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.

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.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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