# CS188 Spring 2010 Section 3: Game Trees

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 CS188 Spring 2010 Section 3: Game Trees 1 Warm-Up: Column-Row You have a 3x3 matrix of values like the one below. In a somewhat boring game, player A first selects a row, and then player B selects a column. The game is over after these two moves and the outcome of the game is the value in the square that lies in the intersection of the chosen row and column For the following questions, assume that player A wants to maximize the final number that is selected. For each question state which action the player takes and justify your decision in one sentence. (a) What is player A s move if player B is trying to minimize the final number? Draw out the corresponding game tree. (b) What is player A s move if player B is moving randomly? Draw out the corresponding game tree, labeling non-leaf nodes with their expected value assuming B moves randomly and A maximizes expected value. (c) What is player A s move if player B shares A s value function (i.e. wants to maximize the final value)? Draw out the corresponding game tree. 1

2 2 Min-Max Search In this problem, we will explore adversarial search. Consider the zero-sum game tree shown below. Trapezoids that point up, such as at the root, represent choices for the player seeking to maximize; trapezoids that point down represent choices for the minimizer. Outcome values for the maximizing player are listed for each leaf node. It is your move, and you seek to maximize the expected value of the game. (a) Assuming both opponents act optimally, carry out the min-max search algorithm. Write the value of each node inside the corresponding trapzoid. What move should you make now? How much is the game worth to you? (b) Now reconsider the same game tree, but use α-β pruning (the tree is printed on the next page). Expand successors from left to right. In the brackets [, ], record the [α, β] pair that is passed down that edge (through a call to MIN- VALUE or MAX-VALUE). In the parentheses ( ), record the value (v) that is passed up the edge (the value returned by MIN-VALUE or MAX-VALUE). Circle all leaf nodes that are visited. Put an X through edges that are pruned off. How much is the game worth according to α-β pruning? 2

3 (b) 3

4 3 Non zero-sum games The standard Minimax algorithm calculates worst-case values in a zero-sum two player game, i.e. a game in which for all terminal states s, the utilities for players A (max) and B (min) obey U A (s) + U B (s) = 0. In the zero sum case, we know that U A (s) = U B (s), and so we can think of player B as simply minimizing U A (s). In this problem, you will consider the non zero-sum generalization in which the sum of the two players utilities are not necessarily zero. Because player A s utility no longer determines player B s utility exactly, the leaf utilities are written as pairs (U A, U B ), with the first and second component indicating the utility to A and B respecively. In this generalized setting, A seeks to maximize U A, while B seeks to maximize U B. (a) Consider the non zero-sum game tree below. Propagate the terminal utility pairs up the tree using the appropriate generalization of the minimax algorithm on this game tree. Fill in the values (as pairs) at each of the internal nodes. Assume that each player maximizes their own utility and that the root node is an A node. In cases of ties, choose the leftmost child. (b) Briefly explain why no α-β style pruning is possible in the general non zero-sum case. Hint: think first about the case where U A = U B for all nodes. (c) For minimax, we know that the value v computed at the root (say for player A = MAX) is a worst-case value, in that, if the opponent MIN doesn t act optimally, the actual outcome v for MAX can only be better, never worse, than v. In the general non zero-sum setup, can we also say that the value v A computed at the root is a worst-case value, or can A s outcome be worse than the computed v A if B plays suboptimally? Briefly justify. 4

5 Now consider the nearly zero sum case, in which case U A (s) + U B (s) ɛ for some ɛ which is known in advance. For example, the game tree from part (a) is nearly zero sum for ɛ = 2. (d) In the nearly zero sum case, pruning is possible. List the nodes in the game tree above that could be pruned with the appropriate generalization of α-β pruning. Assume that the exploration is done in the standard left to right depth first order, and that the value of ɛ is known to be 2. Make sure you make use of ɛ in your reasoning. (e) Give a general condition under which a child n of a B node b can be pruned. Your condition should generalize alpha-pruning and should be stated in terms of quantities such as the utilities U A (s) and/or U B (s) of relevant nodes s in the game tree, the bound ɛ, and so on. Do not worry about ties. (f) In the nearly zero sum case with bound ɛ, what guarantee, if any, can we make for the actual outcome u for player A (in terms of the value U A of the root) in the case where player B might act suboptimally? 5

### CS188 Spring 2010 Section 3: Game Trees

CS188 Spring 2010 Section 3: Game Trees 1 Warm-Up: Column-Row You have a 3x3 matrix of values like the one below. In a somewhat boring game, player A first selects a row, and then player B selects a column.

