Digitising a Turn-Based Strategy Board Game: Implementation of Spellcaster Using the Mini-Max Algorithm

In computerised version of board games, player satisfaction can be augmented by providing explanation of what the computer based AI analytical processes are. This helps the players to understand the reasoning behind the action taken by the computer AI opponent. This paper proposes a method that provides the mechanism for a game AI to communicate its evaluation processes using descriptive auto-explanation through symbolic reasoning. A case study is presented in an implementation of a game AI opponent that is capable of describing its inferential processes in a tabletop war game.

The game 2048 has attracted millions of people with its simple yet challenging gameplay, leading to the development of numerous computer players. Most successful computer players for 2048 use evaluation functions trained through temporal difference learning (TD learning) or its variants. While TD learning is highly effective and can improve evaluation functions quickly, the performance of these functions often plateaus after a certain number of timesteps. Therefore, it is important to refine those evaluation functions to further enhance the performance of computer players. In this paper, we extend the conventional TD learning approach and propose two refinement algorithms for 2048. Firstly, we conducted detailed experiments to refine the best open-source neural network, and achieved significant performance improvements, increasing the average score from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.49 \times 10^{5}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3.37 \times 10^{5}$</tex-math></inline-formula> in greedy play (1-ply lookahead) and from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.87 \times 10^{5}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.45 \times 10^{5}$</tex-math></inline-formula> with 3-ply expectimax search. We also applied our refinement method to the state-of-the-art N-tuple network, improving the average score from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.85\times 10^{5}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$6.10\times 10^{5}$</tex-math></inline-formula> with 6-ply expectimax search and the tile-downgrading trick.

Accuracy of evaluation functions is one of the critical factors in computer game players. Evaluation functions are usually constructed manually as a weighted linear combination of evaluation features that characterize game positions. Selecting evaluation features and tuning their weights require deep knowledge of the game and largely alleviates such efforts. In this paper, we propose a new fast and scalable method to automatically generate game position features based on game records to be used in evaluation functions. Our method treats two-class problems which is widely applicable to many types of games. Evaluation features are built as conjunctions of the simplest features representing positions. We select these features based on two measures: frequency and conditional mutual information. To evaluate the proposed method, we applied it to 200,000 Othello positions. The proposed selection method is found to be effective, showing much better results than when simple features are used. The naive Bayesian classifier using automatically generated features showed the accuracy close to 80% in win/lose classification. We also show that this generation method can be parallelized easily and can treat large scale problems by converting these selection algorithms into incremental selection algorithms

It is well-known that laboratory subjects often do not play mixed strategy equilibrium games according to the equilibrium predictions. In particular, subjects often mix with the incorrect proportions and their actions often exhibit serial correlation. However, little is known about the role of cognition in these observations. We conduct an experiment where subjects play a repeated hide and seek game against a computer opponent programmed to play either a strategy that can be exploited by the subject (a naive strategy) or designed to exploit suboptimal play of the subject (an exploitative strategy). The subjects play with either fewer available cognitive resources (under a high cognitive load) or with more available cognitive resources (under a low cognitive load). While we observe that subjects do not mix in the predicted proportions and their actions exhibit serial correlation, we do not find strong evidence these are related to their available cognitive resources. This suggests that the standard laboratory results on mixed strategies are not associated with the availability of cognitive resources. Surprisingly, we find evidence that subjects under a high load earn more than subjects under a low load. However, we also find that subjects under a low cognitive load exhibit a greater rate of increase in earnings across rounds than subjects under a high load.

An Evaluation of Two Alternatives to Minimax

A deeper game-tree search can yield a higher decision quality in a heuristic minimax algorithm. However, exceptions can occur as a result of pathological nodes, which are considered to exist in all game trees and can cause a deeper game-tree search, resulting in worse play. To reduce the impact of pathological nodes on the search quality, we propose an iterative optimal minimax (IOM) algorithm by optimizing the backup rule of the classic minimax algorithm. The main idea is that calculating the state values of the intermediate nodes involves not only the static evaluation function involved but also a search into the future, where the latter is given a higher weight. We experimentally demonstrated that the proposed IOM algorithm improved game-playing performance compared to the existing algorithms.

