Adversarial Search and Game Playing Examples Game Tree

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Adversarial Search and Game Playing Examples

Adversarial Search and Game Playing Examples

Game Tree MAX nodes MAX’s play MIN nodes MIN’s play Terminal state (win for

Game Tree MAX nodes MAX’s play MIN nodes MIN’s play Terminal state (win for MAX) Here, symmetries have been used to reduce the branching factor

Game Tree MAX’s play MIN’s play Terminal state (win for MAX) In general, the

Game Tree MAX’s play MIN’s play Terminal state (win for MAX) In general, the branching factor and the depth of terminal states are large Chess: • Number of states: ~1040 • Branching factor: ~35 • Number of total moves in a game: ~100

Example: Tic-tac-Toe e(s) = number of rows, columns, and diagonals open for MAX -

Example: Tic-tac-Toe e(s) = number of rows, columns, and diagonals open for MAX - number of rows, columns, and diagonals open for MIN 8 -8 = 0 6 -4 = 2 3 -3 = 0

Backing up Values Tic-Tac-Toe tree at horizon = 2 1 Best move -1 1

Backing up Values Tic-Tac-Toe tree at horizon = 2 1 Best move -1 1 -2 6 -5=1 5 -5=0 4 -5=-1 5 -4=1 6 -4=2 5 -6=-1 5 -5=0 5 -6=-1 6 -6=0 4 -6=-2

Continuation 1 2 1 3 1 1 2 0 2 1 1 3 1

Continuation 1 2 1 3 1 1 2 0 2 1 1 3 1 2 0 2 1 1 0

Example

Example

Example b=2 2 The beta value of a MIN node is an upper bound

Example b=2 2 The beta value of a MIN node is an upper bound on the final backed-up value. It can never increase

Example The beta value of a MIN node is an upper bound on the

Example The beta value of a MIN node is an upper bound on the final backed-up value. It can never increase b=1 2 1

Example a=1 The alpha value of a MAX node is a lower bound on

Example a=1 The alpha value of a MAX node is a lower bound on the final backed-up value. It can never decrease b=1 2 1

Example a=1 b = -1 b=1 2 1 -1

Example a=1 b = -1 b=1 2 1 -1

Example a=1 b = -1 b=1 Search can be discontinued below any MIN node

Example a=1 b = -1 b=1 Search can be discontinued below any MIN node whose beta value is less than or equal to the alpha value of one of its MAX ancestors 2 1 -1

An example of Alpha-beta pruning 0 max min 0 0 -3 -3 3 max

An example of Alpha-beta pruning 0 max min 0 0 -3 -3 3 max 0 5 -3 3 3 -3 0 2 -2 3

Example of Alpha-beta pruning Final tree max min max 0 5 -3 3 3

Example of Alpha-beta pruning Final tree max min max 0 5 -3 3 3 -3 0 2 -2 3

An example of Alpha-beta pruning 0 5 -3 3 3 -3 0 2 -2

An example of Alpha-beta pruning 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 5 -3 3 3 -3 0 2 -2 3 5 2

Example 0 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 5 -3 3 3 -3 0 2 -2 3 5

Example 0 0 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 -3 0 5 -3 3 3 -3 0 2 -2 3

Example 0 0 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 -3 0 5 -3 3 3 -3 0 2 -2 3

Example 0 0 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 0 5 -3 3 3 -3 0 2 -2

Example 0 0 0 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0

Example 0 0 0 -3 3 3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 5 0 5 -3 3 3 -3

Example 0 0 0 -3 3 3 5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 2 2 0 5 -3 3 3

Example 0 0 0 -3 3 3 2 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 3 3 2 2 0 5 -3 3 3

Example 0 0 0 -3 3 3 2 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3

Example 0 0 0 -3 2 2 3 3 2 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 5 0 5

Example 0 0 0 -3 2 2 3 3 2 2 5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 1 1 0

Example 0 0 0 -3 2 2 3 3 2 2 1 1 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 1 1 -3

Example 0 0 0 -3 2 2 3 3 2 2 1 1 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 3 3 2 2 1 1 -3

Example 0 0 0 -3 2 2 3 3 2 2 1 1 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1 1 -3 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1 1 -3 -5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1 1 -3 -5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1 -5 -3 -5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1

