Summary Solving Othello A Computational Milestone arxiv.org
5,644 words - PDF document - View PDF document
One Line
The computational solution of Othello (Reversi) using the alpha-beta search algorithm resulted in a draw, potentially paving the way for solving Chess next.
Slides
Slide Presentation (9 slides)
Key Points
- Othello, also known as Reversi, is a complex and popular game that has yet to be computationally solved.
- Othello has approximately 10 octodecillion possible game records and 10 octillion possible game positions.
- Othello has now been weakly solved, with perfect play by both players leading to a draw.
- Solving Othello enables software to play the game perfectly and determine the outcome of every possible position.
- Othello's strategic richness is due to its vast exploration space, with an estimated 10^58 possible game records and 10^28 possible board positions.
Summaries
20 word summary
Othello (Reversi) has been computationally solved, resulting in a draw. The alpha-beta search algorithm was used. Chess may be next.
79 word summary
Othello, also known as Reversi, has been solved computationally. Perfect play by both players results in a draw. The game has been weakly solved on an 8x8 board, with the initial position proven to be a draw. The alpha-beta search algorithm was used, and the proofs obtained are nearly indisputable. This is a significant milestone for computer science and AI technology. Chess may be the next game to be weakly solved, but it requires computational power and theoretical breakthroughs.
152 word summary
Othello, also known as Reversi, has been computationally solved, proving that perfect play by both players leads to a draw. Solving Othello allows software to determine the outcome of every possible position. The complexity of Othello comes from its vast exploration space, but it has now been weakly solved on an 8x8 board, with the initial position proven to be a draw. While software has been developed to play other games at superhuman strength, they cannot perfectly solve them. The alpha-beta search algorithm was used to solve Othello, with modifications made to improve search efficiency. The computational proofs obtained in this study are nearly indisputable and can be easily recalculated if needed. This achievement is a significant milestone for computer science and AI technology, showcasing advances in computational power and algorithms. Chess may be the next game to be weakly solved, but it will require improvements in computational power and theoretical breakthroughs.
402 word summary
Othello, also known as Reversi, is a complex game that has been computationally solved. With an enormous number of possible game records and positions, solving Othello has been a challenge in computer science. However, it has now been proven that perfect play by both players leads to a draw.
Solving Othello allows software to play the game perfectly by determining the outcome of every possible position. Othello software has traditionally used heuristic search techniques, but by solving the game, the results for all possible positions can be determined.
Othello's complexity comes from its vast exploration space, with an estimated number of possible game records and positions. In this study, Othello on an 8x8 board has been weakly solved, with the initial position proven to be a draw.
While software has been developed to play games like chess, Go, Shogi, and Othello at superhuman strength, these programs cannot perfectly solve the games.
Solving a game means determining the final result under perfect play by both players. Games can be classified as ultra-weakly solved, weakly solved, or strongly solved. Othello is now weakly solved, with both the game-theoretic value and the strategy to achieve it from the initial position determined.
Othello is a popular game played worldwide since the 19th century. World Championships have been held annually since 1977.
To solve Othello, an alpha-beta search algorithm was used. The existing Othello software, Edax, was modified to improve search efficiency. These modifications reduced the number of positions that needed to be explored.
The process of solving Othello involved solving positions with 36 empty squares. Algorithms were used to generate subsets of positions and estimate the game-theoretic value for these positions. The results confirmed that the initial position results in a draw.
The computational proofs obtained in this study are nearly indisputable. The calculations were executed on a computer cluster with ECC memory to minimize computational errors. In the unlikely event of errors, they can be easily recalculated using the publicly released software.
This achievement in solving Othello is a significant milestone for computer science and AI technology, showcasing advances in computational power and algorithms. Chess may be the next game to be weakly solved, but it will require improvements in computational power and theoretical breakthroughs.
In conclusion, Othello has been weakly solved, with the initial position proven to be a draw. This study provides insights into the methods used and the implications of this research.
612 word summary
Othello, also known as Reversi, is a complex and popular game that has yet to be computationally solved. With approximately 10 octodecillion possible game records and 10 octillion possible game positions, solving Othello has been a grand challenge in computer science. However, a significant milestone has been achieved: Othello is now solved. It has been computationally proven that perfect play by both players leads to a draw.
Solving a game like Othello provides the solution that enables software to play the game perfectly. Othello software has long been built using heuristically designed search techniques. By solving the game, the outcome of every possible position that may arise during gameplay can be determined.
Othello's strategic richness is due to its vast exploration space. With an estimated 10^58 possible game records and 10^28 possible board positions, Othello has remained unsolved until now. In this study, Othello (8 x 8 board) is weakly solved, with the game-theoretic value of the initial position proven to be a draw.
Mastering pure strategy games like chess has been a symbol of human intelligence and a subject of artificial intelligence (AI) research. Superhuman-strength software has been developed for popular games like chess, Go, Shogi (Japanese chess), and Othello. However, these programs cannot perfectly solve the games.
Solving games of perfect information means determining the final result, or game-theoretic value, of the game under perfect play by both players. Solved games are classified into ultra-weakly solved, weakly solved, and strongly solved. Ultra-weakly solved games reveal the game-theoretic value of the initial position but not the winning strategy. Weakly solved games determine both the game-theoretic value and a strategy to achieve it from the initial position. Strongly solved games calculate the outcomes for all possible positions during gameplay.
Othello is a highly popular game known for its deep strategic nature. It was invented in the 19th century and has gained widespread appeal across the globe. The annual World Championships have been held since 1977.
To solve Othello, a search algorithm called alpha-beta search was utilized. The existing Othello software called Edax was modified to improve search efficiency. The modified algorithm disabled aspiration search during iterative deepening and ignored shallow search results from the transposition table. These modifications helped reduce the number of positions that needed to be explored.
The process of solving Othello involved solving positions with 36 empty squares. Algorithm 1 was used to generate a subset of positions with 50 empty squares, which, if solved correctly, would prove the game-theoretic value of the initial position. Algorithm 2 estimated the game-theoretic value of positions with 36 empty squares using alpha-beta search. Algorithm 3 calculated upper and lower bounds of the game-theoretic value for these positions.
The positions with 36 empty squares were solved using a computer cluster and Edax software. The results of these calculations confirmed the hypotheses formulated for the initial position and proved that it results in a draw.
The computational proofs obtained in this study are nearly indisputable. The calculations were executed on a computer cluster with ECC memory, minimizing the chance of computational errors. In the unlikely event of errors, they can be easily recalculated using the publicly released software.
This achievement in solving Othello is a significant milestone for computer science and AI technology. It demonstrates the remarkable advances in computational power and algorithms. While chess may be the next game to be weakly solved, it may require both improvements in computational power and theoretical breakthroughs.
In conclusion, Othello has been weakly solved, with the game-theoretic value of the initial position proven to be a draw. This study provides insights into the methods used to solve Othello and the implications of this research. The raw