The article considers labyrinths in the context of the task of their creation and completion for use in the gaming IT industry. Artificial intelligence is currently used to simulate human behavior in computer games, which, depending on the algorithms, more or less imitates the intelligent behavior of a computer opponent. The peculiarity of a computer player is that at the software level, computer opponents have access to all objects of the game situation: the level map, the game board, etc. For a better human imitation of the behavior of the agent, the data coming to it is suppressed in such a way that it coincides with the data that a person in the same situation can receive using the senses. Therefore, it is important to apply appropriate algorithms for finding a way out of it, as well as recognizing their structure. The study of path-finding algorithms and the structure of the labyrinth for the detection of "human-like" approaches, and the evaluation of the effectiveness of such algorithms, allows us to identify better algorithms on the basis of which it is possible to develop games with a more interesting plot. Thus, this work is devoted to the research of algorithms for finding the structure of a labyrinth. Achieving the final goal involves the practical development of software in the Java language for visualizing their structure and obtaining specific values of the performance parameters of the selected algorithms. The work provides basic information about labyrinths, their main varieties and structures, and provides a mathematical model of an ideal labyrinth. Questions related to the selection of parameters for evaluating the effectiveness of their work, the direct analysis of algorithms, the design of a test application in Java and the analysis of the obtained results are investigated and resolved. During the performance evaluation, several structure research algorithms were analyzed in terms of speed of operation, and recommendations were given to choose the most optimal of the ones presented.

This paper presents findings on machine learning agent behavior prediction in a board game application developed by a group of students. The goal of this research is to create a model facilitating collaboration between a user and an AI to play together in the board game using a Human-in-the-Loop architecture. By injecting explainability, the aim is to enhance communication and understanding between the user and the AI agent. Featuring a competitive Artificial Intelligence (AI) based on the Proximal Policy Optimization model, this research explores methods to make AI decisions transparent for enhanced player understanding. Two predictive models, a Decision Tree (DT) and a Deep Learning (DL) classifier, were developed and compared. The results show that the DT model is effective for short-term predictions but limited in broader applications, while the DL classifier shows potential for long-term prediction without requiring direct access to the game's AI. This study contributes to understanding human-AI interaction in gaming and offers insights into AI decision-making processes.

Development of a Computer Player for Seejeh (A.K.A Seega, Siga, Kharbga) Board Game with Deep Reinforcement Learning

Evaluation function is one of the core components of the computer game system. The traditional way to build evaluation function is usually to use a number of features on the board extracted by human, according to experience and game rules, which gives a set of parameters, and design a static linear evaluation function to calculate the evaluation value of current situation. This paper proposes a method to dynamically adjust and optimize the parameters in the evaluation function by least mean squares, and implements a dynamic evaluation function. Experiments based on Surakarta chess show that the method of dynamic evaluation is effective.

Introduction: The application of Artificial Intelligence in games has evolved significantly, allowing for dynamic content generation. However, its use as a core gameplay co-creation tool remains underexplored. Objective: This paper proposes SpellForger, a game where players create custom spells by writing natural language prompts, aiming to provide a unique experience of personalization and creativity. Methodology: The system uses a supervised-trained BERT model to interpret player prompts. This model maps textual descriptions to one of many spell prefabs and balances their parameters (damage, cost, effects) to ensure competitive integrity. The game is developed in the Unity Game Engine, and the AI backend is in Python. Expected Results: We expect to deliver a functional prototype that demonstrates the generation of spells in real time, applied to an engaging gameplay loop, where player creativity is central to the experience, validating the use of AI as a direct gameplay mechanic.

BENEFITS OF MINIMAX SEARCH

Recent advances in face-tracking technology have made it possible to recognize head movements using a commodity web-camera. This development has created exciting possibilities for enhancing player enjoyment during computer game play. In order to ascertain the real-world potential for head gestural input to First Person Shooter games, we have developed seven diverse interaction techniques and integrated these with a modern games engine. Evaluation of the techniques was carried out with four focus groups made up of expert games developers and experienced end-users. One of the techniques was further refined and subjected to a follow-up comparison test with promising results. A set of guidelines for the future development of head interaction techniques for computer games has been derived from the studies. All of the techniques have been built upon freely available software and open-sourced to encourage further research in this area.

Artificial intelligence algorithms have been applied on computer board games since 1953. Among all computer board games, because of its low branching property, Othello can easily defeat humans by designing with min-max search and alpha-beta pruning. Nowadays, the goal of compute Othello is no longer to challenge people but to compete against other computer programs. This paper improves the computer Othello’s opening strategy, mid-game strategy, and end-game strategy. The opening strategy is enhanced by improving self-learning efficiency using pattern recognition. The evaluation function is designed by combining the Line-pattern evaluation with other evaluation functions and by using an improved genetic algorithm to optimize the parameters. Then implement dynamic programming in min-max search and alpha-beta pruning to make the searching engine more efficient and to improve the depth of perfect-searching. Keywords : Genetic Algorithm, Self-Learning, Computer Othello 1. Introduction

In this study, we developed computer players for a single-player stochastic game 2048 using an existing neural-network evaluation function and a version of Monte-Carlo tree search. We applied the Monte-Carlo softmax search (MCSS) algorithm, with some modifications in order to adapt it to the stochastic game, and designed six methods of controlling the search algorithm. We evaluated the MCSS players in an exhaustive manner and also conducted longer experiments for two MCSS players by changing the number of simulations per move. Our MCSS player achieved an average score of 533 542 under the limit of 2000 simulations per move. This result was better than Expectimax players that used the same evaluation function.