### CS188 Spring 2014 Section 3: Games

CS188 Spring 2014 Section 3: Games 1 Nearly Zero Sum Games The standard Minimax algorithm calculates worst-case values in a zero-sum two player game, i.e. a game in which for all terminal states s, the

### ARTIFICIAL INTELLIGENCE (CS 370D)

Princess Nora University Faculty of Computer & Information Systems ARTIFICIAL INTELLIGENCE (CS 370D) (CHAPTER-5) ADVERSARIAL SEARCH ADVERSARIAL SEARCH Optimal decisions Min algorithm α-β pruning Imperfect,

### mywbut.com Two agent games : alpha beta pruning

Two agent games : alpha beta pruning 1 3.5 Alpha-Beta Pruning ALPHA-BETA pruning is a method that reduces the number of nodes explored in Minimax strategy. It reduces the time required for the search and

### Adversary Search. Ref: Chapter 5

Adversary Search Ref: Chapter 5 1 Games & A.I. Easy to measure success Easy to represent states Small number of operators Comparison against humans is possible. Many games can be modeled very easily, although

### CS188 Spring 2011 Written 2: Minimax, Expectimax, MDPs

Last name: First name: SID: Class account login: Collaborators: CS188 Spring 2011 Written 2: Minimax, Expectimax, MDPs Due: Monday 2/28 at 5:29pm either in lecture or in 283 Soda Drop Box (no slip days).

Artificial Intelligence Adversarial Search (Game Playing) Chapter 5 Adapted from materials by Tim Finin, Marie desjardins, and Charles R. Dyer Outline Game playing State of the art and resources Framework

### game tree complete all possible moves

Game Trees Game Tree A game tree is a tree the nodes of which are positions in a game and edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing

### CSC 380 Final Presentation. Connect 4 David Alligood, Scott Swiger, Jo Van Voorhis

CSC 380 Final Presentation Connect 4 David Alligood, Scott Swiger, Jo Van Voorhis Intro Connect 4 is a zero-sum game, which means one party wins everything or both parties win nothing; there is no mutual

### Game-playing: DeepBlue and AlphaGo

Game-playing: DeepBlue and AlphaGo Brief history of gameplaying frontiers 1990s: Othello world champions refuse to play computers 1994: Chinook defeats Checkers world champion 1997: DeepBlue defeats world

### 2 person perfect information

Why Study Games? Games offer: Intellectual Engagement Abstraction Representability Performance Measure Not all games are suitable for AI research. We will restrict ourselves to 2 person perfect information

### CS 2710 Foundations of AI. Lecture 9. Adversarial search. CS 2710 Foundations of AI. Game search

CS 2710 Foundations of AI Lecture 9 Adversarial search Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square CS 2710 Foundations of AI Game search Game-playing programs developed by AI researchers since

### Adversarial Search. Robert Platt Northeastern University. Some images and slides are used from: 1. CS188 UC Berkeley 2. RN, AIMA

Adversarial Search Robert Platt Northeastern University Some images and slides are used from: 1. CS188 UC Berkeley 2. RN, AIMA What is adversarial search? Adversarial search: planning used to play a game

### Midterm Examination. CSCI 561: Artificial Intelligence

Midterm Examination CSCI 561: Artificial Intelligence October 10, 2002 Instructions: 1. Date: 10/10/2002 from 11:00am 12:20 pm 2. Maximum credits/points for this midterm: 100 points (corresponding to 35%

