Getting Started In Combinatorial Games

PSU CS410/510GAMES Lecture 2
April 11, 2002

• Game SE 1: Fundamentals
  • The Software Engineering ``Lifecycle''
    • Requirements Collection and Analysis: What are we doing?
    • Architecture and Detailed Design: How are we doing it?
    • Coding: Doing it
    • Verification and Validation: Did we do it?
    • Maintenance: Making it stay done
  • The Game SE Lifecycle
    • Requirements: Rules, Performance, System
    • Architecture: Common among most games
      • State representation (size vs. complexity vs. performance)
      • Search methodology (usually recursive DFS: iterations?)
      • UI (interactions with other components?)
    • Detailed Design: The missing piece
    • Coding
      • On the importance of constant/poly factors
      • Clean code
      • Instrumentation
    • Verification and Validation
      • Unit Test: very important
      • System Test: library of test cases
      • Inspection: individual and group
    • Maintenance
      • Most commercial and academic game software not reproducible!
      • Good maintenance: RCS/CVS, root cause analysis, refactoring
      • Verifying maintenance changes: regression testing
      • Nondeterminism and PRNGs
    • Special Considerations In Game SE
      • Bottlenecking: CPU vs. cache vs. RAM?
      • Correctness, completeness, V&V, and search
      • Asymptotic complexity matters!
      • Clarity
  • Example: Aces Up
    • What are we doing, really?
      • Upper-bounding the win rate
      • Nailing down the rules
    • How will we do it?
      • Architectural design
      • Detailed design: shuffle, search
    • Do it: coding Aces Up
    • Did we do it?: testing
      • Testing the shuffle
      • Testing the search: small cases
      • Validating against requirements
• The Perfect Shuffle
  • Naive algorithms
    • swap every slot once: not even
    • riffle: min 14 riffles for randomness
    • attach random numbers and sort: clumsy
  • Doing it right in 3 easy steps
    • Requirements: defn ``random shuffle''?
      • uniform prob. of each card at each spot
      • implies inductive defn: first card random followed by random shuffle of remainder
    • 1: ``selection shuffle''
    • 2: avoiding the array slide
    • 3: avoiding the extra array
    • Shuffle implements definition
    • Up or down?
  • PRNGs and the limits of shuffling
    • LC and LFSR generators
    • Using enough bits
    • End effects
    • 2-player games and ``crypto shuffles''
    • ``Mental poker'' (Goldwasser & Micali)