Mohandas Karamchand Gandhi was born on 2.10.1869 in Porbandar , in his ancestral home.
An eye for eye only ends up making the whole world blind. -Mohandas Karamchand Gandhi, born October...
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Transcript of An eye for eye only ends up making the whole world blind. -Mohandas Karamchand Gandhi, born October...
An eye for eye only ends up making the whole world blind. -Mohandas Karamchand Gandhi, born October 2nd, 1869.
Lecture of October 2nd, 2001
Sunday, May 11th, 1997
What makes DeepBlue Tick?
Game Playing (Adversarial Search)
2
<= 2
Cut
14
<= 14
5
<= 5
2
<= 2
•Whenever a node gets its “true” value, its parent’s bound gets updated
•When all children of a node have been evaluated (or a cut off occurs below that node), the current bound of that node is its true value
•Two types of cutoffs:
•If a min node n has bound <=k, and a max ancestor of n, say m, has a bound >=l, then cutoff occurs as long as l >=k
•If a max node n has bound >=k, and a min ancestor of n, say m, has a bound <=l, then cutoff occurs as long as l <=k
Von Neuman(Min-Max theorem)
Claude Shannon(finite look-ahead)
Chaturanga, India (~550AD)(Proto-Chess)
John McCarthy (pruning)
Donald Knuth(analysis)
Lecture of 4th October, 2001
Searching Tic Tac Toe using Minmax
Click for an animation of Alpha-beta search in action on Tic-Tac-Toe
Evaluation Functions: TicTacToe
If win for Max +inftyIf lose for Max -inftyIf draw for Max 0Else # rows/cols/diags open for Max - #rows/cols/diags open for Min
Why is “deeper” better?
• Possible reasons– Taking mins/maxes of the evaluation values of
the leaf nodes improves their collective accuracy
– Going deeper makes the agent notice “traps” thus significantly improving the evaluation accuracy
• All evaluation functions first check for termination states before computing the non-terminal evaluation
RTA*
S n
m
k
G
S
n mG=1H=2F=3
G=1H=2F=3
kG=2H=3F=5
infty
--Grow the tree to depth d --Apply f-evaluation for the leaf nodes--propagate f-values up to the parent nodes f(parent) = min( f(children))
Multi-player Games