In game theory, the behavior of humans, animals, and computer systems is analyzed in terms of strategic decisions. The objective of this chapter is to use game theory concepts to analyze tic-tac-toe. The chapter introduces the game, explains its history and evolution, and defines key terms such as zero-sum games, payoff matrices, and Nash equilibrium. As part of an exploration of the classic board game, pure and mixed strategies, as well as the minimax algorithm, are discussed. In this chapter, winning strategies are categorized based on whether the players start first or second and where the Xs and Os are placed at the beginning of the game. On the basis of the opponent’s starting positions, statistical probabilities of winning are graphically displayed.

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Tic-Tac-Toe: A Game Theory Analysis

  • Shivani Kalyan,
  • Reetika Singh

摘要

In game theory, the behavior of humans, animals, and computer systems is analyzed in terms of strategic decisions. The objective of this chapter is to use game theory concepts to analyze tic-tac-toe. The chapter introduces the game, explains its history and evolution, and defines key terms such as zero-sum games, payoff matrices, and Nash equilibrium. As part of an exploration of the classic board game, pure and mixed strategies, as well as the minimax algorithm, are discussed. In this chapter, winning strategies are categorized based on whether the players start first or second and where the Xs and Os are placed at the beginning of the game. On the basis of the opponent’s starting positions, statistical probabilities of winning are graphically displayed.