Game Theory: Winning Tic-Tac-Toe
Original article: http://article.sapub.org/10.5923.j.jgt.20200901.01.html#Sec3
In high school, I had a classmate who was obsessed with playing tic-tac-toe. Whenever there was free time, he would challenge those around him to a game. And he was quite good too; he’d win most of the time, especially if the opponent was distracted. Anyway, that got me thinking about how we can apply tic-tac-toe strategies to the analysis of game theory.
In a 3 x 3 game of tic-tac-toe, two opponents alternate making moves by drawing X’s and O’s on the chart. The game ends when a player reaches 3 marks in a row in any direction or once the last spot is filled up, whichever comes first. We can create a payoff matrix based on different strategies for the two players. Though neither player has a dominant strategy, the way players decide which strategy to use depends on the other player’s placement markings. The maximum payoff one could get from the game would be winning, and having a tie would give a better payoff to both players than losing.
The article references the symmetrical nature of the game and the logic decision trees used by the simulator. There is something called the minimax algorithm, which calculates the “minimum lose and maximum profit” (Alkaraz et al.). In the case of tic-tac-toe, each player wants to maximize their own chances of winning while minimizing the opponent’s chance of winning. The payoff can be maximized by a win or a fork (trapping the opponent by having 2 Xs or Os in more than one direction). To minimize loss, a player could block the opponent’s 2 Xs or Os in a row.
Now it’s time to try out some tic-tac-toe strategies now and fork-trap your opponent!