### Computer Science and Software Engineering University of Wisconsin - Platteville. 4. Game Play. CS 3030 Lecture Notes Yan Shi UW-Platteville

Computer Science and Software Engineering University of Wisconsin - Platteville 4. Game Play CS 3030 Lecture Notes Yan Shi UW-Platteville Read: Textbook Chapter 6 What kind of games? 2-player games Zero-sum

Adversarial Search 1 Adversarial Search The ghosts trying to make pacman loose Can not come up with a giant program that plans to the end, because of the ghosts and their actions Goal: Eat lots of dots

### COMP9414: Artificial Intelligence Adversarial Search

CMP9414, Wednesday 4 March, 004 CMP9414: Artificial Intelligence In many problems especially game playing you re are pitted against an opponent This means that certain operators are beyond your control

### Module 3. Problem Solving using Search- (Two agent) Version 2 CSE IIT, Kharagpur

Module 3 Problem Solving using Search- (Two agent) 3.1 Instructional Objective The students should understand the formulation of multi-agent search and in detail two-agent search. Students should b familiar

### Game Engineering CS F-24 Board / Strategy Games

Game Engineering CS420-2014F-24 Board / Strategy Games David Galles Department of Computer Science University of San Francisco 24-0: Overview Example games (board splitting, chess, Othello) /Max trees

### CS510 \ Lecture Ariel Stolerman

CS510 \ Lecture04 2012-10-15 1 Ariel Stolerman Administration Assignment 2: just a programming assignment. Midterm: posted by next week (5), will cover: o Lectures o Readings A midterm review sheet will

### CSE 473: Artificial Intelligence Fall Outline. Types of Games. Deterministic Games. Previously: Single-Agent Trees. Previously: Value of a State

CSE 473: Artificial Intelligence Fall 2014 Adversarial Search Dan Weld Outline Adversarial Search Minimax search α-β search Evaluation functions Expectimax Reminder: Project 1 due Today Based on slides

### Game-playing AIs: Games and Adversarial Search I AIMA

Game-playing AIs: Games and Adversarial Search I AIMA 5.1-5.2 Games: Outline of Unit Part I: Games as Search Motivation Game-playing AI successes Game Trees Evaluation Functions Part II: Adversarial Search

### UNIVERSITY of PENNSYLVANIA CIS 391/521: Fundamentals of AI Midterm 1, Spring 2010

UNIVERSITY of PENNSYLVANIA CIS 391/521: Fundamentals of AI Midterm 1, Spring 2010 Question Points 1 Environments /2 2 Python /18 3 Local and Heuristic Search /35 4 Adversarial Search /20 5 Constraint Satisfaction

### CS 1571 Introduction to AI Lecture 12. Adversarial search. CS 1571 Intro to AI. Announcements

CS 171 Introduction to AI Lecture 1 Adversarial search Milos Hauskrecht milos@cs.pitt.edu 39 Sennott Square Announcements Homework assignment is out Programming and experiments Simulated annealing + Genetic

### Game-playing AIs: Games and Adversarial Search FINAL SET (w/ pruning study examples) AIMA

Game-playing AIs: Games and Adversarial Search FINAL SET (w/ pruning study examples) AIMA 5.1-5.2 Games: Outline of Unit Part I: Games as Search Motivation Game-playing AI successes Game Trees Evaluation

### Game Tree Search. CSC384: Introduction to Artificial Intelligence. Generalizing Search Problem. General Games. What makes something a game?

