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Group 1 :
 Game playing was one of the first tasks
undertaken in AI
 Study of games brings us closer to :
 Machines capable of logical deduction
 Machines for making strategic decisions
 Analyze the limitations of machines to human
thought process
 Games are an idealization of worlds
 World state is fully accessible
 Actions & outcomes are well-defined
Outline of the presentation
 Evaluation Functions
 Algorithms
 Deep Blue
 Conclusions from Deep Blue
 Conclusion
 References
 Neither too simple
 Nor too difficult for satisfactory solution
 Requires “thinking” for a skilled player
 Designing a chess playing program
 Perfect chess playing : INTRACTABLE
 Legal Chess : TRIVIAL
 Play tolerably good game : SKILLFULLY
Evaluation Function
Evaluation Function
 Utility function
 Whole game tree is explored
 computationally expensive task !!
 Estimates the expected utility of a state
 Evaluation functions
 cut off the exploration depth by estimating
whether a state will lead to a win or loss
Evaluation Function (cont.)
 A good evaluation function should
 not take too long
 Preserve ordering of the terminal states otherwise it
will lead to bad decision making
 Consider strategic moves that lead to long term
Evaluation Function (cont.)
Typically includes :
Material Advantage (difference in total material of both sides)
f (P) = 200(k – k’) + 9(q – q’) + 5(r – r’)
+ 3(b – b’) + (p – p’) + g(P) + h(P)
Positions of pieces
Rook on open file
double rooks
rook on seventh rank etc. and their relative positions.
Pawn Formation
Evaluation function is an attempt to write a mathematical
formula for intelligence 
Games as Search Problems
 Initial states
Where game starts
 Initial position in chess
 Successor function
 List of all legal moves from current position
 Terminal State
 Where the game is concluded
 Utility function
 Numeric value for all terminal states
Minimax Strategy
Minimax Strategy
 Optimal strategy
 Assumption : opponent plays his best possible
 An option is picked which
 Minimizes damage done by opponent
 Does most damage to the opponent
 Idea:
 For each node find minimum minimax value
 Choose the node with maximum of such values
 This will ensure best value against most damage
done by opponent
Strategy of Minimax
 Opponent tries to reduce utility function’s
 For any move made by opponent in reply of
computer’s move, choose minimum reduced
value by opponent
 Find the move with maximum such value
 Algorithm is complete for complete tree only
 Not best strategy against irrational opponent
 According to definition
 Time complexity :O(bm)
 b = max. no. of possible moves
 m = max. depth of tree
 In chess even in average case, b = 35 and
m = 100 => time exceeds practical limits
 # of states grows exponentially as per number of
moves played
α-β Pruning
α-β Pruning
 The problem of minimax search
 # of state to examine: exponential in number of
 Returns same moves as minimax does
 Prunes away branches that can’t influence final
 α: the value of the best (highest) choice so far in
search of MAX
 β: the value of the best (lowest) choice so far in
search of MIN
 Order of considering successor
Algorithm for α-β Pruning
 Current highest β is found and assigned as α
 β is current lowest for α’s from that move
 For next possible node, while finding β, if some α
is found lower than current highest β:
 It will only give lesser value of final β
 S0, other α’s are not found for that node
 After calculating β for this node, α is replaced by
max(α,β for this node)
 In this way after all possible set of moves final
value of α is found
α-β Pruning (2)
If m is
better than
n for
Player, we
will never
get to n in
and just
prune it.
Analysis of α-β Pruning:
Improvement over minimax algorithm
 Does not affect final results
 Worthwhile to examine that successor first which
is likely to be best
 Time complexity: O(b(m/2))
 Effective branching factor = √b
 i.e. 6 rather than 35
 In case of random ordering :
 Total number of nodes examined is of the order
Transposition table
 Dynamic programming
 Multiple paths to the same position
 Savings through memorization
 Use a hash table of evaluated positions
Iterative Deepening
 Sometime chess is played under a strict time
 Depth of search depend on time
 Use of Breadth first Search
 Advantage : program know which move was
best at previous level
Horizon Effect
 Problem with fixed
depth search
 Positive Horizon
 Negative horizon
Quiescence Search
 Search till “quiet” position
 Quiet Position
 Doesn’t affect the current position so much
 Example : no capture of any piece, no check, no
pawn promotions/threats
State of the art : DEEP BLUE
Defeats Gary Kasparov
 Won a match in 1997
 Brute force computing power
 Massive, parallel architecture
 Special purpose hardware for chess
 Parameters of the evaluation function
 Learnt by studying many master games
 Different evaluation function for different
 Utilized heavily loaded endgame databases
Humans vs. Computers
Lower Computational Speed
Errors Possible
Error Free
Tend to be instinctive
No instincts
High Learning Capabilities
Not Inductive
Some intricacies of a chess
playing system
 Should not play the same sequence of moves again
 A player wins a match against the computer
 Starts playing the same sequence of moves
 Hence, a statistical element is required
 Opponent can learn the algorithm used by computer
 Hence, again the need for a statistical element
 Different game play during different phases
 Start Game
 Mid Game
 End Game
 Computer chess as a search problem
 Good enough decisions
 Simulation of “skill” by “knowledge”
 Limitations of computers to humans
 Future work :
 Better evaluation functions through learning
 Need for different AI techniques to play chess
 Claude E. Shannon: Programming a
Computer for Playing Chess, Philosophical
Magazine, Ser.7, Vol. 41, No. 314, March
 S.Russel & P. Norvig: Artificial Intelligence: A
Modern Approach 2/E, Prentice Hall, ISBN-10:
 Wikipedia
Thank You
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