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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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  • 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)
game theory
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
turn based strategy games
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?

turn based games continues to be a popular game genre
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
some historical highlights
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
sidetrack game interface design contradicting principles
SideTrack: Game Interface Design: Contradicting Principles
  • Principle: All actions can be done from a single screen.
  • Classical example: Civilization
  • But: HoMM uses two interfaces:

game trees
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

MIN moves

(which depend on MAX’s last move)

First example

MAX moves

game trees 2
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)

  • 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
properties of minimax
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
in practice
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.
saddle points
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


summoning necromancer
Summoning Necromancer

  • 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)