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INC 551 Artificial Intelligence

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INC 551 Artificial Intelligence Lecture 5 Adversarial Search (Game Playing) [-2,2 ... – PowerPoint PPT presentation

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Title: INC 551 Artificial Intelligence


1
INC 551 Artificial Intelligence
  • Lecture 5
  • Adversarial Search
  • (Game Playing)

2
Game Playing
Environment ?????????? enemies ???? hostile
agents
Enemies are unpredictable
To deal with the problem Consider every
possibility of reply
3
Types of Games
4
Search Technique
????????????? search ?????????????????????????????
?????????????? enemies ?????? branching factor
???? ???????????????? minimax algorithm
?????????????
5
?????? node ??? Game O-X ??????? 2 ?? ???? Max
??? Min
6
Minimax Algorithm
??????????? depth 2 ???? terminal states ???????
7
Minimax Algorithm
8
Property of Minimax
Complete ??? search tree ??????????? Optimal
yes ??? opponent optimal Time Complexity
Space Complexity (??? Depth-first)
For a normal chess game b35, m100 Time?? -gt
infeasible
9
Real Problem with Minimax
???????? cut-off ???????? depth ???????????
search ???? ??? node ??????????????????
evaluation function (heuristic) ?????????????????
?? node ????
10
Heuristics for Game Search
?? game ?????? ????????????????? node
?????????????? (?????????) Heuristics
????????????????????????? state ??? game ?????
depth ??????????????????
11
Heuristic in chess material value Pawn1,
knight3, bishop3, rook5, queen9
12
Minimax ?? case ??? opponent??????????
13
Alpha-beta Pruning
Use with minimax for eliminating the nodes
that looks bad Each node will keep the lower
limit and upper limit of possible score, called
alpha and beta value alpha,beta Will follow
the rules to stop expanding nodes
14
Rules for Terminating searchon nodes
  • Stop below any MIN node have a beta value less
    than
  • or equal to alpha value of any of its MAX
    ancestors
  • Stop below any MAX node have an alpha value
    greater than
  • or equal to beta value of any of its MIN
    ancestors

15
Alpha-beta Pruning
????? expand node ??????????????????????
16
(3,8)
(3,3)
17
(3,8)
(3,3)
(-8,2)
18
(3,8)
(3,3)
(-8,14)
(-8,2)
19
(3,8)
(3,3)
(-8,5)
(-8,2)
20
(3,3)
(2,2)
(3,3)
(-8,2)
21
Alpha-Beta Algorithm
22
Property of Pruning
  • Final result ??????????????
  • ????????????? Good move ????????
  • ??????? pruning ??

23
Deterministic Games in Practice
24
Games with chance
Backgammon
25
Search Technique with Chance
????? chance ????????????????? node
???? ?????????????? probability
???????????????????
26
Coin-flipping Game
???????????????????????????????????????????????
???????
?????????
???????
27
Alpha-Beta Pruning
?????????????? non-deterministic problems
???????? ????????????????????? node ????????????
pruning ???????????????? deterministic problems
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??????????????????????? bound
???????????????? -2,2
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42
Case Study (Othello)
43
Standard Board Size 8x8 64 squares Depth
about 60 moves Branching factor varied
0-20 Estimated search time for depth 32 3
days Estimated search time for depth 60 2,100
years
44
Game playing Tactic
  • Opening (around move 1-12)
  • Use opening book
  • Mid game (around move 13 35)
  • Use Evaluation function
  • End game (around move 36-end)
  • Use exhaustive search

45
Opening
There are 3 ways of opening in Othello. Use
statistic records for 100,000 games to
determine which opening win the most.
46
Mid Game
  • Evaluation function use heuristics to give score
    to board
  • position
  • Dont play on certain square
  • Prefer corner
  • Want great mobility
  • Edge and corner patterns

Evaluation function is the key to strong Othello
program
47
End Game
Search to the end
48
Breakthrough Event
Year 1997 6 game match
Takeshi Murakami (Othello world
champion) vs Logistello (by Michael Buro)
49
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52
Final Result
Takeshi Murakami (Othello world champion) Win 0
match, get 120 discs Logistello (by Michael
Buro) Win 6 matches, get 264 discs
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