Neil Burch

Checkers Is Solved

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 challenging popular game to be solved to date, roughly one million times as complex as Connect Four. Artificial intelligence technology has been used to generate strong heuristic-based game-playing programs, such as Deep Blue for chess. Solving a game takes this to the next level by replacing the heuristics with perfection.

Predicting the performance of IDA* using conditional distributions

Korf, Reid, and Edelkamp introduced a formula to predict the number of nodes IDA* will expand on a single iteration for a given consistent heuristic, and experimentally demonstrated that it could make very accurate predictions. In this paper we show that, in addition to requiring the heuristic to be consistent, their formulas predictions are accurate only at levels of the brute-force search tree where the heuristic values obey the unconditional distribution that they defined and then used in their formula. We then propose a new formula that works well without these requirements, i.e., it can make accurate predictions of IDA*s performance for inconsistent heuristics and if the heuristic values in any level do not obey the unconditional distribution. In order to achieve this we introduce the conditional distribution of heuristic values which is a generalization of their unconditional heuristic distribution. We also provide extensions of our formula that handle individual start states and the augmentation of IDA* with bidirectional pathmax (BPMX), a tech nique for propagating heuristic values when inconsistent heuristics are used. Experimental results demonstrate the accuracy of our new method and all its variations.

Building the Checkers 10-Piece Endgame Databases

In 1993, the Chinook team completed the computation of the 2 through 8-piece checkers endgame databases, consisting of roughly 444 billion positions. Until recently, nobody had attempted to extend this work. In November 2001, we began an effort to compute the 9- and 10-piece databases. By June 2003, the entire 9-piece database and the 5-piece versus 5-piece portion of the 10-piece database were completed. The result is a 13 trillion position database, compressed into 148 GB of data organized for real-time decompression. This represents the largest endgame database initiative yet attempted. The results obtained from these computations are being used to aid an attempt to weakly solve the game. This paper describes our experiences working on building large endgame databases.

Game-Tree search with adaptation in stochastic imperfect-information games

Building a high-performance poker-playing program is a challenging project. The best program to date, PsOpti, uses game theory to solve a simplified version of the game. Although the program plays reasonably well, it is oblivious to the opponents weaknesses and biases. Modeling the opponent to exploit predictability is critical to success at poker. This paper introduces Vexbot, a program that uses a game-tree search algorithm to compute the expected value of each betting option, and does real-time opponent modeling to improve its evaluation function estimates. The result is a program that defeats PsOpti convincingly, and poses a much tougher challenge for strong human players.

Strategy evaluation in extensive games with importance sampling

Typically agent evaluation is done through Monte Carlo estimation. However, stochastic agent decisions and stochastic outcomes can make this approach inefficient, requiring many samples for an accurate estimate. We present a new technique that can be used to simultaneously evaluate many strategies while playing a single strategy in the context of an extensive game. This technique is based on importance sampling, but utilizes two new mechanisms for significantly reducing variance in the estimates. We demonstrate its effectiveness in the domain of poker, where stochasticity makes traditional evaluation problematic.

Automatic move pruning for single-agent search

Move pruning is a low-overhead technique for reducing search cost in single-agent search problems by avoiding the generation of duplicate states. Redundant sequences of moves, where the effect of one sequence is provably identical to some other sequence of moves, are suppressed during search. We present an algorithm for automatically identifying redundant move sequences in a general class of single-agent search problems, and a method for selecting redundant move sequences to prune during search. We demonstrate that the redundant move sequences which are to be pruned must be chosen carefully, and give experimental results using our move pruning method which show a speedup of multiple orders of magnitude in a variety of domains. Finally, we give theoretical results on conditions where move pruning does, and does not, affect the correctness of different search algorithms.

PSVN Manual (June 20, 2014)

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