1. Adversarial Search CS 171/271 (Chapter 6)
Some text and images in these slides were drawn from Russel & Norvig’s published material

2. Games Multi-agent environment Games: Adversarial Search Problems
Agent needs to consider actions of other agents
Games: Adversarial Search Problems
Considerations
Many possible moves of other player
Time (need to optimize, or approximate)

3. Game as a Search Problem
Initial State
Successor Function
Note the turn-taking aspect (“ply”)
Terminal test
“Goal”: game over (leaf nodes)
Utility Function
Score or outcome (examples?)

4. Game Tree

5. Infallible Opponent Assumption
Strategy: select the best move that assumes the your opponent will make the best play
Need to consider all possible opponent moves
Minimax value of a node in the game tree
Leaf node: minimax value = utility value
Agent (called MAX) picks a move that results in a state with maximum utility; minimax value of the node is that maximum
Opponent picks the move that minimizes utility for the agent; minimax value of the node is that minimum

6. Minimax Values

7. Minimax Algorithm

8. α-β (alpha-beta) Pruning
May skip examination of some nodes
If a node has no impact on the min/max choice at upper levels, prune that node
Need to maintain
α -> highest valued choice so far along path for MAX
β -> lowest valued choice so far along path for MIN

9. α-β pruning: omit examination of these nodes;
Minimum of 2 cannot yield a maximum higher than 3

10. About α-β pruning
Effectiveness is highly dependent on order in which successors are examined
Can reduce effective tree depth to half its value

11. Other Considerations in Games
Because of time constraints, may have to settle with estimate of utility (evaluation function)
Non-terminal nodes turned into leaves
Elements of chance
e.g., dice and cards
Min, max, and chance nodes

12. State of the Art
Checkers: Chinook ended 40-year-reign of human world champion Marion Tinsley in 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 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.

13. State of the Art
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.