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Ch. 5 – Adversarial Search

This presentation provides an in-depth look at the Minimax algorithm, specifically applied to the game of Tic-Tac-Toe. It explores the transition model and the functions involved in decision-making, such as Minimax-Decision, Max-Value, and Min-Value. The slides outline how the utility values are calculated, the significance of cutoff limits, and the structure of utility-based agents. By examining the state, actions, and environmental interactions, this resource serves as a valuable guide for students and enthusiasts wanting to understand adversarial search techniques in game theory.

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Ch. 5 – Adversarial Search

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  1. Ch. 5 – Adversarial Search Supplemental slides for CSE 327 Prof. Jeff Heflin

  2. Tic-Tac-Toe Transition Model O tobottom-center O to top-left O totop-center O to top-right

  3. Minimax Algorithm function Minimax-Decision(state) returns an action returnargmaxa  ACTIONS(s)Min-Value(Result(state,a)) function Max-Value(state) returns a utility valueif Terminal-Test(state) then return Utility(state)v -for each ainActions(state) dovMax(v, Min-Value(Result (s,a)))return v function Min-Value(state) returns a utility valueif Terminal-Test(state) then return Utility(state) v +for each a in Actions(state) dovMin(v, Max-Value(Result(s,a)))return v From Figure 5.3, p. 166

  4. Utility-Based Agent sensors State What the world is like now How the world evolves What it will be like if I do action A What my actions do Environment How happy will I be in such a state Utility What action I should do now Agent actuators

  5. Minimax with Cutoff Limit function Minimax-Decision(state) returns an action returnargmaxa  ActionS(s)Min-Value(Result(state,a),0) function Max-Value(state,depth) returns a utility valueif Cutoff-Test(state,depth) then return Eval(state)v -for each ainActions(state) dovMax(v, Min-Value(Result(s,a)), depth+1)return v function Min-Value(state,depth) returns a utility valueif Cutoff-Test(state,depth) then return Eval(state)v +for each a in Actions(state) dovMin(v, Max-Value(Result(s,a)), depth+1)return v

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