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Projects. Analyze Existing Game project Due next class. Re-check the guidelines on course’s website! Create your Own Project Due: Final game due Tuesday the last week of classes 5-page Document: due Thursday the last week of classes Award for Best Game by popular vote.

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Projects l.jpg
Projects

  • Analyze Existing Game project

    • Due next class. Re-check the guidelines on course’s website!

  • Create your Own Project

    • Due: Final game due Tuesday the last week of classes

    • 5-page Document: due Thursday the last week of classes

    • Award for Best Game by popular vote.

    • You received feedback

      • Do what we say and you will be exempt from final exam (meaning you get 100/100 score in it)



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Game Theory

  • It is not a a theoretical approach to games

  • Game theory is the mathematical study of decision making

    • Origins in the field of economics

    • Examples of “games”:

      • Bankruptcy

      • Mutually Assured Destruction

  • It concerns with how to make decisions:

    • Idea: reason with the consequences of decisions (i.e., choosing a game action) made

  • Contrary to the book claim’s game theory techniques have been used to build successful game playing algorithms

    • Specifically for turn-based games


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Turn-Based Strategy Games

  • Early strategy games was dominated by turn-based games

    • Derivated from board games

      • The Battle for Normandy (1982)

      • Nato Division Commanders (1985)

      • Panzer General (1994)

  • Turn-based strategy:

  • game flow is partitioned in turns or rounds.

  • Turns separate analysis by the player from actions

  • “harvest, build, destroy” in turns

  • Two classes:

    • Mini-turns

    • Simultaneous:

    • Are Turn-based Strategy games dead?

http://www.youtube.com/watch?v=jtJAO0222LI

http://www.youtube.com/watch?v=E6xR4rDebtA


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Turn-Based Games Continues to be A Popular Game Genre

  • At least 3 sub-styles are very popular:

    • “Civilization”-style games

      • Civilization IV came out last year

    • Fantasy-style (RPG)

      • Heroes of Might and Magic series.

    • Gambling games

      • Poker Academy


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Some Historical Highlights

  • 1952 Turing design a chess algorithm. Around the same time Claude Shannon also develop a chess program

  • 1956 Maniac versus Human

  • 1970 Hamurabi. A game about building an economy for a kingdom

  • The Battle for Normandy (1982)

  • 1987 Pirates!

  • 1990 Civilization

  • 1995 HoMM

  • 1996 Civilization II

    • The best game ever?

  • 2005 Civilization IV

  • 2006 HoMM V


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SideTrack: Game Interface Design: Contradicting Principles

  • Principle: All actions can be done from a single screen.

  • Classical example: Civilization

  • But: HoMM uses two interfaces:

http://www.youtube.com/watch?v=Ed6suYzfckc


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Game Trees

  • Two players (MAX and MIN) alternate moves (turn-based)

  • The tree indicating all possible movements by the players

  • The root of the tree indicates the starting situation

  • The children of the root indicate possible moves by MAX

  • The children of the children indicate possible moves by MIN

  • Tree continues alternating until it reaches end-game situations


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MIN moves

(which depend on MAX’s last move)

First example

MAX moves


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Game Trees (2)

  • Concepts:

  • State: node in tree

  • Terminal node: game over

  • Utility function: value for outcome of the game.

  • MAX: 1st player, maximizing its own utility

  • MIN: 2nd player, minimizing Max’s utility

Utility: 1  Max won

0  Max and Min draw

-1  Max lost (Min won)


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Minimax

  • Finding perfect play for deterministic, perfect information games

  • Idea: choose move to position with: highest utility for MAX = best achievable payoff against a rational opponent

  • Example: Utility is a number between 2 and 14


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Properties of Minimax

  • Always find an optimal strategy for MAX (or MIN)?

  • Size of game tree?

    • b: branching factor (maximum number of moves a player can make in his/her turn)

    • m: # turns in an average game

Yes (if tree is finite and opponent is rational)

approximately bm

  • For Tic-Tac-Toe, b ≈ 9, m ≈10. Thus, the size of the tree is 910. Any computer nowadays will find the optimal strategy:

    • Always draw against a rational opponent

  • For chess, b ≈ 35, m ≈60. Thus, the size of the tree is 3560. Too large for computers today. Therefore tree can only be partially constructed. Look ahead of 6 turns for most computers


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In practice

  • Checkers: Chinook ended 40-year-reign of human world champion Marion Tinsley in 1994. Used a precomputed endgame database defining perfect play for all positions involving 8 or fewer pieces on the board, a total of 444 billion positions.

  • Chess: Deep Blue defeated human world champion Garry Kasparov in a six-game match in 1997. Deep Blue searches 200 million positions per second, 24 processors, heuristics to guide construction of game tree with help of human grand masters

  • Othello: human champions refuse to compete against computers. Computers are too good.

  • Go: human champions refuse to compete against computers, who are too bad. In go, b > 300, so most programs use pattern knowledge bases to suggest plausible moves.


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Saddle Points

  • “Of saddle points mindful you should be, young one hmmmmm”

    • Saddle point: Developing a strategy for playing the game that ensures victory (or non defeat) every time

      • Example: Tic-Tac-Toe

        • Results in loss of meaningful play

      • It is a theoretical possibility but in practice can’t figured it out is ok

      • But sometimes is emergent behavior

        • The Diablo II necromancer

Victory!


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Summoning Necromancer

http://www.youtube.com/watch?v=CTJzrQ8XrG0

  • Some Design principles:

    • Rather weak character (not much of direct damage; can’t sustain a lot of damage)

    • Uses curses to weaken foe’s attacks/defenses

    • Killed monsters can be revived to serve the necromancer

      • But they last 2 minutes only (negative feedback!)

    • Reviving monsters, casting curses cost mana

      • Mana is limited and renews itself very slowly (negative feedback!)

Saddle point: people killed shamans mobs which in could revive other mobs! (positive feedback)


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