CSC384: Introduction to Artificial Intelligence Generalizing Search Problem Game Tree Search Chapter 5.1, 5.2, 5.3, 5.6 cover some of the material we cover here. Section 5.6 has an interesting overview

### Adversarial Search. Rob Platt Northeastern University. Some images and slides are used from: AIMA CS188 UC Berkeley

Adversarial Search Rob Platt Northeastern University Some images and slides are used from: AIMA CS188 UC Berkeley What is adversarial search? Adversarial search: planning used to play a game such as chess

### CS 4700: Artificial Intelligence

CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 10 Today Adversarial search (R&N Ch 5) Tuesday, March 7 Knowledge Representation and Reasoning (R&N Ch 7)

Adversarial Search Aka Games Chapter 5 Some material adopted from notes by Charles R. Dyer, U of Wisconsin-Madison Overview Game playing State of the art and resources Framework Game trees Minimax Alpha-beta

### Data Structures and Algorithms

Data Structures and Algorithms CS245-2015S-P4 Two Player Games David Galles Department of Computer Science University of San Francisco P4-0: Overview Example games (board splitting, chess, Network) /Max

### Game Playing AI Class 8 Ch , 5.4.1, 5.5

Game Playing AI Class Ch. 5.-5., 5.4., 5.5 Bookkeeping HW Due 0/, :59pm Remaining CSP questions? Cynthia Matuszek CMSC 6 Based on slides by Marie desjardin, Francisco Iacobelli Today s Class Clear criteria

### CS 540: Introduction to Artificial Intelligence

CS 540: Introduction to Artificial Intelligence Mid Exam: 7:15-9:15 pm, October 25, 2000 Room 1240 CS & Stats CLOSED BOOK (one sheet of notes and a calculator allowed) Write your answers on these pages

### Adversarial Search and Game Playing. Russell and Norvig: Chapter 5

Adversarial Search and Game Playing Russell and Norvig: Chapter 5 Typical case 2-person game Players alternate moves Zero-sum: one player s loss is the other s gain Perfect information: both players have

### Introduction to Algorithms / Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/4/14

600.363 Introduction to Algorithms / 600.463 Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/4/14 25.1 Introduction Today we re going to spend some time discussing game

Mustafa Jarrar: Lecture Notes on Games, Birzeit University, Palestine Fall Semester, 204 Artificial Intelligence Chapter 6 Games (adversarial search problems) Dr. Mustafa Jarrar Sina Institute, University

### Homework Assignment #2

CS 540-2: Introduction to Artificial Intelligence Homework Assignment #2 Assigned: Thursday, February 15 Due: Sunday, February 25 Hand-in Instructions This homework assignment includes two written problems

### Game Playing State-of-the-Art

Adversarial Search [These slides were created by Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC Berkeley. All CS188 materials are available at http://ai.berkeley.edu.] Game Playing State-of-the-Art

### Multiple Agents. Why can t we all just get along? (Rodney King)

Multiple Agents Why can t we all just get along? (Rodney King) Nash Equilibriums........................................ 25 Multiple Nash Equilibriums................................. 26 Prisoners Dilemma.......................................

### 2359 (i.e. 11:59:00 pm) on 4/16/18 via Blackboard

CS 109: Introduction to Computer Science Goodney Spring 2018 Homework Assignment 4 Assigned: 4/2/18 via Blackboard Due: 2359 (i.e. 11:59:00 pm) on 4/16/18 via Blackboard Notes: a. This is the fourth homework

### UMBC 671 Midterm Exam 19 October 2009

Name: 0 1 2 3 4 5 6 total 0 20 25 30 30 25 20 150 UMBC 671 Midterm Exam 19 October 2009 Write all of your answers on this exam, which is closed book and consists of six problems, summing to 160 points.

### Announcements. Homework 1 solutions posted. Test in 2 weeks (27 th ) -Covers up to and including HW2 (informed search)

Minimax (Ch. 5-5.3) Announcements Homework 1 solutions posted Test in 2 weeks (27 th ) -Covers up to and including HW2 (informed search) Single-agent So far we have look at how a single agent can search

### Playing Games. Henry Z. Lo. June 23, We consider writing AI to play games with the following properties:

Playing Games Henry Z. Lo June 23, 2014 1 Games We consider writing AI to play games with the following properties: Two players. Determinism: no chance is involved; game state based purely on decisions

### /633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Algorithmic Game Theory Date: 12/6/18

601.433/633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Algorithmic Game Theory Date: 12/6/18 24.1 Introduction Today we re going to spend some time discussing game theory and algorithms.

