Computer Othello
NTest - a strong othello program

Computer Othello refers to computer architecture encompassing computer hardware and computer software capable of playing the game of Othello. It was notably included in Microsoft Windows from 1.0 to XP, where it is simply known as Reversi.

Availability

There are many Othello programs such as NTest, Saio, Edax, Cassio, Pointy Stone, Herakles, WZebra, and Logistello that can be downloaded from the Internet for free. These programs, when run on any up-to-date computer, can play games in which the best human players are easily defeated. This is because although the consequences of moves are predictable for both computers and humans, computers are better at envisaging them.[1]

Search techniques

Computer Othello programs search for any possible legal moves using a game tree. In theory, they examine all positions / nodes, where each move by one player is called a "ply". This search continues until a certain maximum search depth or the program determines that a final "leaf" position has been reached.

A naive implementation of this approach, known as Minimax or Negamax, can only search to a small depth in a practical amount of time, so various methods have been devised to greatly increase the speed of the search for good moves. These are based on Alpha-beta pruning, Negascout, MTD(f), and NegaC*.[2] The alphabeta algorithm is a method for speeding up the Minimax searching routine by pruning off cases that will not be used anyway. This method takes advantage of the fact that every other level in the tree will maximize and every other level will minimize.[3]

Several heuristics are also used to reduce the size of the searched tree: good move ordering, transposition table and selective Search.[4]

To speed up the search on machines with multiple processors or cores, a "parallel search" may be implemented. Several experiments have been made with the game Othello, like ABDADA[5] or APHID[6] On recent programs, the YBWC[7] seems the preferred approach.

Multi-Prob cut

Multi-ProbCut is a heuristic used in alpha–beta pruning of the search tree.[8] The ProbCut heuristic estimates evaluation scores at deeper levels of the search tree using a linear regression between deeper and shallower scores. Multi-ProbCut extends this approach to multiple levels of the search tree. The linear regression itself is learned through previous tree searches, making the heuristic a kind of dynamic search control.[9] It is particularly useful in games such as Othello where there is a strong correlation between evaluations scores at deeper and shallower levels.[10][11]

Evaluation techniques

There are three different paradigms for creating evaluation functions.

Disk-square tables

Different squares have different values - corners are good and the squares next to corners are bad. Disregarding symmetries, there are 10 different positions on a board, and each of these is given a value for each of the three possibilities: black disk, white disk and empty. A more sophisticated approach is to have different values for each position during the different stages of the game; e.g. corners are more important in the opening and early midgame than in the endgame.[12]

Mobility-based

Most human players strive to maximize mobility (number of moves available) and minimize frontier disks (disks adjacent to empty squares). Player mobility and opponent mobility are calculated, and player potential mobility and opponent potential mobility are calculated as well.[13] These measures can be found very quickly, and they significantly increase playing strength. Most programs have knowledge of edge and corner configurations and try to minimize the number of disks during the early midgame, another strategy used by human players.[12]

Pattern-based / pattern coefficients

Mobility maximization and frontier minimization can be broken down into local configurations which can be added together; the usual implementation is to evaluate each row, column, diagonal and corner configuration separately and add together the values, many different patterns have to be evaluated.[12] The process of determining values for all configurations is done by taking a large database of games played between strong players and calculating statistics for each configuration in each game stage from all the games.[12]

The most common choice to predict the final disc difference uses a weighted disk difference measure where the winning side gets a bonus corresponding to the number of disks.[12]

Opening book

Opening books aid computer programs by giving common openings that are considered good ways to counter poor openings. All strong programs use opening books and update their books automatically after each game. To go through all positions from all games in the game database and determine the best move not played in any database game, transposition tables are used to record positions that have been previously searched. This means those positions do not need to be searched again.[12] This is time-consuming as a deep search must be performed for each position, but once this is done, updating the book is easy. After each game played, all new positions are searched for the best deviation.

Other optimizations

Faster hardware and additional processors can improve Othello-playing program abilities, such as deeper ply searching.

Solving Othello

During gameplay, players alternate moves. The human player uses black counters while the computer uses white. The human player starts the game.[1] Othello is strongly solved on 4×4 and 6×6 boards, with the second player (white) winning in perfect play.[14][15] It remains unsolved on a standard 8×8 board, but computer analysis gives thousands of draw lines, or paths to a draw, although no such line has been fully proven.[16]

Othello 4 × 4

Othello 4x4 has a very small game tree and has been solved in less than one second by many simple Othello programs that use the Minimax method, which generates all possible positions (nearly 10 million). The result is that white wins with a +8 margin (3-11).[14]

Othello 6 × 6

Othello 6x6 has been solved in less than 100 hours by many simple Othello programs that use the Minimax method, which generates all possible positions (nearly 3.6 trillion). The result is that white wins with a +4 margin (16-20).[17]

