An%20eye%20for%20eye%20only%20ends%20up%20making%20the%20whole%20world%20blind.%20-Mohandas%20Karamchand%20Gandhi,%20%20%20%20born%20October%202nd,%201869.

1
An eye for eye only ends up making the whole
world blind. -Mohandas Karamchand Gandhi,
born October 2nd, 1869.
Lecture of October 2nd, 2001
2
Sunday, May 11th, 1997
What makes DeepBlue Tick?
3
Game Playing (Adversarial Search)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
lt 2
lt 2
lt 5
lt 14
Cut
2
14
5
2

• Whenever a node gets its true value, its
  parents 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 ltk, and a max ancestor
  of n, say m, has a bound gtl, then cutoff occurs
  as long as l gtk
• If a max node n has bound gtk, and a min ancestor
  of n, say m, has a bound ltl, then cutoff occurs
  as long as l ltk

11
Claude Shannon (finite look-ahead)
Chaturanga, India (550AD) (Proto-Chess)
Von Neuman (Min-Max theorem)
Lecture of 4th October, 2001
Donald Knuth (a-b analysis)
John McCarthy (a-b pruning)
12
Searching Tic Tac Toe using Minmax
13
Click for an animation of Alpha-beta search in
action on Tic-Tac-Toe
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
Evaluation Functions TicTacToe
If win for Max infty If lose for Max
-infty If draw for Max 0 Else
rows/cols/diags open for Max -
rows/cols/diags open for Min
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
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

23
(No Transcript)
24
RTA
S
S n
m
k
G
G1 H2 F3
G1 H2 F3
n
m
G2 H3 F5
k
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))
25
Multi-player Games
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)