Showing papers presented at "Advances in Computer Games in 2004"

Monte-carlo go developments

Abstract: We describe two Go programs, Olga and Oleg, developed by a Monte-Carlo approach that is simpler than Bruegmann’s (1993) approach. Our method is based on Abramson (1990). We performed experiments, to assess ideas on (1) progressive pruning, (2) all moves as first heuristic, (3) temperature, (4) simulated annealing, and (5) depth-two tree search within the Monte-Carlo framework. Progressive pruning and the all moves as first heuristic are good speed-up enhancements that do not deteriorate the level of the program too much. Then, using a constant temperature is an adequate and simple heuristic that is about as good as simulated annealing. The depth-two heuristic gives deceptive results at the moment. The results of our Monte-Carlo programs against knowledge-based programs on 9x9 boards are promising. Finally, the ever-increasing power of computers lead us to think that Monte-Carlo approaches are worth considering for computer Go in the future.

Evaluation in Go by a Neural Network Using Soft Segmentation

Abstract: In this article a neural network architecture is presented that is able to build a soft segmentation of a two-dimensional input. This network architecture is applied to position evaluation in the game of Go. It is trained using self-play and temporal difference learning combined with a rich two-dimensional reinforcement signal. Two experiments are performed, one using the raw board position as input, the other one doing some simple preprocessing of the board. The second network is able to achieve playing strength comparable to a 13-kyu Go program.

Building the Checkers 10-Piece Endgame Databases

Abstract: 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.

DF-PN in Go: An Application to the One-Eye Problem

Abstract: Search algorithms based on the notion of proof and disproof numbers have been shown to be effective in many games. In this paper, we modify the depth-first proof-number search algorithm df-pn, in order to apply it to the game of Go. We develop a solver for one-eye problems, a special case of enclosed tsume-Go [life and death] problems. Our results show that this approach is very promising.

Solving the Oshi-Zumo Game

Abstract: Kotani (2002) determined the part of the state space of the Japanese Oshi-Zumo game in which pure strategies suffice to win. This paper completes the analysis by computing and discussing a Nash-optimal mixed strategy for this game.

New Games Related to Old and New Sequences

Abstract: We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously, is a function f of the size of the piles. Wythoff’s game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences, some of which are related to well-known sequences, but most are new. The main result is a theorem giving necessary and sufficient conditions on f so that the sequences are 2nd player winning positions. Sample games are presented, strategy complexity questions are discussed, and possible further studies are indicated.

Solving 7×7 Hex: Virtual Connections and Game-State Reduction

Abstract: We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination The 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

When One Eye is Sufficient: A Static Classification

Abstract: A new classification for eye shapes is proposed. It allows to decide statically the status of the eye in some restricted conditions. The life property enables to decide when one eye shape is alive regardless the number of opponent stones inside. The method is easy to program and can replace a possibly deep search tree with a fast, reliable and static evaluation.

Computer Programming of Kriegspiel Endings: The Case of KR versus K

Abstract: Kriegspiel is a chess variant invented to make chess more similar to real warfare. In a Kriegspiel game the players have to deal with incomplete information because they are not informed of their opponent’s moves. Each player tries to guess the position of the opponent’s pieces as the game progresses by trying moves that can be either legal or illegal with respect to the real situation: a referee accepts the legal moves and rejects the illegal ones. However the latter are most useful to gain insight into the opponent’s position. While in the past this game has been popular in research centres such as the RAND Institute, currently it is played mostly over the Internet Chess Club.

Search and Knowledge in Lines of Action

Abstract: This paper describes the design and development of two world-class Lines of Action game-playing programs: YL, a three time Computer Olympiad gold-medal winner, and Mona, which has dominated international e-mail correspondence play. The underlying design philosophy of the two programs is very different: the former emphasizes fast and efficient search, whereas the latter focuses on a sophisticated but relatively slow evaluation of each board position. In addition to providing a technical description of each program, we explore some long-standing questions on the trade-offs between search and knowledge. These experimental results confirm the conclusions made by earlier researchers in the domain of chess, thus showing that the trends are not game-specific. In particular, we see diminishing returns with additional search depth, and observe that the knowledge level of a program has a significant impact on the results of such experiments.

Automated Identification of Patterns in Evaluation Functions

Abstract: This paper proposes a general and automated method that generates accurate evaluation functions, without expert players’ knowledge of a target game. Patterns (which are partial descriptions of a game state) are widely used as primitives of evaluation functions in game programming. They have to be carefully selected in order to generate accurate evaluation functions. Our approach consists of three steps: (1) generation of logic formulae by using the specifications of a target game, (2) translation of the formulae into patterns, and (3) selection of a set of suitable patterns from those generated. The problem, in the automated identification of suitable patterns, is that it is difficult either to generate only useful patterns or to examine all possible patterns. The latter obstacle is due to the prohibitive numbers involved. We solved this dilemma by a combination of two methods, where one method generates patterns of good quality, and the other method entails a lightweight selection based on statistics that could handle a large number of candidates. Experiments in Othello revealed that about 100,000 patterns from more than eight million automatically generated patterns could be successfully selected with our method, and that accurate evaluation functions were constructed. This accuracy is comparable to that of specialized Othello programs and is much better than that of the evaluation functions generated by existing general methods.

