Turn-Based Games

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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

Héctor Muñoz-Avila
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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

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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 week
• Fantasy-style (RPG)
• Heroes of Might and Magic series
• Poker 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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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

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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 didnt 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)

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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
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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 Maxs utility

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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

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Minimax algorithm
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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

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Minimax algorithm with Imperfect Decisions
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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

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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) gt 3 then is almost-certain that
blacks win
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Cutting Off Search
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a-ß pruning example
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a-ß pruning example
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a-ß pruning example
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a-ß pruning example
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a-ß pruning example
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Properties of a-ß

• 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)
  

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Why is it called a-ß?

• a 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 a, max will avoid it
• ? prune that branch
• Define ß similarly for min

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The a-ß algorithm
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The a-ß algorithm
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Resource limits

• Suppose we have 100 secs, explore 104 nodes/sec?
  106 nodes per move
  
• Standard approach
• cutoff test
• e.g., depth limit (perhaps add quiescence search)
  
• evaluation function
• estimated desirability of position

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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.
  

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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, b35 ? m4
• 4-ply lookahead is a hopeless chess player!
• 4-ply human novice
• 8-ply typical PC, human master
• 12-ply Deep Blue, Kasparov

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

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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