Minimax And Game Trees

Please observe example and answer, thank you.

Question:

Example:

Application to tic-tac toe Suppose you(X) are playing the game of tic-tac-toe with your friend (O). You are in the middle of the game where the position is the folowing and i is your turn (X to play). f both players play with the best possible strategy, this game will end in a win for X 1.1 Draw a decision tree starting from this position to show all possible moves. Use +1 to score your victory, O for adraw, and-1 for your loss.15 points) 1.2 Use the Minimax algorithm moves). and find the winnling strategy (winning set of to score the positions the 1 point) Note the following comments before drawing the tree 1. You may assume that both players are smart enough so that if they can win in a single move, they will Therefore the state to the right with Xto play has a score of +1. When you draw the game tree you need not expand this position further. 2. In our model of tic-tac-toe game play, a player must block the opponent's mmediate threat of making 3 in a row. Any ather choice is considered ilegal. For instance, in this pasition, the only legal move for O is the top-right comer, and must be played (a forced move). Similarly if a draw is forced (there is exactly one way to play for each player),you do not have to play it out to the end, and you can assign the position a score of o For instance the position shown on the right is a forced draw pasition (O is to play next) because the only legal continuation is a draw (as shown in the two figures below) Application to tic-tac toe Suppose you(X) are playing the game of tic-tac-toe with your friend (O). You are in the middle of the game where the position is the folowing and i is your turn (X to play). f both players play with the best possible strategy, this game will end in a win for X 1.1 Draw a decision tree starting from this position to show all possible moves. Use +1 to score your victory, O for adraw, and-1 for your loss.15 points) 1.2 Use the Minimax algorithm moves). and find the winnling strategy (winning set of to score the positions the 1 point) Note the following comments before drawing the tree 1. You may assume that both players are smart enough so that if they can win in a single move, they will Therefore the state to the right with Xto play has a score of +1. When you draw the game tree you need not expand this position further. 2. In our model of tic-tac-toe game play, a player must block the opponent's mmediate threat of making 3 in a row. Any ather choice is considered ilegal. For instance, in this pasition, the only legal move for O is the top-right comer, and must be played (a forced move). Similarly if a draw is forced (there is exactly one way to play for each player),you do not have to play it out to the end, and you can assign the position a score of o For instance the position shown on the right is a forced draw pasition (O is to play next) because the only legal continuation is a draw (as shown in the two figures below)