A Refinement-Based Heuristic Method for Decision Making in the Context of Ayo Game

Games of strategy, such as chess have served as a convenient test of skills at devising efficient search algorithms, formalizing knowledge, and bringing the power of computation to bear on “intractable” problems. Generally, minimax search has been the fundamental concept of obtaining solution to game problems. However, there are a number of limitations associated with using minimax search in order to offer solution to Ayo game. Among these limitations are: (i.) improper design of a suitable evaluator for moves before the moves are made, and (ii.) inability to select a correct move without assuming that players will play optimally. This study investigated the extent to which the knowledge of minimax search technique could be enhanced with a refinement-based heuristic method for playing Ayo game. This is complemented by the CDG (an end game strategy) for generating procedures such that only good moves are generated at any instance of playing Ayo game by taking cognizance of the opponent strategy of play. The study was motivated by the need to advance the African board game – Ayo – to see how it could be made to be played by humans across the globe, by creating both theoretical and product-oriented framework. This framework provides local Ayo game promotion initiatives in accordance with state-of-the-art practices in the global game playing domain. In order to accomplish this arduous task, both theoretical and empirical approaches were used. The theoretical approach reveals some mathematical properties of Ayo game with specific emphasis on the CDG as an end game strategy and means of obtaining the minimal and maximal CDG configurations. Similarly, a theoretical analysis of the minimax search was given and was enhanced with the Refinement-based heuristics. For the empirical approach, we simulated Ayo game playing on a digital viii computer and studied the behaviour of the various heuristic metrics used and compared the play strategies of the simulation with AWALE (the world known Ayo game playing standard software). Furthermore, empirical judgment was carried out on how experts play Ayo game as a means of evaluating the performance of the heuristics used to evolve the Ayo player in the simulation which gives room for statistical interpretation. This projects novel means of solving the problem of decision making in move selections in computer game playing of Ayo game. The study shows how an indigenous game like Ayo can generate integer sequence, and consequently obtain some self-replicating patterns that repeat themselves at different iterations. More importantly, the study gives an efficient and usable operation support tools in the prototype simulation of Ayo game playing that has improvement over Awal

Review of Kalah Game research and the proposition of a novel heuristic-deterministic algorithm compared to tree-search solutions and human decision-making

The Kalah game represents the most popular version of probably the oldest board game ever-the Mancala game. From this viewpoint, the art of playing Kalah can contribute to cultural heritage. This paper primarily focuses on a review of Kalah history and on a survey of research made so far for solving and analyzing the Kalah game (and some other related Mancala games). This review concludes that even if strong in-depth tree-search solutions for some types of the game were already published, it is still reasonable to develop less time-consumptive and computationally-demanding playing algorithms and their strategies Therefore, the paper also presents an original heuristic algorithm based on particular deterministic strategies arising from the analysis of the game rules. Standard and modified mini-max tree-search algorithms are introduced as well. A simple C++ application with Qt framework is developed to perform the algorithm verification and comparative experiments. Two sets of benchmark tests are made; namely, a tournament where a mid-experienced amateur human player competes with the three algorithms is introduced first. Then, a round-robin tournament of all the algorithms is presented. It can be deduced that the proposed heuristic algorithm has comparable success to the human player and to low-depth tree-search solutions. Moreover, multiple-case experiments proved that the opening move has a decisive impact on winning or losing. Namely, if the computer plays first, the human opponent cannot beat it. Contrariwise, if it starts to play second, using the heuristic algorithm, it nearly always loses. © 2020 by the authors.European Regional Development FundEuropean Union (EU); Ministry of Education, Youth and SportsMinistry of Education, Youth & Sports - Czech Republic [LO1303 (MSMT-7778/2014)]; internal grant agency of VSB Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, Czech Republic [SP2020/46

Modelling of Heuristic Evaluation Strategies in Game Playing: Linear and Configural Effects in Othello

Psychological research on problem solving began with Thorndike's work on trial and error learning with cats, dogs, and monkeys. Kohler later initiated research with apes which convinced him that problems could be solved with insight. Through the 1940's, the study of human problem solving focused on general principles (following the Gestalt tradition) and S-R mechanisms to explain how people solve problems. The advent of computer technology in the 1950's spurred research in artificial intelligence, game playing, and problem solving. Formal definitions of problems outlined the components of a constituting the problem representation. This provided a framework for computer scientists to mechanize problem Solving with algorithms of search. Computer scientists met with success in developing programs to work on well-defined problems, such as games and puzzles, where the components of the problem representation are easily stated. Once the representation is adopted, solution is a matter of search. It has been shown that the efficiency of mechanized search is aided by the use of a ''heuristic evaluation function" (Nilsson, 1971), which has a form similar to psychological models applied in research on human decision making and judgment (Slovic and Lichtenstein, 1972). Samuel (1959), used a regression model of human judgment based on the knowledge of skilled checkers players in order to produce a heuristic evaluation function for a checkers playing program. Another model which can also be used to provide a heuristic evaluation function is based on Anderson's (1962) technique of functional measurement. This approach allows estimation of subjective scale values for the levels of information components relevant to playing a game. In contrast to these linear models, Edgell (1978) has argued that people can utilize configural information when making judgments, an issue which has been avoided by most decision modelling research. Samuel (1967) showed that use of configural infermation by a heuristic evaluation function can augment the skill of a checkers playing program, but the question of whether human players use such information was not researched. This paper reports one pilot experiment and two other experiments which were conducted to investigate whether people do use configural information when evaluating alternative moves in a game situation. The effects of game experience, learning, and training on use of configural information were examined. In addition, the research was conducted in a game playing situation in order to address the issue of ecological validity (Neisser, 1976) in psychological research. As Newell and Simon (1972) have argued, a good psychological theory of how a good chess player plays chess should play good chess

