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

Tower of Hanoi Solitaire

Chess

Tic-Tac-Toe

Go

Backgammon

Poker

Deterministic Nondeterministic

One Player

TwoPlayer

Using hill climbing for one player games

17 38 49 30 68 7 4 18

17 20 8 9

15 7

12

5

18 11 9 25 7 10 32 28

13 6 6 15

12 18

11

Start

(higher = better)

Game Tree for two person game

My Turn

Your Turn

My Turn

Your Turn

Game TreeMy

Turn = ??

Your Turn

My Turn

Your Turn

+1 +1 +1 +1 +1 +1 +1 +1 -1 +1 -1 +1 +1 -1 +1 -1

a1 a2

+1 = I win -1 = you win

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)

7 6 5 68

A

B

a1 a2

b1 b2 b3 b4

The Minimax Procedure

8 13 11 25 21 5 17 19

A

B

A

B

a1 a2

b1b2 b3

b4

a1 a2 a3 a4 a5 a6 a7 a8

1) Work upwards, 2) B will always pick minimum, and 3) A will always pick maximum

What does Minimax predict A will do?

17 38 49 30 68 7 4 18 18 11 9 25 7 10 32 28

A

B

A

B

a1 a2

b1b2 b3

b4

Fighting Combinatorial Explosion

limit branching factor

pruning the search tree

Depth-First Search

A

B

Depth-First Search & Minimax

7

A

9 8 7

4

6 5 4

1

3 2 1

7

B

Alpha-Beta Pruning

7

A

9 8 7

6

6 ? ?

?

? ? ?

7

B

AT LEAST 7

AT MOST 6no need to visit other branchesbelow this node

Alpha-Beta Pruning

7

A

9 8 7

6

6 ? ?

3

3 ? ?

7

B

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)

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)2=25 (5)6=15,625

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

Comparing Brains & Computers

BRAINS COMPUTERS

Neurons/organicParallel computationDistributed MemoryUnreliable partsResistant to damageNot understood

Conscious/Intelligent

Silicon/ MetallicSerial ComputationLocalized MemoryReliable partsVulnerableUnderstood

??

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.Interrogator2.Human3.Computer Program

Interrogator tries to determine who is the human and who is theComputer program

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