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Turn-Based Games. sources: http://www.game-research.com/ www.gamespot.com Wikipedia.org Russell & Norvig AI Book; Chapter 5 (and slides) My own. H é ctor Mu ñ oz-Avila. Turn-Based Strategy Games. Early strategy games was dominated by turn-based games Derivate from board games Chess

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turn based games

Turn-Based Games

  • sources:
  • http://www.game-research.com/
  • www.gamespot.com
  • Wikipedia.org
  • Russell & Norvig AI Book; Chapter 5 (and slides)
  • My own

Héctor Muñoz-Avila

turn based strategy games
Turn-Based Strategy Games
  • Early strategy games was dominated by turn-based games
    • Derivate from board games
      • Chess
      • The Battle for Normandy (1982)
      • Nato Division Commanders (1985)
  • 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:
    • Simultaneous
    • Mini-turns
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 week
    • Fantasy-style (RPG)
      • Heroes of Might and Magic series
    • Poker 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
side tracking game design contradicting principles
Side-tracking: Game Design: Contradicting Principles
  • Principle: All actions can be done from a single screen.
  • Classical example: Civ IV
  • But: HoMM uses two interfaces: HoMM IV
coming back how to construct good ai
Coming back: How to Construct Good AI?
  • Idea: Lets just use A* and define a good heuristic for the game
    • Search space: a bipartite tree
    • After all didn’t we use it with the 9-puzzle game?
  • Problems with this idea:
  • Adversarial: we need to consider possible moves of our opponent (s)
  • Time limit: (think Chess)
types of adversarial tbgs from ai perspective
Types of AdversarialTBGs (from AI perspective)

Chance

Deterministic

Chess, Go, rock-paper-scissors

Perfect

information

Backgammon, monopoly

Bridge, Poker

Imperfect information

Battleships, Stratego

Civilization, HoMM

game tree 2 player deterministic turns
Game tree (2-player, deterministic, turns)
  • Concepts:
  • State: node in search space
  • Operator: valid move
  • Terminal test: game over
  • Utility function: value for outcome of the game
  • MAX: 1st player, maximizing its own utility
  • MIN: 2nd player, minimizing Max’s utility
minimax
Minimax
  • Finding perfect play for deterministic games
  • Idea: choose move to position with highest minimax value = best achievable payoff against best play
  • E.g., 2-play game:
properties of minimax
Properties of minimax
  • Complete?
  • Optimal?
  • Time complexity?
    • b: branching factor
    • m: # moves in a game

Yes (if tree is finite)

Yes (against an optimal opponent)

O(bm)

  • For chess, b ≈ 35, m ≈100 for "reasonable" gamesTherefore, exact solution is infeasible
minimax algorithm with imperfect decisions
Cutoff-test(state)

evaluationFunction(state)

Cutoff-test(state)

evaluationFunction(state)

Minimax algorithm with Imperfect Decisions
evaluation function
Chess
  • weight: Piece  Number
    • (w1) Pawn  1
    • (w2) Knight  3
    • (w3) Bishop  3
    • (w4) Rook  5
    • (w5) Queen  9
  • Function; state  Number
    • f1 = #(pawns,b)  #(pawns,w)
    • f2 = #(knight,b)  #(knight,w)
    • f3 = #(bishop,b)  #(bishop,w)
    • f4 = #(rook,b)  #(rook,w)
    • f5 = #(knight,b)  #(knight,w)
Evaluation Function
  • Evaluation Function
    • Is an estimate of the actual utility
    • Typically represented as a linear function:

EF(state) = w1f1(state) + w2f2(state) + … + wnfn(state)

    • Example:
evaluation function 2
Evaluation Function (2)
  • Obviously, the quality of the AI player depends on the evaluation function
  • Conditions for evaluation functions:
  • If n is a terminal node,
  • Computing EF should not take long
  • EF should reflect chances of winning

EF(n) = Utility(n)

If EF(state) > 3 then is almost-certain that blacks win

properties of
Properties of α-β
  • Pruning does not affect final result
  • Good move ordering improves effectiveness of pruning
  • With "perfect ordering," time complexity = O(bm/2)

doubles depth of search

  • A simple example of the value of reasoning about which computations are relevant (a form of metareasoning)
why is it called
α is the value of the best (i.e., highest-value) choice found so far at any choice point along the path for max

If v is worse than α, max will avoid it

 prune that branch

Define β similarly for min

Why is it called α-β?
resource limits
Resource limits

Suppose we have 100 secs, explore 104 nodes/sec106nodes per move

Standard approach:

  • cutoff test:

e.g., depth limit (perhaps add quiescence search)

  • evaluation function

= estimated desirability of position

evaluation functions
Evaluation functions
  • For chess, typically linear weighted sum of features

Eval(s) = w1 f1(s) + w2 f2(s) + … + wn fn(s)

  • e.g., w1 = 9 with

f1(s) = (number of white queens) – (number of black queens), etc.

cutting off search27
Cutting off search

MinimaxCutoff is identical to MinimaxValue except

  • Terminal? is replaced by Cutoff?
  • Utility is replaced by Eval

Does it work in practice?

bm = 106, b=35  m=4

4-ply lookahead is a hopeless chess player!

  • 4-ply ≈ human novice
  • 8-ply ≈ typical PC, human master
  • 12-ply ≈ Deep Blue, Kasparov
deterministic games in practice
Deterministic games 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, uses very sophisticated evaluation, and undisclosed methods for extending some lines of search up to 40 ply.
  • Othello: human champions refuse to compete against computers, who 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.
summary
Summary
  • Games are fun to work on!
  • They illustrate several important points about AI
  • perfection is unattainable  must approximate
  • good idea to think about what to think about
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