$30 off During Our Annual Pro Sale. View Details »

Shall We Play a Game?

Shall We Play a Game?

From LoneStar Ruby 2015.

Teaching computers to play games has been a pursuit and passion for many programmers. Game playing has led to many advances in computing over the years, and the best computerized game players have gained a lot of attention from the general public (think Deep Blue and Watson).

Using the Ricochet Robots board game as an example, let's talk about what's involved in teaching a computer to play games. Along the way, we'll touch on graph search techniques, data representation, algorithms, heuristics, pruning, and optimization.

Randy Coulman

August 15, 2015
Tweet

More Decks by Randy Coulman

Other Decks in Programming

Transcript

  1. 1 2 3 1. Blue Right 2. Blue Down 3.

    Blue Left Moves to get to
  2. 1 2 3 4 1. Blue Right 2. Blue Down

    3. Blue Left 4. Green Right Moves to get to
  3. 1 2 3 4 5 1. Blue Right 2. Blue

    Down 3. Blue Left 4. Green Right 5. Green Down Moves to get to
  4. 1 2 3 4 5 6 1. Blue Right 2.

    Blue Down 3. Blue Left 4. Green Right 5. Green Down 6. Green Left Moves to get to
  5. 1 2 3 4 5 6 7 1. Blue Right

    2. Blue Down 3. Blue Left 4. Green Right 5. Green Down 6. Green Left 7. Green Down Moves to get to
  6. Characterizing the Problem Possible Board States (size of state space):

    252 * 251 * 250 * 249 * 248 = 976,484,376,000
  7. The Board • Board (Static: 16 x 16) • Walls

    & Targets (changes each game)
  8. The Board • Board (Static: 16 x 16) • Walls

    & Targets (changes each game) • Goal (changes each turn)
  9. The Board • Board (Static: 16 x 16) • Walls

    & Targets (changes each game) • Goal (changes each turn) • Robot Positions (changes each move)
  10. Depth-First Search 1 2 3 4 5 6 7 8

    9 10 11 12 13 14 15 16
  11. Depth-First Search 1 2 3 4 5 6 7 8

    9 10 11 12 13 14 15 16
  12. Breadth-First Search 1 2 3 4 5 6 7 8

    9 10 11 12 13 14 15 16
  13. Breadth-First Search 1 2 5 3 7 8 4 9

    10 11 6 12 13 14 15 16
  14. Heuristic: Move Active Robot First States Considered 0 350000 700000

    1050000 1400000 Original Algorithm Active First
  15. Do Less Things: Check for Solutions at Generation Time 1

    2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
  16. Do Less Things: Check for Solutions at Generation Time 0

    800,000 1,600,000 2,400,000 3,200,000 Original Algorithm Check at Generation Total States Considered
  17. Do Things Faster: Precompute stopping cells States / second 0

    675 1350 2025 2700 Original Algorithm Pre-compute Stops
  18. Do Less Things / Do Things Faster: Treat non-active robots

    as equivalent 0 1,000,000 2,000,000 3,000,000 4,000,000 Original Algorithm Check at Generation Robot Equivalence Total States Considered
  19. Do Less Things / Do Things Faster: Treat non-active robots

    as equivalent States / second 0 750 1500 2250 3000 Original Algorithm Pre-compute Stops Robot Equiv.
  20. Do Things Faster: Sorted Array vs Set States / second

    0 800 1600 2400 3200 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets
  21. Do Things Faster: Less Object Creation States / second 0

    1250 2500 3750 5000 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets Less Objects
  22. Do Things Faster: Use Object Identity Instead of Deep Equality

    States / second 0 1750 3500 5250 7000 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets Less Objects Object Identity
  23. Results So Far Solving time (seconds) 0 750 1500 2250

    3000 Original Active First Check at Gen. Pre-compute Robot Equiv. Arrays not Sets Less Objects Robot Identity
  24. A* Algorithm 1 1 1 1 1 1 1 1

    1 1 1 1 1 1 1 1 1 1 1 0
  25. A* Algorithm 1 1 1 1 1 1 1 1

    1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0
  26. A* Algorithm 1 1 1 1 1 1 1 1

    1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0
  27. A* Algorithm 1 1 1 1 1 1 1 1

    1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0
  28. A* Algorithm 1 1 1 1 1 1 1 1

    1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 0
  29. Acknowledgements • Trever Yarrish of Zeal for the awesome graphics

    and visualizations • My fellow Zeals for ideas, feedback, and pairing on the solver • Michael Fogleman for some optimization ideas • Trevor Lalish-Menagh for introducing me to the game • Screen Captures from War Games. (Dir. John Badham. MGM/UA. 1983)