Othello 8 × 8

The Othello 8x8 game tree size is estimated at 1054 nodes, and the number of legal positions is estimated at less than 1028. As of October 2023, a preprint claims that the game has been solved, with optimal result being draw.[18][19] Computation results is also shared, making it one of the largest publicly available book.[20]

Some top programs have expanded their books for many years now. As a result, many lines are in practice draws or wins for either side. Regarding the three main openings of diagonal, perpendicular and parallel, it appears that both diagonal and perpendicular openings lead to drawing lines, while the parallel opening is a win for black. The drawing tree also seems bigger after the diagonal opening than after the perpendicular opening.[21] The parallel opening has strong advantages for the black player, enabling black to always win in a perfect play.[22]

Milestones in computer Othello

a b c d e f g h
1 a1X b1X c1X d1X e1X f1X g1X h1X 1
2 a2X b2X c2O d2X e2X f2X g2X h2X 2
3 a3X b3X c3X d3O e3X f3X g3O h3X 3
4 a4X b4X c4O d4X e4X f4O g4X h4X 4
5 a5X b5X c5X d5X e5X f5X g5X h5X 5
6 a6X b6X c6X d6O e6X f6X g6X h6X 6
7 a7X b7X c7O d7O e7O f7X g7X h7X 7
8 a8X b8X c8X d8X e8X f8X g8X h8X 8
a b c d e f g h
Logistello vs. Takeshi Murakami (4th Game)
  • 1977: Scientific American made the earliest known published reference to an Othello/Reversi program, written by N. J. D. Jacobs in BCPL.[23] BYTE published "Othello, a New Ancient Game" as a BASIC type-in program in October.[24]
  • 1977: Creative Computing published a version of Othello written by Ed Wright in FORTRAN.[25][26]
  • 1978: Nintendo releases the video game Computer Othello in arcades.[27]
  • 1980: The Othello program The Moor (written by Mike Reeve and David Levy) won one game in a six-game match against world champion Hiroshi Inoue.[28] Peter W Frey of Northwestern University discussed computer and human Othello strategies in BYTE, and discussed his TRS-80 Othello game which, Frey claimed, easily defeated Wright's version running on a CDC 6600.[26] Paul Rosenbloom of Carnegie Mellon University developed IAGO, which finished in third place at a Northwestern University computer tournament.[29] When IAGO played The Moor, IAGO was better at capturing pieces permanently and limiting its opponent's mobility.[28]
  • 1981: IAGO running on a DEC KA10 finished ahead of 19 other contestants at the Santa Cruz Open Othello Tournament at the University of California, Santa Cruz, with the only undefeated record. Charles Heath's TRS 80-based game finished in second place. Microcomputer CPU-based engines won the second through seventh places, ahead of several mainframes and minicomputers; Frey speculated that this was because computer Othello does not benefit from several of the advantages of larger computers, such as faster floating-point arithmetic.[29]
  • Late 1980s: Kai-Fu Lee and Sanjoy Mahajan created the Othello program BILL, which was similar to IAGO but incorporated Bayesian learning. BILL reliably beat IAGO.[28]
  • 1992: Michael Buro began work on the Othello program Logistello. Logistello's search techniques, evaluation function, and knowledge base of patterns were better than those in earlier programs. Logistello perfected its game by playing over 100,000 games against itself.[28]
  • 1997: Logistello won every game in a six-game match against world champion Takeshi Murakami. Though there had not been much doubt that Othello programs were stronger than humans, it had been 17 years since the last match between a computer and a reigning world champion. After the 1997 match, there was no longer any doubt: Logistello was significantly better than any human player.[30][28]
  • 1998: Michael Buro retired Logistello. Research interest in Othello waned somewhat, but some programs, including Ntest, Saio, Edax, Cassio, Zebra and Herakles, continued to be developed.[28]
  • 2004: Ntest became the strongest program, significantly stronger than Logistello.
  • 2005: Ntest, Saio, Edax, Cyrano and Zebra, became significantly stronger than Logistello. Ntest and Zebra retired.
  • 2011: Saio, Edax and Cyrano, became much faster than Logistello and other programs.
  • 2022: Egaroucid appears as strong engine highly inspired by Edax.
  • 2023: Othello is solved using slightly modified Edax. Egaroucid releases self-play data.[31]

List of top Othello/ Reversi programs

  1. NTest (Ntest) by Chris Welty
  2. Edax (Edax Archived 2013-04-06 at the Wayback Machine) by Richard Delorme
  3. Logistello (Logistello) by Michael Buro