### CS 5522: Artificial Intelligence II

CS 5522: Artificial Intelligence II Adversarial Search Instructor: Alan Ritter Ohio State University [These slides were adapted from CS188 Intro to AI at UC Berkeley. All materials available at http://ai.berkeley.edu.]

### Artificial Intelligence

Artificial Intelligence Adversarial Search Instructors: David Suter and Qince Li Course Delivered @ Harbin Institute of Technology [Many slides adapted from those created by Dan Klein and Pieter Abbeel

### Adversarial Search and Game- Playing C H A P T E R 6 C M P T : S P R I N G H A S S A N K H O S R A V I

Adversarial Search and Game- Playing C H A P T E R 6 C M P T 3 1 0 : S P R I N G 2 0 1 1 H A S S A N K H O S R A V I Adversarial Search Examine the problems that arise when we try to plan ahead in a world

### Adversarial Search. Human-aware Robotics. 2018/01/25 Chapter 5 in R&N 3rd Ø Announcement: Slides for this lecture are here:

Adversarial Search 2018/01/25 Chapter 5 in R&N 3rd Ø Announcement: q Slides for this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse471/lectures/adversarial.pdf Slides are largely based

### Lecture 14. Questions? Friday, February 10 CS 430 Artificial Intelligence - Lecture 14 1

Lecture 14 Questions? Friday, February 10 CS 430 Artificial Intelligence - Lecture 14 1 Outline Chapter 5 - Adversarial Search Alpha-Beta Pruning Imperfect Real-Time Decisions Stochastic Games Friday,

### CSE 332: Data Structures and Parallelism Games, Minimax, and Alpha-Beta Pruning. Playing Games. X s Turn. O s Turn. X s Turn.

CSE 332: ata Structures and Parallelism Games, Minimax, and Alpha-Beta Pruning This handout describes the most essential algorithms for game-playing computers. NOTE: These are only partial algorithms:

### Programming Project 1: Pacman (Due )

Programming Project 1: Pacman (Due 8.2.18) Registration to the exams 521495A: Artificial Intelligence Adversarial Search (Min-Max) Lectured by Abdenour Hadid Adjunct Professor, CMVS, University of Oulu

### Computer Game Programming Board Games

1-466 Computer Game Programg Board Games Maxim Likhachev Robotics Institute Carnegie Mellon University There Are Still Board Games Maxim Likhachev Carnegie Mellon University 2 Classes of Board Games Two

### CSE 40171: Artificial Intelligence. Adversarial Search: Game Trees, Alpha-Beta Pruning; Imperfect Decisions

CSE 40171: Artificial Intelligence Adversarial Search: Game Trees, Alpha-Beta Pruning; Imperfect Decisions 30 4-2 4 max min -1-2 4 9??? Image credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188 31

### CS885 Reinforcement Learning Lecture 13c: June 13, Adversarial Search [RusNor] Sec

CS885 Reinforcement Learning Lecture 13c: June 13, 2018 Adversarial Search [RusNor] Sec. 5.1-5.4 CS885 Spring 2018 Pascal Poupart 1 Outline Minimax search Evaluation functions Alpha-beta pruning CS885

### Adversarial Search. CS 486/686: Introduction to Artificial Intelligence

Adversarial Search CS 486/686: Introduction to Artificial Intelligence 1 Introduction So far we have only been concerned with a single agent Today, we introduce an adversary! 2 Outline Games Minimax search

### 16.410/413 Principles of Autonomy and Decision Making

16.10/13 Principles of Autonomy and Decision Making Lecture 2: Sequential Games Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology December 6, 2010 E. Frazzoli (MIT) L2:

### Artificial Intelligence. 4. Game Playing. Prof. Bojana Dalbelo Bašić Assoc. Prof. Jan Šnajder

Artificial Intelligence 4. Game Playing Prof. Bojana Dalbelo Bašić Assoc. Prof. Jan Šnajder University of Zagreb Faculty of Electrical Engineering and Computing Academic Year 2017/2018 Creative Commons

### CS 188: Artificial Intelligence

CS 188: Artificial Intelligence Adversarial Search Instructor: Stuart Russell University of California, Berkeley Game Playing State-of-the-Art Checkers: 1950: First computer player. 1959: Samuel s self-taught

### CMPUT 396 Tic-Tac-Toe Game

CMPUT 396 Tic-Tac-Toe Game Recall minimax: - For a game tree, we find the root minimax from leaf values - With minimax we can always determine the score and can use a bottom-up approach Why use minimax?

