo Italy Michele Borassi Japan Japan Japan Tamaki Miyaoka Germany Liya Ye N/A
2009 Ghent Japan Yusuke Takanashi Japan Japan Germany Matthias Berg Japan Mei Urashima N/A
2010 Rome Japan Yusuke Takanashi Japan Japan Italy Michele Borassi Netherlands Jiska Helmes N/A
2011 Newark Japan Hiroki Nobukawa Japan Japan Thailand Piyanat Aunchulee United States Jian Cai N/A
2012 Leeuwarden Japan Yusuke Takanashi Japan Japan Japan Kazuki Okamoto Sweden Veronica Stenberg N/A
2013 Stockholm Japan Kazuki Okamoto Japan Japan Thailand Piyanat Aunchulee Finland Katie Wu N/A
2014 Bangkok Japan Makoto Suekuni Japan Japan United States Ben Seeley Australia Joanna William N/A
2015 Cambridge Japan Yusuke Takanashi Japan Japan Japan Makoto Suekuni United States Yoko Sano Rose N/A
2016 Mito Thailand Piyanat Aunchulee Japan Japan China Yan Song China Zhen Dong Japan Masaki Wada
2017 Ghent Japan Yusuke Takanashi Japan Japan Japan Akihiro Takahashi Japan Misa Sugawara Japan Akihiro Takahashi
2018 Prague Japan Keisuke Fukuchi Japan Japan Thailand Piyanat Aunchulee Japan Misa Sugawara Japan Keisuke Fukuchi
2019 Tokyo Japan Akihiro Takahashi Japan Japan Japan Yusuke Takanashi Australia Joanna William Japan Akihiro Takahashi
2020 Cancelled
2021 Cancelled
2022[28] Paris Japan Kento Urano Japan Japan Switzerland Arthur Juigner Finland Katie Pihlajapuro Japan Fuyumi Okudaira

References

  1. ^ Note: He was not the Lewis Waterman who patented the Waterman fountain pen in 1884. [citation needed]
  2. ^ "Brief history of Othello". Othello Museum. Beppi.it. Retrieved 4 January 2015.
  3. ^ "Fine New Games and Toys; Now Ready for Distribution by the Agents of Santa Claus. In the Modern Wonderland – Millions Spent for the Amusement and Instruction of Children – Minds Active and Hands Busy All the Time". The New York Times. 1 December 1895. Retrieved 4 January 2015.
  4. ^ 松浦政泰 (December 1907). "裏返へし（レヴアルシー）Reversi". 世界遊戯法大全 (in Japanese). Hakubunkan. pp. 187–189. doi:10.11501/860315.
  5. ^ See Japan Utility Patent Application numbers S46-001435 (JP,1971-001435) and number S47-135869 (JP,1972-135869), available via https://www.j-platpat.inpit.go.jp/web/all/top/BTmTopEnglishPage
  6. ^ "Modern Living: Japanese Othello". Time. 11 November 1976. Retrieved 28 May 2016.
  7. ^ Goro Hasegawa (December 1973). "大流行の『オセロ』ゲームづくり一代". Gendai (in Japanese). 7 (12). Kodansha: 147–151. doi:10.11501/3367321.
  8. ^ Goro Hasegawa (December 2005). オセロ百人物語-オセロ史を飾った名選手たち (in Japanese). Kawade Shobō Shinsha. ISBN 9784309906553.
  9. ^ Goro Hasegawa (1981). オセロの打ち方 How to Othello (in Japanese). p. 136.
  10. ^ The Nihon Keizai Shimbun. Page 24, 20 March 1973
  11. ^ "140 years of history". Retrieved 4 January 2015.
  12. ^ Pages 147–151 of The December issue of GENDAI, published by Kodansha on 1 December 1973. Viewed at National Diet Library of Japan
  13. ^ Pages 110–113 August 25 issue of Yomiuri Weekly, published by Yomiuri Shimbun on 25 August 1973. Viewed at National Diet Library of Japan
  14. ^ Page 23 of Vol.77, No.1811 of JITSUGYO NO NIHON published by Jitsugyo no Nihon Sha, Ltd. on 1 March 1974. Viewed at National Diet Library of Japan
  15. ^ a b Pages 276–281 December issue of The Ushio published by Ushio Publishing Co., Ltd., on 1 December 1974. Viewed at National Diet Library of Japan
  16. ^ "Japanese Othello". Time Magazine. 22 November 1976. Archived from the original on 3 November 2007.
  17. ^ , published by The Japan Othello Association.
  18. ^ GORO, HASEGAWA (1977). HOW TO WIN AT OTHELLO. U.S.: A Harvest / HBJ Book. ISBN 978-0156422154.
  19. ^ "MegaHouse and Co. Pal box signed a transfer agreement part of the business (translated by Google translation)". Archived from the original on 23 September 2015. Retrieved 11 September 2015.
  20. ^ "Britishothello.org.uk" (PDF). Archived from the original (PDF) on 18 February 2019.
  21. ^ Buro, Michael (2003). "The Evolution of Strong Othello Programs". Entertainment Computing. IFIP Advances in Information and Communication Technology. Vol. 112. pp. 81–88. doi:10.1007/978-0-387-35660-0_10. ISBN 978-1-4757-5153-6.
  22. ^ Victor Allis (1994). Searching for Solutions in Games and Artificial Intelligence (PDF). PhD Thesis, University of Limburg, Maastricht, The Netherlands. ISBN 90-900748-8-0.
  23. ^ Richard Delorme. "Book 2008". Abulmo.perso.neuf.fr. Archived from the original on 3 March 2016. Retrieved 17 March 2019.
  24. ^ S. Iwata and T. Kasai (1994). "The Othello game on an n*n board is PSPACE-complete". Theor. Comput. Sci. 123 (2): 329–340. doi:10.1016/0304-3975(94)90131-7.
  25. ^ [1]Archived 29 October 2013 at the Wayback Machine
  26. ^ "World Othello Championship :: World Othello Federation". www.worldothello.org. Retrieved 21 June 2021.
  27. ^ "2006.htm". docs.google.com.
  28. ^ woc2022.worldothello.org/live/
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