Research on Different Heuristics for Minimax Algorithm Insight from Connect-4 Game

Abstract

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 Journal of Intelligent Learning Systems and Applications 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.

Linja: A Mobile Application Based on Minimax Strategy and Game Theory

“…Subindex Red (0,0), (0,1), (0,2), (0,3), (0,4), (0,5), (0,6), (1,0), (2,0), (3,0), (4,0), (5,0) Blue (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (5,7), (0,7), (1,7), (2,7), (3,7), (4,7) Starting from the scenario shown in figure 11, the next step is the simulation of the constraint moves set out in the playing rules (see Figure 11). To transfer the game interface to a graphical user interface (GUI) environment using the libraries provided by the programming language, 'x' and 'y' are represented by red and blue pieces, respectively.…”

“…In this case, Minimax was selected. It is a game theory algorithm used to minimize the maximum expected loss with complete information since each player knows the state of his opponent [3]. According to Muros [4], this algorithm takes care of choosing the best move for the player assuming that his opponent will choose the worst move for the player.…”

Implementation of Min Max Algorithm as Intelligent Agent on Card Battle Game

“…This algorithm provides fast computing time and has fewer iterations than Minimax in computing each step. The research conducted by [9] with the title "Research on Different Heuristics for Minimax Insight from Connect-4 Game Algorithm" studied the application of the Minmax algorithm as the opponent to compete in the Connect-4 game. This research translates the game heuristically and looks for strategies against players.…”

GO Game Inspired Algorithm for Hardware Software Partitioning in Multiprocessor Embedded Systems

“…To choose the best possible move, each of the two players (A and B) uses the MiniMax algorithm. The MiniMax algorithm is explained in (Elnaggar et al, 2014) and in (Kang et al, 2019). The Minimax algorithm is applied in two player deterministic games.…”