Game-Playing & Adversarial Search This lecture topic: Game-Playing & Adversarial Search (two lectures) Chapter 5.1-5.5 Next lecture topic: Constraint Satisfaction Problems (two lectures) Chapter 6.1-6.4,

### Foundations of Artificial Intelligence

Foundations of Artificial Intelligence 42. Board Games: Alpha-Beta Search Malte Helmert University of Basel May 16, 2018 Board Games: Overview chapter overview: 40. Introduction and State of the Art 41.

### Games and Adversarial Search II

Games and Adversarial Search II Alpha-Beta Pruning (AIMA 5.3) Some slides adapted from Richard Lathrop, USC/ISI, CS 271 Review: The Minimax Rule Idea: Make the best move for MAX assuming that MIN always

### Theory and Practice of Artificial Intelligence

Theory and Practice of Artificial Intelligence Games Daniel Polani School of Computer Science University of Hertfordshire March 9, 2017 All rights reserved. Permission is granted to copy and distribute

### Generalized Game Trees

Generalized Game Trees Richard E. Korf Computer Science Department University of California, Los Angeles Los Angeles, Ca. 90024 Abstract We consider two generalizations of the standard two-player game

### CS 188: Artificial Intelligence Spring Announcements

CS 188: Artificial Intelligence Spring 2011 Lecture 7: Minimax and Alpha-Beta Search 2/9/2011 Pieter Abbeel UC Berkeley Many slides adapted from Dan Klein 1 Announcements W1 out and due Monday 4:59pm P2

### Adversarial Search. Read AIMA Chapter CIS 421/521 - Intro to AI 1

Adversarial Search Read AIMA Chapter 5.2-5.5 CIS 421/521 - Intro to AI 1 Adversarial Search Instructors: Dan Klein and Pieter Abbeel University of California, Berkeley [These slides were created by Dan

### Game-Playing & Adversarial Search Alpha-Beta Pruning, etc.

Game-Playing & Adversarial Search Alpha-Beta Pruning, etc. First Lecture Today (Tue 12 Jul) Read Chapter 5.1, 5.2, 5.4 Second Lecture Today (Tue 12 Jul) Read Chapter 5.3 (optional: 5.5+) Next Lecture (Thu

### CS 188: Artificial Intelligence

CS 188: Artificial Intelligence Adversarial Search Prof. Scott Niekum The University of Texas at Austin [These slides are based on those of Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC Berkeley.

ADVERSARIAL SEARCH Today Reading AIMA Chapter 5.1-5.5, 5.7,5.8 Goals Introduce adversarial games Minimax as an optimal strategy Alpha-beta pruning (Real-time decisions) 1 Questions to ask Were there any

Adversarial Search: Game Playing Reading: Chapter 6.5-6.8 1 Games and AI Easy to represent, abstract, precise rules One of the first tasks undertaken by AI (since 1950) Better than humans in Othello and

### CS 440 / ECE 448 Introduction to Artificial Intelligence Spring 2010 Lecture #5

CS 440 / ECE 448 Introduction to Artificial Intelligence Spring 2010 Lecture #5 Instructor: Eyal Amir Grad TAs: Wen Pu, Yonatan Bisk Undergrad TAs: Sam Johnson, Nikhil Johri Topics Game playing Game trees

### Game Playing Part 1 Minimax Search

Game Playing Part 1 Minimax Search Yingyu Liang yliang@cs.wisc.edu Computer Sciences Department University of Wisconsin, Madison [based on slides from A. Moore http://www.cs.cmu.edu/~awm/tutorials, C.

