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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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