Showing papers presented at "Advances in Computer Games in 2005"

An evaluation function for the game of amazons

Abstract: Amazons is a fascinating game that shares properties of chess and Go. We have written a computer program that plays Amazons. This paper reveals the secret of this program: its evaluation function. We describe it by explicit formulas, mention the ideas and goals behind these formulas, and discuss possible refinements. By analysing a tournament game of Amazong against the former computer world champion 8QP we illustrate how the new features of our evaluation function can lead to victory.

Tuning evaluation functions by maximizing concordance

Abstract: Heuristic search effectiveness depends directly upon the quality of heuristic evaluations of states in a search space. Given the large amount of research effort devoted to computer chess throughout the past half-century, insufficient attention has been paid to the issue of determining if a proposed change to an evaluation function is beneficial. We argue that the mapping of an evaluation function from chess positions to heuristic values is of ordinal, but not interval scale. We identify a robust metric suitable for assessing the quality of an evaluation function, and present a novel method for computing this metric efficiently. Finally, we apply an empirical gradient-ascent procedure, also of our design, over this metric to optimize feature weights for the evaluation function of a computer-chess program. Our experiments demonstrate that evaluation function weights tuned in this manner give equivalent performance to hand-tuned weights.

Learning to score final positions in the game of Go

Abstract: This article investigates the application of machine-learning techniques for the task of scoring final positions in the game of Go. Neural network classifiers are trained to classify life and death from labelled 9 × 9 game records. The performance is compared to standard classifiers from statistical pattern recognition. A recursive framework for classification is used to improve performance iteratively. Using a maximum of four iterations our cascaded scoring architecture (CSA*) scores 98.9% of the positions correctly. Nearly all incorrectly scored positions are recognised (they can be corrected by a human operator). By providing reliable score information CSA* opens the large source of Go knowledge implicitly available in human game records for automatic extraction. It thus paves the way for a successful application of machine learning in Go.

Solving 7×7 Hex with domination, fill-in, and virtual connections

Abstract: We present an algorithm that determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player Our algorithm recursively searches the game-tree, combining fixed and dynamic game-state virtual connection composition rules to find a winning virtual connection for one of the two players The search is enhanced by pruning the game-tree according to two new Hex game-state reduction results: under certain conditions, (i) some moves dominate others, and (ii) some board-cells can be "filled-in" without changing the game's outcomeThe algorithm is powerful enough to solve arbitrary 7 × 7 game-states In particular, we use it to determine the outcome of a 7 × 7 Hex game after each of the 49 possible opening moves, in each case finding an explicit proof-tree for the winning player

Bias and pathology in minimax search

Abstract: This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (Are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (Are moves played by deeper minimax search better than those by shallower search?). The experiments were performed in the King-Rook-King (KRK) chess endgame and in randomly generated game trees. The results show that, counter-intuitively, evaluation accuracy may decline with search depth, whereas at the same time decision accuracy improves with depth. In the article, this is explained by the fact that minimax in combination with a noisy evaluation function introduces a bias into the backed-up evaluations, which masks the evaluation effectiveness of minimax, but this bias still permits decision accuracy to improve with depth. This observed behaviour of minimax in the KRK endgame is discussed in the light of previous studies of pathology in minimax. It is shown that explaining the behaviour of minimax in an actual chess endgame in terms of previously known results requires special care.

Selecting evaluation functions in opponent-model search

Abstract: Opponent-Model search is a game-tree search method that explicitly uses knowledge of the opponent. There is some risk involved in using Opponent-Model search. For adequate forecasting, two conditions should be imposed. Both the prediction of the opponent's moves and the judgement of future positions should be of good quality. The two conditions heavily depend on the evaluation functions used.In the article we distinguish evaluation functions by type. Three fundamentally different types are introduced. Thorough analysis of a variety of characteristics leads to eight possible orderings. The role of the evaluation functions is studied by attempting to answer five research questions. Moreover, actual computer game-playing programs investigate the research questions by a series of experiments in which Opponent-Model search is performed. The game of Bao is our test bed, it was selected because of its relatively narrow game tree, which allowed for an appropriate search depth in the experiments. We restrict ourselves to five evaluation functions generated with the help of machine-learning techniques. A set of round-robin tournaments between these evaluation functions show that when the above conditions are met, Opponent-Model search can be applied successfully. Answers to the research questions are given in the conclusions.

Chess endgames: 6-man data and strategy

Abstract: While Nalimov's endgame tables for Western Chess are the most used today, their Depth-to-Mate metric is not the most efficient or effective in use. The authors have developed and used new programs to create tables to alternative metrics and recommend better strategies for endgame play.

Deeper model endgame analysis

Abstract: A reference model of Fallible Endgame Play has been implemented and exercised with the chess-engine WILHELM. Past experiments have demonstrated the value of the model and the robustness of decisions based on it: experiments agree well with a Markov Model theory. Here, the reference model is exercised on the well-known endgame KBBKN.

Static analysis based on formal models and incremental computation in Go programming

Abstract: Computer-Go programs have high computational costs for static analysis, even though most intersections of the board remain unchanged by one move. Therefore, incremental computation as well as theoretical models are essential features for static analysis. This paper describes some formal models for static analysis, and explores how incremental computation is applied to the static analysis in Go programs. The static analysis in this paper includes (1) recognizing blocks and groups of stones and evaluating their properties, (2) determining the life and death of a group by numerical features, (3) finding the numbers of regions enclosed by the groups based on Euler's formula, and (4) analysing capturing races (semeai) and sekis based on an abstract description called the semeai graph. Several operations on the sets of intersections on the board are used for defining the notions on Go boards as well as for describing the analysis methods.