Author:
(1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Related Works Methods Results Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References Additional Information and Declarations Competing Interests The author declares that there are no competing interests. Author Contributions Hiroki Takizawa conceived and designed the research, implemented and performed the computational experiments, analyzed the data, prepared figures and tables, authored drafts of the paper, and approved the final draft. Data Availability The source code of modified Edax is available at GitHub (https://github.com/eukaryo/edax-reversi-AVX-v446mod2), and Zenodo (https://doi.org/10.5281/zenodo.10030906). The raw outputs of analyses are available at figshare (https://doi.org/10.6084/m9.figshare.24420619). The source code for analyses are available at GitHub (https://github.com/eukaryo/reversi-scripts). Funding The author did not receive any academic funding for this study. References [1] Charles Babbage. Passages from the Life of a Philosopher. London: Longman, 1864. [2] Claude E Shannon. Xxii. programming a computer for playing chess. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(314):256–275, 1950. [3] Murray Campbell, A. Joseph Hoane, and Feng-hsiung Hsu. Deep blue. Artif. Intell., 134(1–2):57–83, January 2002. [4] David Silver, Aja Huang, Christopher J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of go with deep neural networks and tree search. nature, 529(7587):484–489, 2016. [5] Tomoyuki Kaneko and Takenobu Takizawa. Computer shogi tournaments and techniques. IEEE Transactions on Games, 11(3):267–274, 2019. [6] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science, 362(6419):1140–1144, 2018. [7] Michael Buro. The othello match of the year: Takeshi murakami vs. logistello. ICGA Journal, 20(3):189–193, 1997. [8] L. V. Allis. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Department of Computer Science, University of Limburg, 1994. [9] Hiroki Takizawa. Strongly solved ostle: calculating a strong solution helps compose high-quality puzzles for recent games. PeerJ Computer Science, 9:e1560, 2023. [10] Jonathan Schaeffer, Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, and Steve Sutphen. Checkers is solved. science, 317(5844):1518–1522, 2007. [11] Ralph Gasser. Solving nine men’s morris. Computational Intelligence, 12(1):24–41, 1996. [12] John W Romein and Henri E Bal. Solving awari with parallel retrograde analysis. Computer, 36(10):26–33, 2003. [13] Donald E Knuth and Ronald W Moore. An analysis of alpha-beta pruning. Artificial intelligence, 6(4):293–326, 1975. [14] Ken Thompson. Retrograde analysis of certain endgames. J. Int. Comput. Games Assoc., 9(3):131–139, 1986. [15] Ayumu Nagai. Df-pn algorithm for searching AND/OR trees and its applications. PhD thesis, Department of Information Science, University of Tokyo, 2002. [16] Akihiro Kishimoto, Mark HM Winands, Martin Müller, and Jahn-Takeshi Saito. Game-tree search using proof numbers: The first twenty years. Icga Journal, 35(3):131–156, 2012. [17] L.Victor Allis, Maarten van der Meulen, and H.Jaap van den Herik. Proof-number search. Artificial Intelligence, 66(1):91–124, 1994. [18] Rainer Feldmann, Burkhard Monien, Peter Mysliwietz, and Oliver Vornberger. Distributed game tree search. Parallel Algorithms for Machine Intelligence and Vision, pages 66–101, 1990. [19] Emil Fredrik Østensen. A complete chess engine parallelized using lazy smp. Master’s thesis, University of Oslo, 2016. [20] Mark Gordon Brockington. Asynchronous Parallel Garne-Tree Search. PhD thesis, University of Alberta, 1998. [21] Jean-Christophe Weill. The abdada distributed minimax search algorithm. In Proceedings of the 1996 ACM 24th Annual Conference on Computer Science, CSC ’96, page 131–138, New York, NY, USA, 1996. Association for Computing Machinery. [22] Richard Delorme. edax-reversi. https://github.com/abulmo/edax-reversi, 2021. Last retrieved 2023-07-07. [23] French Othello Federation. La base wthor. https://www.ffothello.org/informatique/la-base-wthor/, 2021. Last retrieved 2023-10-13. This paper is available on arxiv under CC 4.0 license. Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Author: Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Abstract and Intro Related Works Related Works Methods Methods Results Results Discussion and Conclusions and Acknowledgements Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References Additional Information and Declarations and References Additional Information and Declarations Competing Interests The author declares that there are no competing interests. Author Contributions Hiroki Takizawa conceived and designed the research, implemented and performed the computational experiments, analyzed the data, prepared figures and tables, authored drafts of the paper, and approved the final draft. Data Availability The source code of modified Edax is available at GitHub (https://github.com/eukaryo/edax-reversi-AVX-v446mod2), and Zenodo (https://doi.org/10.5281/zenodo.10030906). The raw outputs of analyses are available at figshare (https://doi.org/10.6084/m9.figshare.24420619). The source code for analyses are available at GitHub (https://github.com/eukaryo/reversi-scripts). Funding The author did not receive any academic funding for this study. References [1] Charles Babbage. Passages from the Life of a Philosopher. London: Longman, 1864. [2] Claude E Shannon. Xxii. programming a computer for playing chess. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(314):256–275, 1950. [3] Murray Campbell, A. Joseph Hoane, and Feng-hsiung Hsu. Deep blue. Artif. Intell., 134(1–2):57–83, January 2002. [4] David Silver, Aja Huang, Christopher J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of go with deep neural networks and tree search. nature, 529(7587):484–489, 2016. [5] Tomoyuki Kaneko and Takenobu Takizawa. Computer shogi tournaments and techniques. IEEE Transactions on Games, 11(3):267–274, 2019. [6] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science, 362(6419):1140–1144, 2018. [7] Michael Buro. The othello match of the year: Takeshi murakami vs. logistello. ICGA Journal, 20(3):189–193, 1997. [8] L. V. Allis. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Department of Computer Science, University of Limburg, 1994. [9] Hiroki Takizawa. Strongly solved ostle: calculating a strong solution helps compose high-quality puzzles for recent games. PeerJ Computer Science, 9:e1560, 2023. [10] Jonathan Schaeffer, Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, and Steve Sutphen. Checkers is solved. science, 317(5844):1518–1522, 2007. [11] Ralph Gasser. Solving nine men’s morris. Computational Intelligence, 12(1):24–41, 1996. [12] John W Romein and Henri E Bal. Solving awari with parallel retrograde analysis. Computer, 36(10):26–33, 2003. [13] Donald E Knuth and Ronald W Moore. An analysis of alpha-beta pruning. Artificial intelligence, 6(4):293–326, 1975. [14] Ken Thompson. Retrograde analysis of certain endgames. J. Int. Comput. Games Assoc., 9(3):131–139, 1986. [15] Ayumu Nagai. Df-pn algorithm for searching AND/OR trees and its applications. PhD thesis, Department of Information Science, University of Tokyo, 2002. [16] Akihiro Kishimoto, Mark HM Winands, Martin Müller, and Jahn-Takeshi Saito. Game-tree search using proof numbers: The first twenty years. Icga Journal, 35(3):131–156, 2012. [17] L.Victor Allis, Maarten van der Meulen, and H.Jaap van den Herik. Proof-number search. Artificial Intelligence, 66(1):91–124, 1994. [18] Rainer Feldmann, Burkhard Monien, Peter Mysliwietz, and Oliver Vornberger. Distributed game tree search. Parallel Algorithms for Machine Intelligence and Vision, pages 66–101, 1990. [19] Emil Fredrik Østensen. A complete chess engine parallelized using lazy smp. Master’s thesis, University of Oslo, 2016. [20] Mark Gordon Brockington. Asynchronous Parallel Garne-Tree Search. PhD thesis, University of Alberta, 1998. [21] Jean-Christophe Weill. The abdada distributed minimax search algorithm. In Proceedings of the 1996 ACM 24th Annual Conference on Computer Science, CSC ’96, page 131–138, New York, NY, USA, 1996. Association for Computing Machinery. [22] Richard Delorme. edax-reversi. https://github.com/abulmo/edax-reversi, 2021. Last retrieved 2023-07-07. [23] French Othello Federation. La base wthor. https://www.ffothello.org/informatique/la-base-wthor/, 2021. Last retrieved 2023-10-13. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

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