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1. This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n Xs and no Os. Similarly, On is the number of rows, columns, or diagonals with just n Os. The utility function assigns +1 to any position with X3=1 and -1 to any position with 03-1. All other terminal positions have utility O. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3x2 (s) + X1(s)-(3 02 (s) + 01(s)). a. Approximately how many possible games of tic-tac-toe are there? b. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one on the board), taking symmetry into account. c. Mark on your tree the evaluations of all the positions at depth 2. d. Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move.

1. This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n Xs and no Os. Similarly, On is the number of rows, columns, or diagonals with just n Os. The utility function assigns +1 to any position with X3=1 and -1 to any position with 03-1. All other terminal positions have utility O. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3x2 (s) + X1(s)-(3 02 (s) + 01(s)). a. Approximately how many possible games of tic-tac-toe are there? b. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one on the board), taking symmetry into account. c. Mark on your tree the evaluations of all the positions at depth 2. d. Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1. This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X's and no Os. Similarly, On is the number of rows, columns, or diagonals with just n Os. The utility function assigns +1 to any position with X3=1 and -1 to any position with 03=1. All other terminal positions have utility O. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)-(3 02 (s)+ 01(s)). a. Approximately how many possible games of tic-tac-toe are there? b. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one on the board), taking symmetry into account. C. Mark on your tree the evaluations of all the positions at depth 2. d. Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move.
Transcribed Image Text:1. This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X's and no Os. Similarly, On is the number of rows, columns, or diagonals with just n Os. The utility function assigns +1 to any position with X3=1 and -1 to any position with 03=1. All other terminal positions have utility O. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)-(3 02 (s)+ 01(s)). a. Approximately how many possible games of tic-tac-toe are there? b. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one on the board), taking symmetry into account. C. Mark on your tree the evaluations of all the positions at depth 2. d. Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move.
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