Example 0 0 0 -3 2 2 1 3 3 1 2 2 1 -5 -3 -5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 0 0 1 0 0 -3 2 2 1 3 3 1 2

Example 0 0 1 0 0 -3 2 2 1 3 3 1 2 2 1 -5 -3 -5 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 1 0 0 0 0 -3 2 2 2 1 3 3 1

Example 1 0 0 0 0 -3 2 2 2 1 3 3 1 2 2 1 -5 2 -3 -5 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Example 1 0 0 0 0 -3 2 2 2 1 3 3 1

Example 1 0 0 0 0 -3 2 2 2 1 3 3 1 2 2 1 -5 2 -3 -5 2 0 5 -3 3 3 -3 0 2 -2 3 5 2 5 -5 0 1 5 1 -3 0 -5 5 -3 3 2

Nondeterminstic games are the games with both an element of chance and Add chance

Nondeterminstic games are the games with both an element of chance and Add chance nodes to tree Example with coin flip instead of dice 0. 5 2 4 0. 5 7 0. 5 4 6 0. 5 0 5 -2

Example with coin flip instead of dice (cont. ) 3 3 -1 0. 5

Example with coin flip instead of dice (cont. ) 3 3 -1 0. 5 2 2 4 4 7 4 6 0. 5 0 -2 0 5 -2

Alpha-Beta prunning in Tic-Tac-Toe 44

Alpha-Beta prunning in Tic-Tac-Toe 44

Adversaries Adversarial examples Adversarial examples Ostrich Adversarial examplesAdversaries Adversarial examples Adversarial examples Ostrich Adversarial examples
Adversarial Search Adversarial Search Game playing Perfect playAdversarial Search Adversarial Search Game playing Perfect play
Adversarial Search game playing search We have experienceAdversarial Search game playing search We have experience
Game Playing Chapter 5 Game playing Search appliedGame Playing Chapter 5 Game playing Search applied
Tree Binary Tree Binary Search Tree 2 TreeTree Binary Tree Binary Search Tree 2 Tree
Adversarial Search and Game Playing Russell and NorvigAdversarial Search and Game Playing Russell and Norvig
Adversarial Search and Game Playing Russell and NorvigAdversarial Search and Game Playing Russell and Norvig
Adversarial Search and Game Playing Where making goodAdversarial Search and Game Playing Where making good
Adversarial Search and Game Playing CHAPTER 5 CMPTAdversarial Search and Game Playing CHAPTER 5 CMPT
Adversarial Search and Game Playing Where making goodAdversarial Search and Game Playing Where making good
Game Playing Adversarial Search Chapter 6 Why studyGame Playing Adversarial Search Chapter 6 Why study
Adversarial Search Game Playing Chapter 6 Outline GamesAdversarial Search Game Playing Chapter 6 Outline Games
Game Playing Adversarial Search Chapter 6 Why studyGame Playing Adversarial Search Chapter 6 Why study
ADVERSARIAL SEARCH GAME PLAYING 2 TEXAS HOLD EMADVERSARIAL SEARCH GAME PLAYING 2 TEXAS HOLD EM
Game Playing Adversarial Search University of Berkeley USAGame Playing Adversarial Search University of Berkeley USA
Game Playing Adversarial Search University of Berkeley USAGame Playing Adversarial Search University of Berkeley USA
CS 534 Spring 2019 Adversarial Search Game PlayingCS 534 Spring 2019 Adversarial Search Game Playing
Chapter 5 Adversarial Search Game Playing Typical assumptionsChapter 5 Adversarial Search Game Playing Typical assumptions
CS 534 Spring 2019 Adversarial Search Game PlayingCS 534 Spring 2019 Adversarial Search Game Playing
Game Playing Adversarial Search Chapter 5 Why studyGame Playing Adversarial Search Chapter 5 Why study
Lecture 02 Part C Game Playing Adversarial SearchLecture 02 Part C Game Playing Adversarial Search
Game Playing Chapter 6 Game Playing and AIGame Playing Chapter 6 Game Playing and AI
Game Playing Chapter 6 Game Playing and AIGame Playing Chapter 6 Game Playing and AI
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