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Machine As One Player in Indian Cowry Board Game: Basic Playing Strategies

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Machine As One Player in Indian Cowry Board Game: Basic Playing Strategies International Journal of Computer Engineering & Technology (IJCET) Volume 10, Issue 1, January-February 2019, pp. 174-183, Article ID: IJCET_10_01_019 Available online at http://iaeme.com/Home/issue/IJCET?Volume=10&Issue=1 Journal Impact Factor (2016): 9.3590(Calculated by GISI) www.jifactor.com ISSN Print: 0976-6367 and ISSN Online: 0976–6375 © IAEME Publication MACHINE AS ONE PLAYER IN INDIAN COWRY BOARD GAME: BASIC PLAYING STRATEGIES Pouyan Davoudian Department of Studies in Computer Science, University of Mysore, India P. Nagabhushan Indian Institute of Information Technology, Allahabad, India; Department of Studies in Computer Science, University of Mysore, India ABSTRACT Cowry game is an ancient board game from India, also known as Chowka Bhara. It is a race game of chance and strategy for 2-4 players, in which playing pieces are moved around a square board according to the throw of special dice (cowry shells). This game involves decision-making under uncertainty and imprecision with multiple players, and therefore can be considered as an appropriate model for real-life problems that contain stochastic components. In this research, we propose and analyze a few basic playing strategies for Cowry game, and describe the framework for the implementation of these strategies. We also provide an experimental comparison of the proposed strategies to evaluate their performances. The comprehensive study of Cowry game presented in this work can be used to gain a better understanding of the game, and may result in the formulation and implementation of more advanced strategies. It can also serve as a basis for producing better artificial players in similar strategic race games. Keywords: Chowka Bhara, Strategy, Random, Fast, Balanced, Cowry shell, Race board game, Artificial player. Cite this Article: Pouyan Davoudian and P. Nagabhushan, Machine as one Player in Indian Cowry Board Game: Basic Playing Strategies, International Journal of Computer Engineering and Technology, 10(1), 2019, pp. 174-183. http://iaeme.com/Home/issue/IJCET?Volume=10&Issue=1 1. INTRODUCTION The idea of programming computers to play board games has been around since the emergence of computation. Complex board games like Chess, Checkers and Go have been historically acknowledged as great test domains for exploring and developing various types of approaches in artificial intelligence and machine learning [1]. As a result, highly optimized http://iaeme.com/Home/journal/IJCET 174 [email protected] Pouyan Davoudian and P. Nagabhushan techniques have been evolved for such games, and they have been improved dramatically to an extent where a machine can play at expert level, competing with world-class human players [2, 3]. Comparatively, far fewer successful programs have been designed to play games like Ludo and its variant race games, most of which are descended from the ancient Indian games Pachisi and Chaupar. We argue that there is a compelling reason behind it. Game theory classifies these games into two fundamentally different categories, and the methods applicable to one are not necessarily suitable for the other. In games such as Chess, Checkers and Go the players have complete knowledge about the current state of the game. They know what options will be available for the next move, as well as the result of every possible move. Even though the players cannot predict their opponent’s future move, they have complete knowledge of all possible moves the opponent will be allowed to make [4]. These games are commonly known as “perfect information”. Race games like Ludo, however, contain an element of chance because of dice. The players cannot predict their dice roll and consequently, they do not know what options they may have for the next move. Similarly, the players do not know in advance what moves their opponent can possibly make because they cannot know of the opponent’s dice roll [4]. Due to uncertainty about the future moves, finding the best move in the current state of these games might be challenging. Therefore, the players are often required to estimate probabilities and calculate risk. This type of game is called “imperfect information”. While a great deal of effort has gone into designing computer programs to play perfect information two-player board games, many strategic games are more complex, involving imperfect information with more than two players. One of such games is Cowry game, popularly known as Chowka Bhara, which is a traditional game of India. It is a multi-player, imperfect information, stochastic, strategic race board game, yet to be played at expert level by a machine. Despite our extensive search in relevant academic literature, we could not identify any scientific work tackling