See also

Notes

  1. 1 2 "Dcs.gla.ac.uk" (PDF). Archived from the original (PDF) on January 3, 2011.
  2. ↑ Jean-Christophe Weill (1992). The NegaC* Search. ICCA Journal, Vol. 15, No. 1, pp. 3-7.
  3. ↑ Armanto, Hendrawan; Santoso, Joan; Giovanni, Daniel; Kurniawan, Faris; Yudianto, Ricky; Gunawan, Steven (October 2012). "Evolutionary Neural Network for Othello Game". Procedia - Social and Behavioral Sciences. 57: 419–425. doi:10.1016/j.sbspro.2012.09.1206.
  4. ↑ Buro, M., "Experiments with Multi-ProbCut and a New High-Quality Evaluation Function for Othello", Games in AI Research, H.J. van den Herik, H. Iida (ed.), ISBN 90-621-6416-1, 2000
  5. ↑ Jean-Christophe Weill (1996). The ABDADA Distributed Minimax Search Algorithm. Proceedings of the 1996 ACM Computer Science Conference, pp. 131-138. ACM, New York, N.Y, reprinted ICCA Journal Vol. 19, No. 1
  6. ↑ Mark Brockington (1997). KEYANO Unplugged - The Construction of an Othello Program. Technical Report TR-97-05, Department of Computing Science, University of Alberta.
  7. ↑ Rainer Feldmann, Peter Mysliwietz, Burkhard Monien (1991). A Fully Distributed Chess Program. Advances in Computer Chess 6
  8. ↑ Buro, Michael (1997). "Experiments with Multi-ProbCut and a New High-Quality Evaluation Function for Othello". Games in AI Research. 34 (4): 77–96.
  9. ↑ Bulitko, Vadim; Lustrek, Mitja; Schaeffer, Jonathan; Bjornsson, Yngvi; Sigmundarson, Sverrir (1 June 2008). "Dynamic control in real-time heuristic search". Journal of Artificial Intelligence Research. 32: 419–452. doi:10.1613/jair.2497.
  10. ↑ Fürnkranz, Johannes (2001). Machines that learn to play games | Guide books. Nova Science Publishers, Inc.6080 Jericho Tpke. Suite 207 Commack, NYUnited States: Nova Science Publishers, Inc. pp. 11–59. ISBN 978-1-59033-021-0.{{cite book}}: CS1 maint: location (link)
  11. ↑ Heinz, Ernst A. (2013). Scalable Search in Computer Chess: Algorithmic Enhancements and Experiments at High Search Depths. Springer Science & Business Media. p. 32. ISBN 978-3-322-90178-1.
  12. 1 2 3 4 5 6 Gunnar Andersson (2007). "Writing an Othello program". radagast.se. Retrieved 2023-02-12.
  13. ↑ How Ntest Works Archived 2011-11-09 at the Wayback Machine March 02, 2005
  14. 1 2 Solution of Othello 4 × 4 Archived 2011-07-07 at the Wayback Machine September 02, 2008
  15. ↑ Perfect play in 6x6 Othello from two alternative starting positions Archived November 1, 2009, at the Wayback Machine November 17, 2004
  16. ↑ "2004 Opening Book Skeleton". www.sfr.fr. 2008. Archived from the original on 2011-01-08. Retrieved 2023-02-12.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  17. ↑ F. Pittner (July 2006). "Tothello home page". www.tothello.com. Retrieved 2023-02-12.
  18. ↑ "Othello is Solved" (PDF). Retrieved 2023-11-04.
  19. ↑ Takizawa, Hiroki. "reversi-scripts". Github. Retrieved 4 November 2023.
  20. ↑ "Analyses of the Game of Othello's Positions". Retrieved 2023-11-04.
  21. ↑ "Strongest othello program in term of artificial intelligent". Archived from the original on 2007-01-09. Retrieved 2010-04-05.
  22. ↑ "SaioApp project – The strongest Othello engine". Retrieved 2023-02-12.
  23. ↑ Gardner, Martin. Mathematical Recreations. Scientific American, April 1977.
  24. ↑ Duda, Richard O (October 1977). "Othello, a New Ancient Game". BYTE. pp. 60–62.
  25. ↑ Wright, Ed (November–December 1977). "Othello". Creative Computing. pp. 140–142. Retrieved 18 October 2013.
  26. 1 2 Frey, Peter W (July 1980). "Simulating Human Decision-Making on a Personal Computer". BYTE. p. 56. Retrieved 18 October 2013.
  27. ↑ "Computer Othello - Videogame by Nintendo".
  28. 1 2 3 4 5 6 "The History of Computer Games" (PDF). Archived from the original (PDF) on January 24, 2011.
  29. 1 2 Frey, Peter W (July 1981). "The Santa Cruz Open / Othello Tournament for Computers". BYTE. p. 16. Retrieved 18 October 2013.
  30. ↑ Michael Buro (20 August 1997). "Othello match of the year". skatgame.net. Retrieved 2023-02-12.
  31. ↑ Yamana, Takuto. "Egaroucid Self-Play Transcripts". Othello AI Egaroucid. Retrieved 5 November 2023.
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