Abstract

Tic Tac Toe is a well-known game played across all age groups. It’s a simple fun game played with two players. There is a 3x3 grid formed by two vertical and two horizontal lines. The user can fill these nine places with either crosses (‘X’) or noughts (‘O’). The aim of the game is to win by placing three similar marks in a horizontal, vertical, or diagonal row. In this paper, a simulation algorithm is presented to predict the win, or draw of a game by knowing the first move of a player. The game of tic-tac-toe is simulated using Min-max algorithm. The concept of combinational game theory is utilized to implement this game. This algorithm calculates only one step ahead using min-max algorithm. In an ideal scenario, a player must calculate all the possibilities to ensure the success. It’s a small 3x3 game, so the state space tree generated will be short.

Highlights

  • INTRODUCTIONThe tic-tac-toe game can be considered as a tree with a root node as the initial state of the game.The child will be the corresponding future possibilities of states Likewise, this tree can be expanded to cover all the possibilities of outcome of the game Once the tree is constructed, it is easy to evaluate the optimal move

  • The tic-tac-toe game is well known simple game The game is played across all the age groups There is a 3x3 grid formed by two vertical and two horizontal lines The user can fill these nine places with either crosses X or noughtsO

  • The aim of the game is to win by placing three similar marks in a horizontal, vertical, or diagonal row.It is so simple that one can predict the win or draw This needs graph theory or combinational game theory,a branchof mathematics that will help to predict the different outcomes of the event

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Summary

INTRODUCTION

The tic-tac-toe game can be considered as a tree with a root node as the initial state of the game.The child will be the corresponding future possibilities of states Likewise, this tree can be expanded to cover all the possibilities of outcome of the game Once the tree is constructed, it is easy to evaluate the optimal move. The grid is formed by two horizontal and two vertical lines, making it a 3×3 grid There are nine places that can be filled with noughts or crosses or empty position there are 39 19,683 possible states Each place is unique. In 4 number of ways to completely fill the noughts and crosses board with 5Xs and 4 Os not including rotations and reflections is evaluated It s little complicated as it makes use of Group Theory The rest of the paper is organized as follows: Sections II discusses the algorithm for the tic-tactoe game. The paper is concluded in section and the references are appended at the end

ALGORITHM FOR TIC-TAC-TOE GAME
Flow chart
SIMULATION RESULTS
CONCLUSION
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