this problem. In this research, we explore, implement, and evaluate a few basic playing strategies for Cowry game, which can result in the discovery of more advanced strategies to improve its gameplay. In the remainder of this paper, we provide a short description of Cowry game, as well as its history in Section 2. We also summarize the rules of the game which are considered for the implementation in this work. Section 3 presents a brief overview of our proposed strategies and the logic behind them. In Section 4, we provide details about designing and programming the game environment. We also give an illustrated description of the framework used for the implementation of the proposed strategies. In Section 5, we evaluate the performance of the strategies and provide a comparative analysis of the obtained experimental results. Finally, Section 6 highlights the achievements and concludes the paper by giving guidelines for future research. 2. GAME DESCRIPTION AND RULES Cowry game is a race board game for two to four players, in which the players race their tokens or “pieces” around the board in a spiral, with the objective of being the first to move all of their pieces to the innermost location of the board. Like many complex race games, Cowry game involves a combination of luck and skill [5]. Piece movement is determined by throwing four cowry shells (a special variety of seashells, shown in Figure 1), and hence it can be considered as a game of chance. However, there is also an element of strategy to the game. Players have four pieces to move, and so with each throw of cowry shells they must choose from different options for moving their pieces, and predict possible countermoves by the opponents. http://iaeme.com/Home/journal/IJCET 175 [email protected] Machine as one Player in Indian Cowry Board Game: Basic Playing Strategies Figure 1 Cowry shells Cowry game is one of the most ancient board games originated in India. Its history can be traced back to the times of epic “Mahabharata”. Cowry game and its variations are still popular and being played in different regions of India under various names, such as Chowka Bara, Chakaara, Katte Mane, Ashta Chamma, Pagdi, Kavidi Kali, Thaayam, etc. Despite several regional variations of this game, the description and rules presented in this section are considered for our standard implementation throughout this research work. The board is normally a square divided into five rows and columns. Each player is assigned a color (typically red, yellow, green and blue), and has four pieces of the same color. The outer middle squares on each side of the board represent the starting squares for each player, where initially four pieces of a player are placed. The starting squares are specially marked on the board and also function as “safe squares”. Only one piece can be placed on any square of the board with the exception of safe squares, which can accommodate any number of pieces. The innermost square of the board is the finishing square for all players. Figure 2 depicts the game board and shows safe squares. The players start on their respective starting squares and proceed to race their pieces anticlockwise around the board along the outer squares. Upon reaching the square on the left side of their starting square, the players continue by moving the pieces up to the inner squares and proceed clockwise towards the finishing square. The path for one of the players is shown in Figure 2 with dotted lines. Figure 2 Board of Cowry game with safe squares, and path for a player http://iaeme.com/Home/journal/IJCET 176 [email protected] Pouyan Davoudian and P. Nagabhushan To start the game, each player throws the cowry shells and the player with the highest value moves first. The players alternate turns around the board in an anticlockwise direction. The first player to bring all four pieces to the finishing square wins. The first winner then leaves the game and others continue playing to identify second and third winners, and the last player is the final loser. Four cowry shells are used to decide how far to move the players’ pieces. They are thrown and the number of cowry shells landing with their openings upwards indicates the number of squares the player should move. However, when all four cowry shells land with their openings downwards, the value of the throw is considered to be 8. Thus, the possible values for a single throw of four cowry shells are 1, 2, 3, 4 and 8. When the players throw either a 4 or an 8, they will receive an additional or “bonus” throw of cowry shells in that turn. If the bonus throw results in a 4 or an 8 again, the players will obtain another bonus throw. However, if the third throw is also a 4 or an 8, they will not be allowed to make any move and the turn will pass to the next player. In case the players get two or more consecutive throws, they can move one or more of their pieces according to the obtained values.
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