First Experimental Results of ProbCut Applied to Chess

Abstract: ProbCut is a selective-search enhancement to the standard alpha-beta algorithm for two-person games. ProbCut and its improved variant Multi-ProbCut (MPC) have been shown to be effective in Othello and Shogi, but there had not been any report of success in the game of chess previously. This paper discusses our implementation of ProbCut and MPC in the chess engine Crafty. Initial test results suggest that the MPC version of Crafty is stronger than the original version of Crafty: it searches deeper in promising lines and defeated the original Crafty +22−10 = 32 (59.4%) in a 64-game match. Incorporating MPC into Crafty also increased its tournament performance against YACE — another strong chess program: Crafty’s speed chess tournament score went up from 51% to 56%.

Evaluation Function Tuning via Ordinal Correlation

Abstract: Heuristic search effectiveness depends directly upon the quality of heuristic evaluations of states in the search space. We show why ordinal correlation is relevant to heuristic search, present a metric for assessing the quality of a static evaluation function, and apply it to learn feature weights for a computer chess program.

Searching with Analysis of Dependencies in a Solitaire Card Game

Abstract: We present a new method for taking advantage of the relative independence between parts of a single-player game. We describe an implementation for improving the search in a solitaire card game called Gaps. Considering the basic techniques, we show that a simple variant of Gaps can be solved by a straightforward depth-first search (DFS); turning to variants with a larger search space, we give an approximation of the winning chances using iterative sampling. Our new method was designed to make a complete search; it improves on DFS by grouping several positions in a block, and searching only on the boundaries of the blocks. A block is defined as a product of independent sequences. We describe precisely how to detect interactions between sequences and how to deal with them. The resulting algorithm may run ten times faster than DFS, depending on the degree of independence between the subgames.

Model Endgame Analysis

Abstract: A reference model of Fallible Endgame Play has been implemented and exercised with the chess engine Wilhelm. Various experiments have demonstrated the value of the model and the robustness of decisions based on it. Experimental results have also been compared with the theoretical predictions of a Markov model of the endgame and found to be in close agreement.

An Evaluation Function for Lines of Action

Abstract: Lines of Action (LOA) is a two-person zero-sum chess-like connection game. Building an evaluation function for LOA is a difficult task because not much knowledge about the game is available. In this paper the evaluation function of the tournament program MIA is explained. This evaluator consists of the following nine features: concentration, centralisation, centre-of-mass position, quads, mobility, walls, connectedness, uniformity, and player to move. These features have resulted in the evaluator MIA IV. The evaluator is tested in a tournament against other LOA evaluators, which have performed well at the previous Computer Olympiads. Experiments show that MIA IV defeats them with large margins. It turns out that the evaluator even performs better at deeper searches.

Search versus Knowledge: An Empirical Study of Minimax on KRK

Abstract: This article presents the results of an empirical experiment designed to gain insight into what is the effect of the minimax algorithm on the evaluation function. The experiment’s simulations were performed upon the KRK chess endgame. Our results show that dependencies between evaluations of sibling nodes in a game tree and an abundance of possibilities to commit blunders present in the KRK endgame are not sufficient to explain the success of the minimax principle in practical game-playing as was previously believed. The article shows that minimax in combination with a noisy evaluation function introduces a bias into the backed-up evaluations and argues that this bias is what masked the effectiveness of the minimax in previous studies.

Chess endgames: 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 only one and not the most effective in use. The authors have developed and used new programs to create tables to alternative metrics and recommend better strategies for endgame play.

The 7-piece perfect play lookup database for the game of checkers

Abstract: Many research teams and individuals have computed endgame databases for the game of chess which use the distance-to-mate metric, enabling their software to forecast the number of moves remaining until the game is over. This is not the case for the game of checkers. Only one programming team has generated a checkers database capable of announcing the distance to the terminal position. This paper examines the benefits and detriments associated with computing three different types of checkers endgames databases, demonstrates the solutions to the longest wins in the 7-piece checkers database, presents tables of longest wins for positions including all permutations of four pieces and fewer against three pieces and fewer, and offers major improvements to some previously published play.

Static Analysis by 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 after one move. Therefore, we introduced the method of incremental computation as an essential feature in Go programming. This paper explores how incremental computation is applied to the static analysis in Go programs, and describes two types of analysis and pattern recognition. One type is determination in cases where the territories of groups are almost determined. This includes (1) the methods of determining the life and death of a group by numerical features and (2) the method of finding the numbers of regions enclosed by the groups based on Euler’s formula. The other type is estimation of groups of stones and territories by analysing the influence of stones using an “electric charge model” in cases where the density of stones is rather low. In the analysis, operations on sets of intersections are used for mathematical descriptions when applying incremental computation as well as definitions of the notions on the Go board.

Static Recognition of Potential Wins in KNNKB and KNNKN

Abstract: The fact that the strong side cannot enforce a win in KNNK makes many chess players (both humans and computers) prematurely regard KNNKB and KNNKN to be trivially drawn too. This is not true, however, because there are several tricky mate themes in KNNKB and KNNKN which occur more frequently and require more complicated handling than common wisdom thinks. The text analyzes the mate themes and derives rules from them which allow for the static recognition of potential wins in KNNKB and KNNKN without further lookahead by search. Although endgame databases achieve the same goal, they are normally far less efficient at doing so because of their additional I/O and memory requirements (even when compressed).