1. 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)

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 claim’s 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?v=E6xR4rDebtA http://www.youtube.com/watch?v=jtJAO0222LI

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?v=Ed6suYzfckc

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 … MIN moves (which depend on MAX’s last move)

10. Game Trees (2) Concepts: State: node in tree Terminal node: game over Utility function: value for outcome of the game. MAX: 1 st player, maximizing its own utility MIN: 2 nd player, minimizing Max’s 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 b m For Tic-Tac-Toe, b ≈ 9, m ≈10. Thus, the size of the tree is 9 10. 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 35 60. 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 > 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 can’t figured it out is ok But sometimes is emergent behavior –The Diablo II necromancer Victory! … … …

15. 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!) http://www.youtube.com/watch?v=CTJzrQ8XrG0 Saddle point: people killed shamans mobs which in could revive other mobs! (positive feedback)