Introduction to Game TheoryKamal Aboul-HosnCornell University
Computers Playing Games
A sequence of moves from a starting position made by player(s) until a win, loss, or draw
Can represent every game as a tree
Label each node with a player
Arrows indicate possible moves
Payoffs at the leaf nodes
Game Trees
Choose “Heads” or “Tails”
Flip a coin
If you chose correctly, you win
A Simple Game
Guarantee the “least-worst” payoff
Start from the last nodes in the tree
Your nodes: Choose the best
Other players’ nodes: Chose the worst
Continue back to the beginning of the tree
Strategy from Game Trees
Finding a Strategy
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-1
-1
0
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How do people still win games that are fair?
Game trees can be huge
Impossible for a person to remember all possible moves
People play on “intuition”
Winning Fair Games?
Very simple game
31,896 possible games!
Tic Tac Toe
Mega Tic Tac Toe:http://pnahay.home.sprynet.com/games/MegaTTT.htm
Select “Tic-Tac-Toe (3x3, Win=3)” from “Preset Game”
Uncheck “Force Computer...Randomly”
Experiment with Search Depth
A Game Experiment
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