As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves...As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves on increasing Connect-4 grid sizes. The objective of this study is to evaluate the effectiveness of the Minimax search algorithm in making optimal moves under different circumstances and to understand how well the algorithm scales. To answer this question we tested and analyzed the algorithm several times on different grid sizes with a time limit to see its performance as the complexity increases, we also looked for the average search depth for each grid size. The obtained results show that despite larger grid sizes, the Minimax search algorithm stays relatively consistent in terms of performance.展开更多
Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the cod...Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.展开更多
文摘As computers have become faster at performing computations over the decades, algorithms to play games have also become more efficient. This research paper seeks to see how the performance of the Minimax search evolves on increasing Connect-4 grid sizes. The objective of this study is to evaluate the effectiveness of the Minimax search algorithm in making optimal moves under different circumstances and to understand how well the algorithm scales. To answer this question we tested and analyzed the algorithm several times on different grid sizes with a time limit to see its performance as the complexity increases, we also looked for the average search depth for each grid size. The obtained results show that despite larger grid sizes, the Minimax search algorithm stays relatively consistent in terms of performance.
文摘Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.
