3a. Game playing algorithm A variation of the two-player game Nim starts with a single stack of 7 tokens. At each move a player removes one, two or three tokens, leaving a non-empty pile. A player who has to remove the last token loses the game. Max plays first. Draw the complete game tree for this game. The utility function is defined as follows: Utility = -1 for a terminal state if Min wins the game Utility = 1 for a terminal state if Max wins the game Using the Minimax algorithm, assign utility values to all states in the game tree. If both Min and Max play a perfect game (always makes correct moves), who will win? Explain your answer and show the winning path(s) for Max or Min.
3a. Game playing algorithm A variation of the two-player game Nim starts with a single stack of 7 tokens. At each move a player removes one, two or three tokens, leaving a non-empty pile. A player who has to remove the last token loses the game. Max plays first. Draw the complete game tree for this game. The utility function is defined as follows: Utility = -1 for a terminal state if Min wins the game Utility = 1 for a terminal state if Max wins the game Using the Minimax algorithm, assign utility values to all states in the game tree. If both Min and Max play a perfect game (always makes correct moves), who will win? Explain your answer and show the winning path(s) for Max or Min.
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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3a. Game playing
A variation of the two-player game Nim starts with a single stack of 7 tokens. At each move
a player removes one, two or three tokens, leaving a non-empty pile. A player who has to
remove the last token loses the game. Max plays first.
Draw the complete game tree for this game.
The utility function is defined as follows:
Utility = -1 for a terminal state if Min wins the game
Utility = 1 for a terminal state if Max wins the game
Using the Minimax algorithm, assign utility values to all states in the game tree.
If both Min and Max play a perfect game (always makes correct moves), who will win?
Explain your answer and show the winning path(s) for Max or Min.
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