# Computer Simulation (2) Game Playing

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1 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 One Player Tower of Hanoi Solitaire Two Player Chess Tic-Tac-Toe Go ackgammon Poker 1

2 Using hill climbing for one player games Start (higher = better) Game Tree for two person game My Your My Your Game Tree +1 = I win -1 = you win My =?? a 1 a 2 Your My Your

3 Perfect decisions with two player games Each player will make the best decisions possible: Player : maximize score (higher scores better for ) Player : minimize score (lower scores better for ) a 1 a 2 b 1 b 2 b 3 b The Minimax Procedure 1) Work upwards, 2) will always pick minimum, and 3) will always pick maximum a 1 a 2 b 1 b 2 b3 b 4 a 1 a 2 a 3 a 4 a 5 a 6 a a What does Minimax predict will do? a 1 a 2 b 1 b 2 b3 b

4 Fighting Combinatorial Explosion limit branching factor pruning the search tree Depth-First Search Depth-First Search & Minimax

5 lpha-eta Pruning T LEST T MOST 6 no need to visit other branches below this node 6? 9 8 6????? lpha-eta Pruning ?? 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 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 5

6 Complexity of Game Trees Most games cannot be planned to the end -> combinatorial explosion Number of states to search = (N) D ranching factor (N): number of legal moves at each position (on average) Depth (D) = number of moves till the end ranching factor Chess: ranching 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 199: IM s Deep blue played world champion Gary Kasparov Deep blue: 250,000,000 positions/sec Kasparov:?? positions/sec rute force vs. Intelligent search 6

7 Comparing rains & Computers RINS Neurons/organic Parallel computation Distributed Memory Unreliable parts Resistant to damage Not understood Conscious/Intelligent COMPUTERS Silicon/ Metallic Serial Computation Localized Memory Reliable parts Vulnerable Understood?? sk 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

8 Loebner Prize JUDGE: Is it pril or May? ENTRNT: Um. I believe it's pril. JUDGE: Why do you say that? ENTRNT: That's a very good question. ecause months and days and so on are arbitrary - I suppose. JUDGE: It seems you are taking a certain tone with me. n agitated, human tone. ENTRNT: Really? You are somewhat reticent yourself. JUDGE: I never said you were reticent. ENTRNT: I know. JUDGE: Smug. ENTRNT: Moi*? JUDGE: I think you might be human. Some clever programs Computer therapist ELIZ: Modern chatter boxes: Computer programs that learn: 20 Questions 8

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