It is 's move in the Tic-Tac-Toe game (above). Which of the moves gave above (1, 2, 3, 4, 5) is the best move for ?
Assume both players intend to win the game and plays optimally.
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CASE 1 :-
If O plays 1 . Then X who plays optimally would play 5 . Then O would definitely lose because , in the next turn it can play either 2 or the square to the right of the bottom X . But, in the next turn, X would definitely win.
CASE 2 :-
If O plays 2 . Then X who plays optimally would play in the square right of the bottom X . Then O would definitely lose because , in the next turn it can play either 3 or 5 . But, in the next turn, X would definitely win.
CASE 3 :-
If O plays 3 . Then X who plays optimally would play 5 . Then O would definitely lose because , in the next turn it can play either 2 or the square to the right of the bottom X . But, in the next turn, X would definitely win.
CASE 4 :-
If O plays 4 . Then X who plays optimally would play in the square left of the bottom X . Then O would definitely lose because , in the next turn it can play either 3 or 5 . But, in the next turn, X would definitely win.
CASE 5 :-
If O plays 5 . Now, the optimal player X can't do anything to defeat the optimal player O because now X would not succeed in forming a two path trap (like the ones in the above cases).
So, the best move for O is 5 .