A new challenge: approaching Tetris Link with AI

Decades of research have been invested in making computer programs for playing games such as Chess and Go. This paper introduces a board game, Tetris Link, that is yet unexplored and appears to be highly challenging. Tetris Link has a large branching factor and lines of play that can be very deceptive, that search has a hard time uncovering. Finding good moves is very difficult for a computer player, our experiments show. We explore heuristic planning and two other approaches: Reinforcement Learning and Monte Carlo tree search. Curiously, a naive heuristic approach that is fueled by expert knowledge is still stronger than the planning and learning approaches. We, therefore, presume that Tetris Link is more difficult than expected. We offer our findings to the community as a challenge to improve upon.LIACS-Managemen

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Towards the unification of intuitive and formal game concepts with applications to computer chess

In computer game development, an interesting point which has been little or no studied at all is the formalization of intuition such as game playing concepts, including playing style. This work is devoted to bridge the gap between human reasoning in game playing and heuristic game playing algorithms. The idea is motivated as follows. In most chess-like games there exist many intuition-oriented concepts such as capture, attack, defence, threaten, blocked position, sacrifice, zugzwang position and different playing styles such as aggressive, conservative, tactical and positional. Most human players use to manage these concepts, pergaps in an intuitive way, as they were not well formalized in a precise manner. A good formalization of these concepts would be an important step towards the automation of human reasoning in chess (and other strategy games) for better understanding of the game, thus leading to better playing. The goal of this research is to take a first step towards the unification of both "paradigms", namely human reasoning in game play and more formal heuristic concepts. We focus on computer chess as an example but the result could be also applied to most two-player zero-sum perfect information games. The applications of such a formulation are practical, such as better game understanding and opponent modeling, as well as educational: it would be nice to have these concepts somehow formalized. Then we suggest a way of transfering these intuitions into formal definitions. We propose an interpretation technique for describing chess positions and evaluation functions. The technique consists of interpreting and mapping part of the algorithmic scenario into quantities such as integer numbers. With such a mapping a given concept is likely to be described in a very precise way. As an application we look for candidate definitions of the following concepts: attack, defence, threat, sacrifice, zugzwang, aggressive play and defensive play. For each one of them we use the previous technique and propose a formal definition. Thus we give the first formulation of game playing styles -at least to the author\u27s knowledge- and we show how this definition goes through for the game of chess. We describe different possibilities when moving from intuition to the formal setting, varying from a simple formulation through a connectionist approach. Then we show as an application how an evaluation function can be modified in order to include a given concept. This new evaluation function should take into account the degree of presence of the given concept (eg. how defensive is a given position) and thus it can be incorporated into a computer chess program. An advantage of allowing one to modify in such a manner an evaluation function is that one can combine different evaluation functions and -perhaps- get the better of each one of them. Although this is a first step in the given direction, some more difficult tasks will remain, such as the formalization of the so called positional, strategic and tactical play. References B. Abramson. Learning expected-outcome evaluators in chess. In H. Berliner, editor, Proceedings of the AAAI Spring Symposium on Computer Game Playing, pages 26-28, Stanford University, 1988. B. Abramson. On learning and testing evaluation functions. Journal of Experimental and Theoretical Artificial Intelligence, 2(3):182-193, 1990. T. S. Anantharaman. Evaluation tuning for computer chess: Linear discriminant methods. International Computer Chess Association Journal, 20(4):224-242, 1997. E. B. Baum, Warren D. Smith. Best Play for Imperfect Players and Game Tree Search. 1993 J. Fürnkranz. Machine Learning in Computer Chess: The Next Generation Austrian Research Institute for Artificial Intelligence, Vienna, TR-96-11, 1996. A. Plaat, J. Schaeffer, W. Pijls and A. De Bruin. Best-First Fixed-Depth Game-Tree Search in Practice. IJCAI\u2795, Montreal. J. Schaeffer, P. Lu, D. Szafron and R. Lake. A Re-examination of Brute-Force Search Games: Planning and Learning, Chapel Hill, N.C., pp. 51-58, 1993. AAAI Report FS9302