### Game Playing. Why do AI researchers study game playing? 1. It s a good reasoning problem, formal and nontrivial.

Game Playing Why do AI researchers study game playing? 1. It s a good reasoning problem, formal and nontrivial. 2. Direct comparison with humans and other computer programs is easy. 1 What Kinds of Games?

### CS188: Artificial Intelligence, Fall 2011 Written 2: Games and MDP s

CS88: Artificial Intelligence, Fall 20 Written 2: Games and MDP s Due: 0/5 submitted electronically by :59pm (no slip days) Policy: Can be solved in groups (acknowledge collaborators) but must be written

### Announcements. Homework 1. Project 1. Due tonight at 11:59pm. Due Friday 2/8 at 4:00pm. Electronic HW1 Written HW1

Announcements Homework 1 Due tonight at 11:59pm Project 1 Electronic HW1 Written HW1 Due Friday 2/8 at 4:00pm CS 188: Artificial Intelligence Adversarial Search and Game Trees Instructors: Sergey Levine

### Game Tree Search. Generalizing Search Problems. Two-person Zero-Sum Games. Generalizing Search Problems. CSC384: Intro to Artificial Intelligence

CSC384: Intro to Artificial Intelligence Game Tree Search Chapter 6.1, 6.2, 6.3, 6.6 cover some of the material we cover here. Section 6.6 has an interesting overview of State-of-the-Art game playing programs.

### CSE 473 Midterm Exam Feb 8, 2018

CSE 473 Midterm Exam Feb 8, 2018 Name: This exam is take home and is due on Wed Feb 14 at 1:30 pm. You can submit it online (see the message board for instructions) or hand it in at the beginning of class.

### Game Playing State-of-the-Art. CS 188: Artificial Intelligence. Behavior from Computation. Video of Demo Mystery Pacman. Adversarial Search

CS 188: Artificial Intelligence Adversarial Search Instructor: Marco Alvarez University of Rhode Island (These slides were created/modified by Dan Klein, Pieter Abbeel, Anca Dragan for CS188 at UC Berkeley)

### Adversarial Search. Chapter 5. Mausam (Based on slides of Stuart Russell, Andrew Parks, Henry Kautz, Linda Shapiro) 1

Adversarial Search Chapter 5 Mausam (Based on slides of Stuart Russell, Andrew Parks, Henry Kautz, Linda Shapiro) 1 Game Playing Why do AI researchers study game playing? 1. It s a good reasoning problem,

### Adversarial Search. CS 486/686: Introduction to Artificial Intelligence

Adversarial Search CS 486/686: Introduction to Artificial Intelligence 1 AccessAbility Services Volunteer Notetaker Required Interested? Complete an online application using your WATIAM: https://york.accessiblelearning.com/uwaterloo/

### CSC384: Introduction to Artificial Intelligence. Game Tree Search

CSC384: Introduction to Artificial Intelligence Game Tree Search Chapter 5.1, 5.2, 5.3, 5.6 cover some of the material we cover here. Section 5.6 has an interesting overview of State-of-the-Art game playing

### Adversarial Search and Game Theory. CS 510 Lecture 5 October 26, 2017

Adversarial Search and Game Theory CS 510 Lecture 5 October 26, 2017 Reminders Proposals due today Midterm next week past midterms online Midterm online BBLearn Available Thurs-Sun, ~2 hours Overview Game

### Game Playing Beyond Minimax. Game Playing Summary So Far. Game Playing Improving Efficiency. Game Playing Minimax using DFS.

