Computer Simulation (2)
Game Playing
Different Types of Games
• How many players?
– One
– Two
• Element of chance?
– Deterministic
– Nondeterministic
• Outcome
– Zero sum (what one player wins, the other loses)
– Non-zero sum
Different types of Games
Deterministic
Nondeterministic
Tower of Hanoi
Solitaire
Chess
Tic-Tac-Toe
Go
Backgammon
Poker
One
Player
Two
Player
1
Using hill climbing for one player games
Start
5
12
11
7
15
17
20
17 38 49 30 68
8
9
7
18
12
4
13
18
6
18 11
9
6
25
7
15
10 32 28
(higher = better)
Game Tree for two person game
My
Turn
Your
Turn
My
Turn
Your
Turn
+1 = I win
Game Tree
-1 = you win
My
Turn = ??
a1
a2
Your
Turn
My
Turn
Your
Turn
+1 +1
+1 +1 +1 +1
+1 +1
-1
+1
-1
+1 +1 -1
+1 -1
2
Perfect decisions with two player games
• Each player will make the best decisions possible:
Player A: maximize score (higher scores better for A)
Player B: minimize score (lower scores better for B)
A
a1
a2
b2
b3
B
b1
6
7
b4
68
5
The Minimax Procedure
1) Work upwards, 2) B will always pick minimum, and 3) A
will always pick maximum
A
a1
a2
B
b2
b1
b4
b3
A
a1
a2
8
a3
13
a4
11
a5
25
a6
21
a7
5
a8
17
19
B
What does Minimax predict A will do?
A
a1
a2
B
b1
b2
b4
b3
A
B
17 38 49 30 68
7
4
18
18 11
9
25
7
10 32 28
3
Fighting Combinatorial Explosion
Æ limit branching factor
Æ pruning the search tree
Depth-First Search
A
B
Depth-First Search & Minimax
A
7
9
8
7
6
5
B
1
4
7
4
3
2
1
4
Alpha-Beta Pruning
AT LEAST 7
8
7
?
6
B
?
6
7
9
AT MOST 6
no need to visit other branches
below this node
A
7
?
?
?
?
Alpha-Beta Pruning
A
7
9
8
7
6
?
B
3
6
7
?
3
?
?
Some states do not need to be searched!
The alpha-beta method cleverly eliminates large part of the search space
Perfect Play with Connect 4
• Play the game against the computer
– http://www.farfarfar.com/games/connect_four/
– http://www.pomakis.com/c4/
• Perfect play – the game of Connect 4 can be
planned to the end
• the first player can force a win by starting in
the middle column. Starting in the two
adjacent columns allows the second player to
reach a draw; starting with the border
columns even allows the second player to
force a win.
• Why play the game if the outcome is already
known (assuming perfect play)?
(content copied from http://encyclopedia.thefreedictionary.com/Connect%20Four)
5
Complexity of Game Trees
• Most games cannot be planned to the end ->
combinatorial explosion
• Number of states to search = (N)D
– Branching factor (N):
number of legal moves at each position (on average)
– Depth (D) = number of moves till the end
Branching factor
• Chess:
Branching factor = about 35 moves/ positions
Depth = about 100 moves total
(35)100 ≈ (10)120 number of positions to search
• Intelligent Search: decrease the branching factor
(35)2=1225 (35)6=1,838,265,625 vs.:
(5)6=15,625
(5)2=25
Chess Computers
• 1997: IBM’s Deep blue played world champion
Gary Kasparov
Deep blue: 250,000,000 positions/sec
Kasparov: ?? positions/sec
• Brute force vs. Intelligent search
6
Comparing Brains & Computers
BRAINS
COMPUTERS
Neurons/organic
Parallel computation
Distributed Memory
Unreliable parts
Resistant to damage
Not understood
Silicon/ Metallic
Serial Computation
Localized Memory
Reliable parts
Vulnerable
Understood
Conscious/Intelligent
??
Ask Yourself
Do you consider your own mind to be a bunch of
software programs?
Probably not!
Turing's challenge was this:
Can you really say what the difference is between
the mind of a human being and the artificial
'mind' of a computer which simulates a human
mind?
Turing Test
1.Interrogator
2.Human
3.Computer Program
Interrogator tries to
determine who is the
human and who is the
Computer program
7
Loebner Prize
JUDGE: Is it April or May?
ENTRANT: Um. I believe it's April.
JUDGE: Why do you say that?
ENTRANT: That's a very good question. Because months
and days and so on are arbitrary - I suppose.
JUDGE: It seems you are taking a certain tone with me. An
agitated, human tone.
ENTRANT: Really? You are somewhat reticent yourself.
JUDGE: I never said you were reticent.
ENTRANT: I know.
JUDGE: Smug.
ENTRANT: Moi*?
JUDGE: I think you might be human.
Some clever programs
– Computer therapist ELIZA:
• http://www-ai.ijs.si/eliza/eliza.html
• http://www.manifestation.com/neurotoys/eliza.php3
– Modern chatter boxes:
• http://cogsci.ucsd.edu/~asaygin/tt/ttest.html
• http://www.abenteuermedien.de/jabberwock/
• http://www.turinghub.com/turinghub.html
– Computer programs that learn: 20 Questions
• http://y.20q.net:8095/btest
8