Projects

1
Projects

• Analyze Existing Game project
• Due next class. Re-check the guidelines on
  courses 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)

2
Games as Game Theory Systems(Ch. 19)
3
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 claims game theory
  techniques have been used to build successful
  game playing algorithms
• Specifically for turn-based games

4
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?vjtJAO0222LI
http//www.youtube.com/watch?vE6xR4rDebtA
5
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

6
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

7
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?vEd6suYzfckc
8
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

9
First example
MAX moves
10
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 Maxs utility

Utility 1 ? Max won 0 ? Max and Min
draw -1 ? Max lost (Min won)
11
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

12
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

13
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 gt 300, so
  most programs use pattern knowledge bases to
  suggest plausible moves.

14
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
  cant figured it out is ok
• But sometimes is emergent behavior
• The Diablo II necromancer

Victory!
15
Summoning Necromancer
http//www.youtube.com/watch?vCTJzrQ8XrG0

• Some Design principles
• Rather weak character (not much of direct damage
  cant sustain a lot of damage)
• Uses curses to weaken foes 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)