Game Playing Summary So Far Game tree describes the possible sequences of play is a graph if we merge together identical states Minimax: utility values assigned to the leaves Values backed up the tree

### Project 1. Out of 20 points. Only 30% of final grade 5-6 projects in total. Extra day: 10%

Project 1 Out of 20 points Only 30% of final grade 5-6 projects in total Extra day: 10% 1. DFS (2) 2. BFS (1) 3. UCS (2) 4. A* (3) 5. Corners (2) 6. Corners Heuristic (3) 7. foodheuristic (5) 8. Suboptimal

### CS440/ECE448 Lecture 9: Minimax Search. Slides by Svetlana Lazebnik 9/2016 Modified by Mark Hasegawa-Johnson 9/2017

CS440/ECE448 Lecture 9: Minimax Search Slides by Svetlana Lazebnik 9/2016 Modified by Mark Hasegawa-Johnson 9/2017 Why study games? Games are a traditional hallmark of intelligence Games are easy to formalize

### Artificial Intelligence 1: game playing

Artificial Intelligence 1: game playing Lecturer: Tom Lenaerts Institut de Recherches Interdisciplinaires et de Développements en Intelligence Artificielle (IRIDIA) Université Libre de Bruxelles Outline

Lecture 7 How can we use search to plan ahead when other agents are planning against us? 1 Agenda Games: context, history Searching via Minimax Scaling α β pruning Depth-limiting Evaluation functions Handling

### Game Playing State-of-the-Art CSE 473: Artificial Intelligence Fall Deterministic Games. Zero-Sum Games 10/13/17. Adversarial Search

CSE 473: Artificial Intelligence Fall 2017 Adversarial Search Mini, pruning, Expecti Dieter Fox Based on slides adapted Luke Zettlemoyer, Dan Klein, Pieter Abbeel, Dan Weld, Stuart Russell or Andrew Moore

### More on games (Ch )

More on games (Ch. 5.4-5.6) Announcements Midterm next Tuesday: covers weeks 1-4 (Chapters 1-4) Take the full class period Open book/notes (can use ebook) ^^ No programing/code, internet searches or friends

### UMBC CMSC 671 Midterm Exam 22 October 2012

Your name: 1 2 3 4 5 6 7 8 total 20 40 35 40 30 10 15 10 200 UMBC CMSC 671 Midterm Exam 22 October 2012 Write all of your answers on this exam, which is closed book and consists of six problems, summing

### 4. Games and search. Lecture Artificial Intelligence (4ov / 8op)

4. Games and search 4.1 Search problems State space search find a (shortest) path from the initial state to the goal state. Constraint satisfaction find a value assignment to a set of variables so that

### Adversarial Search and Game Playing

Games Adversarial Search and Game Playing Russell and Norvig, 3 rd edition, Ch. 5 Games: multi-agent environment q What do other agents do and how do they affect our success? q Cooperative vs. competitive

### CS 188: Artificial Intelligence Spring 2007

CS 188: Artificial Intelligence Spring 2007 Lecture 7: CSP-II and Adversarial Search 2/6/2007 Srini Narayanan ICSI and UC Berkeley Many slides over the course adapted from Dan Klein, Stuart Russell or

### CS61B Lecture #22. Today: Backtracking searches, game trees (DSIJ, Section 6.5) Last modified: Mon Oct 17 20:55: CS61B: Lecture #22 1

CS61B Lecture #22 Today: Backtracking searches, game trees (DSIJ, Section 6.5) Last modified: Mon Oct 17 20:55:07 2016 CS61B: Lecture #22 1 Searching by Generate and Test We vebeenconsideringtheproblemofsearchingasetofdatastored

### 2/5/17 ADVERSARIAL SEARCH. Today. Introduce adversarial games Minimax as an optimal strategy Alpha-beta pruning Real-time decision making

ADVERSARIAL SEARCH Today Introduce adversarial games Minimax as an optimal strategy Alpha-beta pruning Real-time decision making 1 Adversarial Games People like games! Games are fun, engaging, and hard-to-solve

### Midterm. CS440, Fall 2003

Midterm CS440, Fall 003 This test is closed book, closed notes, no calculators. You have :30 hours to answer the questions. If you think a problem is ambiguously stated, state your assumptions and solve

### More on games (Ch )

More on games (Ch. 5.4-5.6) Alpha-beta pruning Previously on CSci 4511... We talked about how to modify the minimax algorithm to prune only bad searches (i.e. alpha-beta pruning) This rule of checking