Checkers Is Solved

@article{Schaeffer2007CheckersIS,
  title={Checkers Is Solved},
  author={J. Schaeffer and Neil Burch and Y. Bj{\"o}rnsson and Akihiro Kishimoto and Martin M{\"u}ller and R. Lake and P. Lu and S. Sutphen},
  journal={Science},
  year={2007},
  volume={317},
  pages={1518 - 1522}
}
The game of checkers has roughly 500 billion billion possible positions (5 × 1020). The task of solving the game, determining the final result in a game with no mistakes made by either player, is daunting. Since 1989, almost continuously, dozens of computers have been working on solving checkers, applying state-of-the-art artificial intelligence techniques to the proving process. This paper announces that checkers is now solved: Perfect play by both sides leads to a draw. This is the most… Expand
View on AAAS
cs.cornell.edu
404 Citations
Highly Influential Citations
15
Background Citations
140
Methods Citations
32
Results Citations
3

404 Citations

Citation Type

Citation Type

Computer Games
TLDR
Results from a preliminary study on how to best use the data to improve the play of a Chinese Checkers program are reported. Expand
Gardner's Minichess Variant is Solved
TLDR
Gardner's minichess variant in which all pieces are set as in a standard chessboard is considered, which has roughly 9x10^{18} legal positions and is comparable in this respect with checkers. Expand
Game-Tree Search Using Proof Numbers: The First Twenty Years
TLDR
An overview of the research on Proof-Number Search and its many variants and enhancements is provided. Expand
Solving Jungle Checkers
TLDR
Using endgame databases constructed by retrograde analysis, this work tries to ultra-weakly solve Jungle Checkers by using the concept of a proof tree: both alpha-beta pruning and proof-number search algorithms are applied. Expand
The dark side of the board: advances in chess Kriegspiel
TLDR
This thesis presents, documents and tests a multi-sided effort towards making a strong Kriegspiel player, using heuristic searching, retrograde analysis and Monte Carlo tree search algorithms to achieve increasingly higher levels of play. Expand
On Strongly Solving Chinese Checkers
TLDR
An overview of what is required to strongly solve versions of Chinese Checkers, including a complete set of rules needed to solve the game, is provided. Expand
Countdown Numbers Game: Solved, Analysed, Extended
The Countdown Numbers Game is a popular arithmetical puzzle which has been played as a two-player game on French and British television weekly for decades. We have solved this game in the sense that… Expand
Combinatorial Games: From Theoretical Solving to AI Algorithms
TLDR
In the current survey, the basics of the best AI programs will be presented, and in particular the well-known Minimax and Monte-Carlo Tree Search approaches. Expand
Game Over: Black to Play and Draw in Checkers
  • J. Schaeffer
  • Computer Science
  • J. Int. Comput. Games Assoc.
  • 2007
TLDR
Checkers is the largest popular game that has been solved to date, and perfect play by both sides leads to a draw. Expand
A New Chess Variant for Gaming AI
TLDR
A newly-invented chess variant called Switch-Side Chain-Chess, which states that players have the choice to switch sides with each other if a continuous link of pieces is created on the board, increases significantly the complexity of chess. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
Solving Checkers
TLDR
One of the most challenging checkers openings has been solved-the White Doctor opening is a draw, which will result in the game-theoretic value of checkers being determined. Expand
Programming a computer for playing chess
This paper is concerned with the problem of constructing a computing routine or “program” for a modern general purpose computer which will enable it to play chess. Although perhaps of no practical… Expand
Games solved: Now and in the future
TLDR
It is concluded that decision complexity is more important than state-space complexity as a determining factor in games solved in the domain of two-person zero-sum games with perfect information and there is a trade-off between knowledge-based methods and brute-force methods. Expand
XXII. Programming a Computer for Playing Chess 1
This paper is concerned with the problem of constructing a computing routine or "program" for a modern general purpose computer which will enable it to play chess. Although perhaps of no practical… Expand
An Analysis of Alpha-Beta Pruning
TLDR
The alpha-beta procedure for searching game trees is shown to be optimal in a certain sense, and bounds are obtained for its running time with various kinds of random data. Expand
Solving awari with parallel retrograde analysis
A parallel search algorithm running on a large computer cluster solves a popular board game by computing the best moves from all reachable positions. The resulting databases contain scores for 889… Expand
Empirical Measurements of Disk Failure Rates and Error Rates
TLDR
SATA uncorrectable read errors are not yet a dominant system-fault source - they happen, but are rare compared to other problems, and UER (uncorrectable error rate) is not the relevant metric for data architects needs. Expand
Supporting online material Materials and methods
We use a 48-km square horizontal by 24-km vertical domain with uniform 500-m horizontal by 375-m vertical grid spacing. A dynamics model (S1) integrates the anelastic equations for deep convection… Expand
The retinex theory of color vision.
  • E. Land
  • Physics, Medicine
  • Scientific American
  • 1977
To whom correspondence should be addressed
...
1
2
3
...